diff --git a/DEFERRED.md b/DEFERRED.md
index 795c8e253..2adfbfa86 100644
--- a/DEFERRED.md
+++ b/DEFERRED.md
@@ -45,6 +45,10 @@ provenance and AI-review deviation-documentation: a row here (or in
 | **`LPDiD` non-absorbing exit-event dynamics** (Dube et al. 2025 online Appendix C `eta_h^{g,n}`): the shipped `non_absorbing` modes estimate the **entry-effect** estimands (Eq. 12/13) only; separate dynamic event-studies for treatment switch-*offs* are not implemented. Needs the exit-event clean-sample derivation + estimand contract. | `lpdid.py`, REGISTRY | PR-C follow-up | Low |
 | MMM interop, survey/RC totals for the five `aggregate('total')` adopters (CS/DMLDiD/EfficientDiD/ImputationDiD/TwoStageDiD; the shipped v1 is panel non-survey only and fails closed with `NotImplementedError` on repeated-cross-section-routed fits, fits declaring a `survey_design=`, and the CS/DMLDiD bare-`cluster=` divergent corner where the cohort-mass weighting disagrees with the complete-case count): needs (a) DESIGN-AWARE raw-mass recovery - analytic pweight/aweight resolved weights are normalized to sum = n and CS retains no raw record (fit-time RAW retention required there; CS accepts pweight only), while EDiD's analytic fweight fits and all replicate-design fits already retain raw scale in the kits and Imputation/TwoStage retain raw `SurveyMetadata.sum_weights` - and (b) the mass-uncertainty `att*dC` variance derivation (the shipped relay conditions on the realized mass and omits it). Never ship a survey/RC total from normalized masses. | `diff_diff/staggered_results.py`, `diff_diff/survey.py` | mmm-interop | Low |
 | **`LPDiD` non-absorbing interior-gap support**: non-absorbing modes require a gap-free panel within each unit's observed span and raise on interior time gaps (the `[t-L, t+h]` window conditions can't be verified across a gap). The absorbing path already reindexes interior gaps to the calendar grid; extending that fail-closed handling (per-window gap masking) to non-absorbing is deferred. | `lpdid.py::_prepare_panel` | PR-C follow-up | Low |
+| Bad-control lane on repeated cross sections: Caetano et al. (2026) Remark 1 calls the approach unavailable "to a large extent" with repeated cross sections (`X_{g-1}` and `X_t` must be observed for the same unit); an RCS variant needs its own derivation. `DMLDiD(panel=False).fit(bad_control=)` fails closed. | `dml_did.py` | bad-controls PR-B | Low |
+| Limited-anticipation extension of the bad-control lane: MP-2 assumes no anticipation for `Y` AND `X`; the base-period convention for `X` and `W` under `anticipation > 0` is not developed by the paper. `DMLDiD(anticipation=k).fit(bad_control=)` fails closed. | `dml_did.py` | bad-controls PR-B | Low |
+| Universal-base bad-control pre-test: MP-5 conditions on the immediately preceding period, and under `base_period="universal"` a pre cell with `t < g - 1` would read `X_t` earlier than `X_{g-1}` / `W`, inverting the ordering; a universal-base version needs its own derivation. `DMLDiD(base_period="universal").fit(bad_control=)` fails closed. | `dml_did.py` | bad-controls PR-B | Low |
+| Bad-control lane under `survey_design=`: the nested second-stage nuisances under design weights (Hajek moments, `sample_weight` into the nested fits) and the replicate-weight variance of the nested scores are unvalidated; fails closed (bare `cluster=` is supported). | `dml_did.py` | bad-controls PR-B | Low |
 
 ## Needs external reference (R / Stata / Julia)
 
@@ -111,7 +115,7 @@ For survey-specific limitations (`NotImplementedError` paths), see the
 | Rust local-method `estimate_model` → unify to `solve_wls_svd` (the global-method's SVD helper) for sub-1e-14 bootstrap-SE parity. The local-method bootstrap parity test passes at `atol=1e-5`; the residual ~1e-7 is roundoff, not a user-visible correctness bug. | `rust/src/trop.rs`, `rust/src/linalg.rs` | follow-up | Low |
 | Validate the `.txt` AI guides (`llms-full.txt`, `llms-practitioner.txt`) as executable snippets — **not low-lift** (re-scoped 2026-06-01): only ~20% of ~112 fenced blocks are standalone-runnable; the rest are signature pseudo-code, context fragments, or data-shape-specific. Needs signature-block detection + a context/data skip-allowlist + per-snippet fixtures. | `tests/test_doc_snippets.py` | #239 | Low |
 | `TestWorkflowDoesNotExecutePRHeadCode` (CodeQL #14 guard) doesn't model `bash/sh/./source <script>` execution, multi-line `python3 -c` bodies, shell-var indirection, `eval`, `find -exec`, `xargs -I`. Catches common accidental regressions (16 forms); closing the residuals needs multi-line shell parsing + script-exec allowlists — diminishing return given the documented threat model. | `tests/test_openai_review.py`, `.github/workflows/ai_pr_review.yml` | #436 | Low |
-| Calendar-time aggregation (R `did` feature gap) — blocks 1 ported test in `test-att_gt.R`. | — | — | Low |
+| Calendar-time aggregation (R `did` feature gap) — blocks 1 ported test in `test-att_gt.R`; not supported by CallawaySantAnna or DMLDiD (incl. the bad-control lane). | `staggered_results.py`, `dml_did_results.py` | — | Low |
 | **Speculative / low-value performance notes** (relocated from the old `## Performance Optimizations`): numba JIT for bootstrap loops — **blocked by the numpy/pandas/scipy-only dependency policy**; generic sparse-matrix handling for large FE; QR+SVD rank-detection redundancy in `solve_ols` (QR overhead is minimal vs the SVD solve — correctness over micro-opt; `skip_rank_check` already exists for known-full-rank hot paths); incomplete `check_finite=False` bypass (scipy's QR in `_detect_rank_deficiency()` still validates; edge-case only). All `Low`, none correctness-affecting. | `linalg.py::solve_ols` | — | Low |
 | `SpilloverDiD` `covariates=` support (Wave B MVP scope cut): the full covariate path mirroring `TwoStageDiD._fit_untreated_model` (stage-1 residualization on the untreated-and-unexposed subsample, then subtraction before stage 2) — appending covariates only at stage 2 would silently bias `tau_total`/`delta_j`; rejected at `fit()` with `NotImplementedError`. | `spillover.py` | Wave B | Low |
 | `SpilloverDiD` estimator-level end-to-end vcov reconstruction tests (`bread @ meat @ bread` against `res.vcov`): requires exposing the estimator's internal `X_2_kept` design arrays; the surface is currently pinned from different angles (uniform-weight bit-identity, drift goldens, manual lincom reconstruction at rtol=1e-6). | `spillover.py`, `tests/test_spillover.py` | follow-up | Low |
diff --git a/README.md b/README.md
index c85a6da35..ed4667db3 100644
--- a/README.md
+++ b/README.md
@@ -121,11 +121,12 @@ Full guide: `diff_diff.get_llm_guide("practitioner")`.
 - [LPDiD](https://diff-diff.readthedocs.io/en/stable/api/lpdid.html) - Dube, Girardi, Jorda & Taylor (2025) Local Projections DiD: per-horizon long-difference event study on clean controls (no negative weighting), variance- or equally-weighted ATT, for absorbing or non-absorbing (reversible) treatment
 - [ChangesInChanges](https://diff-diff.readthedocs.io/en/stable/api/changes_in_changes.html) - Athey & Imbens (2006) nonlinear/distributional DiD for the 2x2 design: full counterfactual distribution and quantile treatment effects via CDF transformation, plus the QDiD comparison estimator via `method="qdid"`; bootstrap inference; R qte parity. Alias `CiC`
 - [LWDiD](https://diff-diff.readthedocs.io/en/stable/api/lwdid.html) - Lee & Wooldridge (2025, 2026) rolling-transformation DiD: unit-specific demean/detrend converts panel to cross-section, staggered adoption, `estimation_method` in `reg`/`ipw`/`dr`/`psm` (the papers' RA/IPW/IPWRA plus propensity-score matching), exact small-N inference on the classical collapsed regression
-- [DMLDiD](https://diff-diff.readthedocs.io/en/stable/api/dml_did.html) - Chang (2020) double/debiased machine learning DiD: staggered ATT(g,t) with cross-fitted ML nuisance learners (DML2) and Neyman-orthogonal scores, for flexible/high-dimensional covariate adjustment under conditional parallel trends; panel or declared repeated cross sections (`panel=False`); survey/cluster support on both lanes
+- [DMLDiD](https://diff-diff.readthedocs.io/en/stable/api/dml_did.html) - Chang (2020) double/debiased machine learning DiD: staggered ATT(g,t) with cross-fitted ML nuisance learners (DML2) and Neyman-orthogonal scores, for flexible/high-dimensional covariate adjustment under conditional parallel trends; panel or declared repeated cross sections (`panel=False`); survey/cluster support on both lanes (bad-control lane: panel only, `cluster=` only); Caetano, Callaway, Payne & Sant'Anna (2026) bad-control score via `fit(bad_control=, bad_control_covariates=)`
 - [BaconDecomposition](https://diff-diff.readthedocs.io/en/stable/api/bacon.html) - Goodman-Bacon (2021) decomposition for diagnosing TWFE bias in staggered settings
 
 ## Diagnostics & Sensitivity
 
+- [Bad-control pre-test](https://diff-diff.readthedocs.io/en/stable/api/dml_did.html) - Caetano, Callaway, Payne & Sant'Anna (2026) Remark 6 `ATT_X(g,t)`: the effect of treatment on a suspected bad control itself, per (g,t) cell (`DMLDiDResults.bad_control_summary()`; analytical SE; pre-period rows pre-test the identifying assumptions MP-5 / MP-8 and should be zero, post-period rows are the Condition-2 check that treatment affects the covariate)
 - [RD Plots](https://diff-diff.readthedocs.io/en/stable/api/regression_discontinuity.html) - Calonico, Cattaneo & Titiunik (2015) optimal data-driven RD plots (`RDPlot`): all 8 rdrobust `binselect` bin selectors, implied-scale/WIMSE-weight reporting, optional matplotlib rendering
 - [Manipulation Testing](https://diff-diff.readthedocs.io/en/stable/api/regression_discontinuity.html) - Cattaneo, Jansson & Ma (2020) density-discontinuity test (`RDDensityTest`): rddensity 3.0 parity, robust bias-corrected inference, unrestricted/restricted models, mass-point adjustment
 - [Parallel Trends Testing](https://diff-diff.readthedocs.io/en/stable/api/diagnostics.html) - simple and Wasserstein-robust parallel trends tests, equivalence testing (TOST)
diff --git a/TODO.md b/TODO.md
index 96e8d23b9..ac97adcaf 100644
--- a/TODO.md
+++ b/TODO.md
@@ -57,6 +57,12 @@ Related tracking surfaces:
 | `WooldridgeDiD` does not apply the W2025 Sec 5.4 `D_{G_max} x X` covariate normalization, and three sibling covariate rank deficiencies are pre-existing. Measured with the period range pinned and only the never-treated units toggled: (1) time-invariant `exovar` is absorbed by the unit FE, 4 of 26 columns, IDENTICALLY with and without never-treated units; (2) `xgvar`'s cell x covariate block, 19 of 41, identical on both panels; (3) `xtvar` under `demean_covariates=False` does exhibit the `sum_g D_g x = x` dependency that the default demeaning removes; (4) the newly-reachable case -- time-VARYING data passed through `exovar`, which its own docstring reserves for time-invariant covariates -- where the paper's `dT_i` rule would give a deterministic `D_{G_max} x X` drop instead of QR's arbitrary pick (coefficients unaffected, `1.35e-14`; `rank_deficient_action="error"` raises). REGISTRY's narrowed Sec 5.4 note cross-references this row. **Trap for whoever takes it:** `xtvar` under the DEFAULT `demean_covariates=True` is FULL RANK -- the raw block carries demeaned values while `D_g x X` carries raw ones -- and forcing the drop there moves `overall_att` 1.11903 -> 1.46269. Pinned as-is by `TestComparisonSupportFiltering::test_cells_derived_groups_did_not_leak_into_the_design`. | `diff_diff/wooldridge.py` | #729-followup | Heavy | Medium |
 | `WooldridgeDiD.n_control_units` counts never-treated UNITS on `control_group="never_treated"` regardless of method, but on the nonlinear paths (`logit`/`poisson`) treated units' pre-treatment rows ARE the identifying comparison -- only the OLS path absorbs them into their own cells. So the reported count under-states the comparison pool exactly where the REGISTRY control-pool asymmetry note applies. Widen to `not_yet_treated or (never_treated and method != "ols")`, or document the count as never-treated-units-by-definition. Behavior is PRE-EXISTING; documented for now in the REGISTRY control-pool Note rather than changed, because widening moves a public results field and wants its own ledger row and test matrix. | `diff_diff/wooldridge.py` | #729-followup | Mid | Low |
 | `WooldridgeDiD` has no opt-out for comparison-support period filtering: a user who would rather see the refusal than a reduced sample cannot ask for it. Adding one means a constructor parameter (`get_params`/`set_params` propagation, transactional validation), a ledger row, and a test matrix across both predicate branches and all three `rank_deficient_action` modes -- deliberately out of scope for the change that introduced the filter. The always-on warning is the interim answer. | `diff_diff/wooldridge.py` | #729-followup | Mid | Low |
+| Bad-control imputation estimator (Caetano et al. 2026 Section 6.1, Eqs. 5-7, S8 influence function) on a CallawaySantAnna `estimation_method="reg"` host: two untreated-sample OLS fits per cell plus the generated-regressor IF line. | `staggered.py` | bad-controls PR-B | Heavy | Low |
+| Bad-control SC "parallel trends for X" variant (Caetano et al. 2026 Section 7 / S17): a linearity-based alternative to covariate unconfoundedness with its own estimand. | `dml_did.py` | bad-controls PR-B | Heavy | Low |
+| `ATT_X(g,t)` event-study aggregation + bootstrap replay for the bad-control pre-test (today analytical per-cell only; never aggregated). | `dml_did_results.py` | bad-controls PR-B | Mid | Low |
+| Remark-4-weighted overall ATT for the bad-control lane (`sum_g sum_{t>=g} [P(G=g given G in G_bar)/(T-g+1)] ATT(g,t)`: cohort mass among the ever-treated divided by the cohort's post-period count); the headline `att` is CS "simple" (REGISTRY DMLDiD Note). | `staggered_aggregation.py` | bad-controls PR-B | Mid | Low |
+| Allow empty `Z` on the bad-control lane (the paper's `Z` may be empty; DMLDiD's covariates-required gate currently applies). | `dml_did.py` | bad-controls PR-B | Quick | Low |
+| Recover the Supplementary Appendix DGPs 2 / 3 / 5 (nonlinear `W` / `X` terms) on the bad-control ML lane - needs a flexible-learner fixture via the duck-typed learner route (the parametric built-ins are inconsistent there by design, Table S1). | `tests/test_methodology_dml_did.py` | bad-controls PR-B | Mid | Low |
 
 ### Performance
 
@@ -95,3 +101,4 @@ generic sparse-FE, QR+SVD rank-detection redundancy, `check_finite` bypass — m
 | Clean-negative precision re-run: Campaign 1's `s3_negative` plans were base_sha-contaminated (real defects at the pinned base), so hallucination rate cleared (dual 3.4%) but trivia-flooding on a *genuinely* clean plan is unmeasured. Small future run (~30 s3-style reviews on 3-5 constructed-clean plans, not the full 120-matrix). | `tools/plan-review-eval/` | campaign-1 verdict | Mid | Low |
 | `trop-silent-drop` criteria regression: the rewritten `criteria.md` dropped a silent-failure catch the OLD criteria had (arm A caught it, B/C missed — campaign-1 A-vs-B contrast). Patch the criteria + re-validate (re-opens the criteria identity, so gated behind a re-validation run). | `.claude/skills/plan-review/criteria.md`, `tools/plan-review-eval/` | campaign-1 verdict | Mid | Medium |
 | The Stata `jwdid` parity arms cover BALANCED panels only. `jwdid_alltreated` pins the all-eventually-treated cell set, `N` and SE ratio on the `mpdta` subset (191 units, 955 rows, 764 estimated), but every arm is a balanced frame, so REGISTRY's parity claim is scoped to that case. The comparison-support predicate's UNBALANCED behavior -- where `G_max` may be unobserved at later periods so the closed form `t < G_max - anticipation` does not hold and support is set by whichever cohorts are actually observed -- is verified against the predicate directly, not against Stata. Add an unbalanced `jwdid` arm to close that gap. | `benchmarks/stata/generate_etwfe_cs_golden.do`, `tests/test_etwfe_cs_stata_parity.py` | #729-followup | Mid | Low |
+| Bad-controls tutorial section for `docs/tutorials/32_dml_did.ipynb` (PR-C): the `fit(bad_control=)` workflow, the `ATT_X(g,t)` pre-test reading, and the Approach-1 comparison via CS base-period covariates. | `docs/tutorials/32_dml_did.ipynb` | bad-controls PR-B | Quick | Medium |
diff --git a/benchmarks/R/README.md b/benchmarks/R/README.md
index 1651e7b5b..4d39726c0 100644
--- a/benchmarks/R/README.md
+++ b/benchmarks/R/README.md
@@ -216,3 +216,64 @@ every synthetic sample at 17 significant digits (R RNG streams are not
 reproducible from numpy), and aborts loudly if the mass-point fixtures fail
 to separate the two `nLocalMin`/`nUniqueMin` regularization gates (the
 floor-gate configs exist to pin exactly that behavior).
+
+# badcontrols (Caetano, Callaway, Payne & Sant'Anna 2026) black-box goldens
+
+`benchmarks/data/badcontrols_golden.json` (+ the shared input panel
+`benchmarks/data/badcontrols_panel.csv`) anchors the `DMLDiD` bad-control
+lane (`fit(..., bad_control=, bad_control_covariates=)`) against the
+authors' R package `badcontrols`. Consumed by
+`tests/test_dml_did_bad_controls_parity.py`.
+
+## Why this package, and the GPL black-box rule
+
+`badcontrols` is the authors' reference implementation of the paper's
+doubly-robust / DML estimator (arXiv:2608.03881). It is **GPL-3**; diff-diff
+is MIT. The Python lane is derived from the paper alone
+(`docs/methodology/papers/caetano-2026-review.md`), and the R package is
+used ONLY as an executed oracle: the generator calls `didbc()` and records
+its outputs. Contributors must never read `R/*.R` of that package while
+working on `diff_diff/` (a direct port was rejected on licensing grounds).
+
+## Regenerating
+
+```sh
+Rscript benchmarks/R/requirements.R              # installs badcontrols at the pinned commit + ptetools 1.0.0
+Rscript benchmarks/R/generate_badcontrols_golden.R
+pytest tests/test_dml_did_bad_controls_parity.py  # must NOT skip locally
+```
+
+The generator hard-fails unless `badcontrols` is 1.0.0 installed from
+GitHub commit `651ccc925776125bb9233d76867c862107ea0ba5` (no tags or
+releases exist and HEAD also reports 1.0.0, so the `RemoteSha` is the pin)
+and `ptetools` is 1.0.0.
+
+## What is recorded
+
+`simulate_bad_controls(n = 1000, T_max = 4)` under `set.seed(20260905)`,
+then four `didbc(est_method = "dr_ml", nuisance_method = "parametric",
+xformula = ~Z, base_period = "varying", anticipation = 0, bstrap = FALSE,
+overlap_threshold = 1, nfolds = 5)` runs: `bad_control_formula = ~X` with
+`bad_control_cov_formula = ~W` (not-yet-treated, then never-treated), `~Y`
+(Remark 5's lagged outcome, not-yet-treated), and a no-bad-control run
+(characterization only - R's `dr_ml` path is not the plain Chang score).
+`overlap_threshold = 1` disables the package's silent fallback to its
+imputation estimator on high-propensity cells.
+
+Each run is recorded as the per-cell mean over `n_seeds = 10` seeds
+(`att_gt_mean`: `group, t, att, V_analytical, att_seed_sd, n, n_treated`)
+plus every per-seed table (`att_gt_per_seed`). `V_analytical` is the
+diagonal of `att_gt$V_analytical` (the analytical covariance; `att_gt$se`
+is bootstrap-based even with `bstrap = FALSE`) and the parity SE is
+`sqrt(V_analytical / n)`. `true_att_gt` carries the simulator's truth.
+
+## Tolerance rationale and skip behavior
+
+`didbc()` cross-fits with its own fold draw (`nfolds = 1` errors), so no
+bit-exact target exists; single-seed fold noise is ~0.1-0.25 SE on most
+cells and up to ~0.5 SE on the smallest ones. Averaging `n_seeds` seeds on
+both sides shrinks the noise of the difference of means to ~0.1-0.2 SE, and
+the test asserts `|mean_att_py - mean_att_R| < 0.5 SE_R` per cell plus an
+SE ratio within 30% (runs 1-2 and run 3's post cells); run 3's pre cells
+and run 4 are characterizations at 1.0 SE. A missing fixture skips the
+module (isolated-install CI jobs copy `tests/` only).
diff --git a/benchmarks/R/generate_badcontrols_golden.R b/benchmarks/R/generate_badcontrols_golden.R
new file mode 100644
index 000000000..0eae6fed4
--- /dev/null
+++ b/benchmarks/R/generate_badcontrols_golden.R
@@ -0,0 +1,175 @@
+# Black-box parity fixture for the DMLDiD bad-control lane (Caetano, Callaway,
+# Payne & Sant'Anna 2026, "Difference-in-differences with 'bad controls'",
+# arXiv:2608.03881) against the authors' R package `badcontrols`.
+#
+# LICENSE POSTURE: `badcontrols` is GPL-3; diff-diff is MIT. This script only
+# EXECUTES the package as a black-box oracle. Its source (R/*.R) is never read
+# by the implementer, and nothing in diff_diff/ derives from it - the Python
+# lane is derived from the paper alone (docs/methodology/papers/
+# caetano-2026-review.md).
+#
+# Usage:
+#   Rscript benchmarks/R/requirements.R    # installs the pinned packages
+#   Rscript benchmarks/R/generate_badcontrols_golden.R
+#
+# Output:
+#   benchmarks/data/badcontrols_panel.csv   (the simulated panel, shared input)
+#   benchmarks/data/badcontrols_golden.json (per-(g,t) R results + metadata)
+#
+# Python test loader: tests/test_dml_did_bad_controls_parity.py.
+#
+# Parity is TOLERANCE-based, not bit-exact: `didbc()` cross-fits with its own
+# fold draw (nfolds=1 errors); single-seed fold noise is ~0.25-0.35 analytical SE
+# on the smallest cells, so every run is recorded as the per-cell mean over
+# N_SEEDS seeds (per-seed rows kept too) and the Python side averages the same
+# number of its own seeds. `att_gt$se` is bootstrap-based
+# even with bstrap=FALSE, so the analytical variance `att_gt$V_analytical`
+# (SE = sqrt(V/n)) is recorded instead. `overlap_threshold = 1` disables the
+# package's silent fallback to its imputation estimator on high-propensity
+# cells (the fallback would change both the estimand and the RNG stream).
+#
+# Pins: badcontrols 1.0.0 at GitHub commit 651ccc92 (no tags/releases exist),
+# ptetools 1.0.0 (CRAN). Bump here AND in the parity test's
+# `test_metadata_versions_match` and requirements.R when re-anchoring.
+
+suppressPackageStartupMessages({
+  library(jsonlite)
+  library(badcontrols)
+  library(ptetools)
+})
+
+BADCONTROLS_SHA <- "651ccc925776125bb9233d76867c862107ea0ba5"
+stopifnot(packageVersion("badcontrols") == "1.0.0")
+stopifnot(packageVersion("ptetools") == "1.0.0")
+remote_sha <- packageDescription("badcontrols")$RemoteSha
+if (is.null(remote_sha) || !identical(remote_sha, BADCONTROLS_SHA)) {
+  stop(sprintf(
+    "badcontrols must be installed from GitHub at %s (found RemoteSha=%s); run Rscript benchmarks/R/requirements.R",
+    BADCONTROLS_SHA, if (is.null(remote_sha)) "NULL" else remote_sha
+  ))
+}
+
+SEED <- 20260905
+N <- 1000
+T_MAX <- 4
+set.seed(SEED)
+sim <- simulate_bad_controls(n = N, T_max = T_MAX)
+panel <- sim$data
+write.csv(panel, "benchmarks/data/badcontrols_panel.csv", row.names = FALSE)
+
+# Complete-case treated count per (g, t) cell on the panel: didbc's per-cell
+# `n` is the cell size; the parity test also wants the treated mass to
+# diagnose any systematic 1/pi vs 1/(1-pi) normalization gap.
+n_treated_in <- function(g) sum(panel$G == g & panel$period == min(panel$period))
+
+run_didbc <- function(run_seed, control_group, bad_control = TRUE, cov_formula = NULL) {
+  set.seed(run_seed)
+  args <- list(
+    yname = "Y", gname = "G", tname = "period", idname = "id", data = panel,
+    xformula = ~Z,
+    est_method = "dr_ml", nuisance_method = "parametric",
+    control_group = control_group, base_period = "varying", anticipation = 0,
+    bstrap = FALSE, overlap_threshold = 1, nfolds = 5
+  )
+  if (bad_control) {
+    args$bad_control_formula <- ~X
+    if (!is.null(cov_formula)) args$bad_control_cov_formula <- cov_formula
+  }
+  res <- do.call(didbc, args)
+  gt <- res$att_gt
+  # V_analytical is the full (n_cells x n_cells) analytical covariance of the
+  # cell estimates in att_gt row order; the per-cell variance is its diagonal.
+  V <- gt$V_analytical
+  if (is.matrix(V)) {
+    stopifnot(nrow(V) == length(gt$att), ncol(V) == length(gt$att))
+    V <- diag(V)
+  }
+  stopifnot(length(V) == length(gt$att))
+  data.frame(
+    group = as.numeric(gt$group),
+    t = as.numeric(gt$t),
+    att = as.numeric(gt$att),
+    V_analytical = as.numeric(V),
+    n = as.numeric(gt$n),
+    n_treated = vapply(gt$group, n_treated_in, numeric(1))
+  )
+}
+
+runs <- list(
+  list(key = "w_nyt", seed = 101, control_group = "notyettreated", bad_control = TRUE, cov = ~W,
+       description = "bad_control=X, W=[W], not-yet-treated (Proposition 2)"),
+  list(key = "w_nt", seed = 102, control_group = "nevertreated", bad_control = TRUE, cov = ~W,
+       description = "bad_control=X, W=[W], never-treated"),
+  list(key = "ylag_nyt", seed = 103, control_group = "notyettreated", bad_control = TRUE, cov = ~Y,
+       description = "bad_control=X, W=[Y] (Remark 5 lagged outcome), not-yet-treated"),
+  list(key = "plain_nyt", seed = 104, control_group = "notyettreated", bad_control = FALSE, cov = NULL,
+       description = "no bad control (xformula=~Z only), not-yet-treated; CHARACTERIZATION only")
+)
+
+N_SEEDS <- 10
+results <- list()
+for (r in runs) {
+  message(sprintf("Running %s (%d seeds) ...", r$key, N_SEEDS))
+  per_seed <- list()
+  for (i in seq_len(N_SEEDS)) {
+    seed_i <- r$seed * 10 + i
+    df <- run_didbc(seed_i, r$control_group, r$bad_control, r$cov)
+    per_seed[[i]] <- list(seed = seed_i, att_gt = df)
+  }
+  # Seed-mean of the per-cell point estimates and variances (all seeds share
+  # the att_gt row order; asserted).
+  base <- per_seed[[1]]$att_gt
+  for (ps in per_seed) stopifnot(identical(ps$att_gt$group, base$group), identical(ps$att_gt$t, base$t))
+  att_mean <- Reduce(`+`, lapply(per_seed, function(ps) ps$att_gt$att)) / N_SEEDS
+  V_mean <- Reduce(`+`, lapply(per_seed, function(ps) ps$att_gt$V_analytical)) / N_SEEDS
+  att_sd <- apply(do.call(cbind, lapply(per_seed, function(ps) ps$att_gt$att)), 1, sd)
+  results[[r$key]] <- list(
+    control_group = r$control_group,
+    bad_control = r$bad_control,
+    bad_control_cov_formula = if (is.null(r$cov)) NULL else deparse(r$cov),
+    description = r$description,
+    seeds = vapply(per_seed, function(ps) ps$seed, numeric(1)),
+    att_gt_mean = data.frame(group = base$group, t = base$t, att = att_mean,
+                             V_analytical = V_mean, att_seed_sd = att_sd,
+                             n = base$n, n_treated = base$n_treated),
+    att_gt_per_seed = lapply(per_seed, function(ps) ps$att_gt)
+  )
+}
+
+true_att_gt <- sim$true_att_gt
+out <- list(
+  meta = list(
+    generator = "benchmarks/R/generate_badcontrols_golden.R",
+    generated_at = format(Sys.time(), "%Y-%m-%dT%H:%M:%S%z"),
+    r_version = R.version.string,
+    badcontrols_version = as.character(packageVersion("badcontrols")),
+    badcontrols_remote_sha = remote_sha,
+    ptetools_version = as.character(packageVersion("ptetools")),
+    seed = SEED, n = N, T_max = T_MAX,
+    panel_csv = "benchmarks/data/badcontrols_panel.csv",
+    columns = list(unit = "id", time = "period", first_treat = "G", outcome = "Y",
+                   bad_control = "X", covariates = list("Z"), bad_control_covariate = "W"),
+    python_mapping = paste(
+      "DMLDiD(control_group=<cg>, base_period='varying', pscore_trim=1e-6, seed=0)",
+      ".fit(panel, outcome='Y', unit='id', time='period', first_treat='G',",
+      "covariates=['Z'], bad_control='X', bad_control_covariates=[<W or Y>])"
+    ),
+    common_args = list(est_method = "dr_ml", nuisance_method = "parametric",
+                       base_period = "varying", anticipation = 0, bstrap = FALSE,
+                       overlap_threshold = 1, nfolds = 5, xformula = "~Z"),
+    se_convention = "SE = sqrt(V_analytical / n) with V_analytical = diag(att_gt$V_analytical) and n = att_gt$n (the panel unit count); att_gt$se is bootstrap-based even with bstrap=FALSE",
+    n_seeds = N_SEEDS,
+    tolerance_rationale = paste(
+      "didbc cross-fits with its own fold draw (nfolds=1 errors); single-seed fold noise",
+      "is ~0.25-0.35 SE per implementation on the smallest cells (att_seed_sd records it),",
+      "so each run is recorded as the mean over N_SEEDS seeds and the Python side averages",
+      "the same number of seeds: parity is |mean_att_py - mean_att_R| < 0.5 * SE_R per cell",
+      "and |mean_se_py / SE_R - 1| < 0.3, never bit-exact"
+    ),
+    license_note = "badcontrols is GPL-3 and used ONLY as an executed black-box oracle; its source is never read"
+  ),
+  true_att_gt = true_att_gt,
+  runs = results
+)
+write_json(out, "benchmarks/data/badcontrols_golden.json", digits = 17, auto_unbox = TRUE, pretty = TRUE, null = "null")
+message("Wrote benchmarks/data/badcontrols_golden.json")
diff --git a/benchmarks/R/requirements.R b/benchmarks/R/requirements.R
index 7e3cb8695..c85a33f4e 100644
--- a/benchmarks/R/requirements.R
+++ b/benchmarks/R/requirements.R
@@ -19,6 +19,7 @@ required_packages <- c(
   "nprobust",      # Calonico-Cattaneo-Farrell local-linear (DIDHAD dependency)
   "Synth",         # Abadie-Diamond-Hainmueller (2010) synthetic control (SyntheticControl R-parity; ships data(basque))
   "qte",           # Callaway qte package (Athey-Imbens CiC + QDiD R-parity; ships data(lalonde))
+  "ptetools",      # Callaway ptetools (badcontrols dependency; bad-control DMLDiD lane black-box parity)
 
   # Utilities
   "jsonlite",      # JSON output for Python interop
@@ -77,7 +78,10 @@ pinned_versions <- list(
   # quantreg is pinned too: the covariate (xformla) golden fixtures embed
   # quantreg's rq/predict.rqs behavior, not just qte's.
   qte = "1.3.1",
-  quantreg = "6.1"
+  quantreg = "6.1",
+  # Bad-control DMLDiD lane (generate_badcontrols_golden.R +
+  # tests/test_dml_did_bad_controls_parity.py): badcontrols depends on ptetools.
+  ptetools = "1.0.0"
 )
 
 install_github_if_missing <- function(pkg, repo) {
@@ -92,6 +96,28 @@ install_github_if_missing <- function(pkg, repo) {
   }
 }
 
+# Commit-pinned GitHub package. `badcontrols` (Caetano, Callaway, Payne &
+# Sant'Anna 2026) has no tags or releases and HEAD also reports 1.0.0, so a
+# version check alone cannot detect drift: install from the pinned commit and
+# verify the installed RemoteSha (NULL-safe: a non-remotes install carries no
+# RemoteSha and must be replaced). LICENSE NOTE: badcontrols is GPL-3 and is
+# used ONLY as an executed black-box oracle by the golden generator; its
+# source is never read by diff-diff contributors (see benchmarks/R/README.md).
+install_github_pinned <- function(pkg, repo, ref, version) {
+  if (requireNamespace(pkg, quietly = TRUE)) {
+    sha <- packageDescription(pkg)$RemoteSha
+    if (as.character(packageVersion(pkg)) == version && !is.null(sha) && identical(sha, ref)) {
+      message(sprintf("%s is already at pinned version %s (%s).", pkg, version, substr(ref, 1, 8)))
+      return(invisible(NULL))
+    }
+  }
+  message(sprintf("Installing %s == %s from %s@%s ...", pkg, version, repo, substr(ref, 1, 8)))
+  if (!requireNamespace("remotes", quietly = TRUE)) {
+    install.packages("remotes", repos = "https://cloud.r-project.org/", quiet = TRUE)
+  }
+  remotes::install_github(paste0(repo, "@", ref), upgrade = "never", quiet = TRUE)
+}
+
 # Install CRAN packages
 message("Installing CRAN packages...")
 lapply(required_packages, install_if_missing)
@@ -111,9 +137,16 @@ for (pkg in names(github_packages)) {
   install_github_if_missing(pkg, github_packages[[pkg]])
 }
 
+# Commit-pinned GitHub packages (after the CRAN pins so ptetools is at 1.0.0).
+message("\nInstalling commit-pinned GitHub packages...")
+install_github_pinned(
+  "badcontrols", "hugosantanna/badcontrols",
+  ref = "651ccc925776125bb9233d76867c862107ea0ba5", version = "1.0.0"
+)
+
 # Verify installation
 message("\nVerifying installation...")
-all_packages <- c(required_packages, names(github_packages))
+all_packages <- c(required_packages, names(github_packages), "badcontrols")
 installed <- sapply(all_packages, requireNamespace, quietly = TRUE)
 
 if (all(installed)) {
@@ -127,5 +160,10 @@ if (all(installed)) {
 message("\nInstalled versions:")
 for (pkg in all_packages) {
   version <- as.character(packageVersion(pkg))
-  message(sprintf("  %s: %s", pkg, version))
+  sha <- packageDescription(pkg)$RemoteSha
+  if (is.null(sha)) {
+    message(sprintf("  %s: %s", pkg, version))
+  } else {
+    message(sprintf("  %s: %s (RemoteSha %s)", pkg, version, sha))
+  }
 }
diff --git a/benchmarks/data/badcontrols_golden.json b/benchmarks/data/badcontrols_golden.json
new file mode 100644
index 000000000..7b65eecc6
--- /dev/null
+++ b/benchmarks/data/badcontrols_golden.json
@@ -0,0 +1,3402 @@
+{
+  "meta": {
+    "generator": "benchmarks/R/generate_badcontrols_golden.R",
+    "generated_at": "2026-09-07T07:42:41-0400",
+    "r_version": "R version 4.5.2 (2025-10-31)",
+    "badcontrols_version": "1.0.0",
+    "badcontrols_remote_sha": "651ccc925776125bb9233d76867c862107ea0ba5",
+    "ptetools_version": "1.0.0",
+    "seed": 20260905,
+    "n": 1000,
+    "T_max": 4,
+    "panel_csv": "benchmarks/data/badcontrols_panel.csv",
+    "columns": {
+      "unit": "id",
+      "time": "period",
+      "first_treat": "G",
+      "outcome": "Y",
+      "bad_control": "X",
+      "covariates": [
+        "Z"
+      ],
+      "bad_control_covariate": "W"
+    },
+    "python_mapping": "DMLDiD(control_group=<cg>, base_period='varying', pscore_trim=1e-6, seed=0) .fit(panel, outcome='Y', unit='id', time='period', first_treat='G', covariates=['Z'], bad_control='X', bad_control_covariates=[<W or Y>])",
+    "common_args": {
+      "est_method": "dr_ml",
+      "nuisance_method": "parametric",
+      "base_period": "varying",
+      "anticipation": 0,
+      "bstrap": false,
+      "overlap_threshold": 1,
+      "nfolds": 5,
+      "xformula": "~Z"
+    },
+    "se_convention": "SE = sqrt(V_analytical / n) with V_analytical = diag(att_gt$V_analytical) and n = att_gt$n (the panel unit count); att_gt$se is bootstrap-based even with bstrap=FALSE",
+    "n_seeds": 10,
+    "tolerance_rationale": "didbc cross-fits with its own fold draw (nfolds=1 errors); single-seed fold noise is ~0.25-0.35 SE per implementation on the smallest cells (att_seed_sd records it), so each run is recorded as the mean over N_SEEDS seeds and the Python side averages the same number of seeds: parity is |mean_att_py - mean_att_R| < 0.5 * SE_R per cell and |mean_se_py / SE_R - 1| < 0.3, never bit-exact",
+    "license_note": "badcontrols is GPL-3 and used ONLY as an executed black-box oracle; its source is never read"
+  },
+  "true_att_gt": [
+    {
+      "g": 2,
+      "t": 2,
+      "att": 1
+    },
+    {
+      "g": 2,
+      "t": 3,
+      "att": 1.6499999999999999
+    },
+    {
+      "g": 2,
+      "t": 4,
+      "att": 2.3999999999999999
+    },
+    {
+      "g": 3,
+      "t": 3,
+      "att": 1.1000000000000001
+    },
+    {
+      "g": 3,
+      "t": 4,
+      "att": 1.7999999999999998
+    },
+    {
+      "g": 4,
+      "t": 4,
+      "att": 1.2
+    }
+  ],
+  "runs": {
+    "w_nyt": {
+      "control_group": "notyettreated",
+      "bad_control": true,
+      "bad_control_cov_formula": "~W",
+      "description": "bad_control=X, W=[W], not-yet-treated (Proposition 2)",
+      "seeds": [1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020],
+      "att_gt_mean": [
+        {
+          "group": 2,
+          "t": 2,
+          "att": 0.95834471150576039,
+          "V_analytical": 1.3670817630314469,
+          "att_seed_sd": 0.0016864795815592004,
+          "n": 1000,
+          "n_treated": 250
+        },
+        {
+          "group": 3,
+          "t": 2,
+          "att": -0.017086906026156347,
+          "V_analytical": 1.5509052195362609,
+          "att_seed_sd": 0.0021428310392669729,
+          "n": 1000,
+          "n_treated": 250
+        },
+        {
+          "group": 4,
+          "t": 2,
+          "att": 0.029451012924035617,
+          "V_analytical": 2.6295034411221527,
+          "att_seed_sd": 0.0044481238791753116,
+          "n": 1000,
+          "n_treated": 250
+        },
+        {
+          "group": 2,
+          "t": 3,
+          "att": 1.6334669840458595,
+          "V_analytical": 2.5243316004028951,
+          "att_seed_sd": 0.0053943429339091079,
+          "n": 1000,
+          "n_treated": 250
+        },
+        {
+          "group": 3,
+          "t": 3,
+          "att": 1.126994963495211,
+          "V_analytical": 1.755073081838828,
+          "att_seed_sd": 0.0034294074124839704,
+          "n": 1000,
+          "n_treated": 250
+        },
+        {
+          "group": 4,
+          "t": 3,
+          "att": -0.12759747058272369,
+          "V_analytical": 42.658466226147226,
+          "att_seed_sd": 0.047237034486409375,
+          "n": 1000,
+          "n_treated": 250
+        },
+        {
+          "group": 2,
+          "t": 4,
+          "att": 2.3929639140746217,
+          "V_analytical": 4.8194183323904083,
+          "att_seed_sd": 0.0096129933427861365,
+          "n": 1000,
+          "n_treated": 250
+        },
+        {
+          "group": 3,
+          "t": 4,
+          "att": 1.7281956617449601,
+          "V_analytical": 7.7273223520855865,
+          "att_seed_sd": 0.010849624932630463,
+          "n": 1000,
+          "n_treated": 250
+        },
+        {
+          "group": 4,
+          "t": 4,
+          "att": 1.1109578892079539,
+          "V_analytical": 8.3084898121578643,
+          "att_seed_sd": 0.019305484896016779,
+          "n": 1000,
+          "n_treated": 250
+        }
+      ],
+      "att_gt_per_seed": [
+        [
+          {
+            "group": 2,
+            "t": 2,
+            "att": 0.95980381079518595,
+            "V_analytical": 1.3675253428326939,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 3,
+            "t": 2,
+            "att": -0.018305498565866812,
+            "V_analytical": 1.5680990923248177,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 4,
+            "t": 2,
+            "att": 0.029025406662408694,
+            "V_analytical": 2.6001293718859038,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 2,
+            "t": 3,
+            "att": 1.6243323331490831,
+            "V_analytical": 2.5359898270319112,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 3,
+            "t": 3,
+            "att": 1.1236341597292114,
+            "V_analytical": 1.7729418446369054,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 4,
+            "t": 3,
+            "att": -0.20790734278133016,
+            "V_analytical": 64.773192957561434,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 2,
+            "t": 4,
+            "att": 2.3919295486327905,
+            "V_analytical": 5.0891749683712559,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 3,
+            "t": 4,
+            "att": 1.7239949380070005,
+            "V_analytical": 8.0348527771936098,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 4,
+            "t": 4,
+            "att": 1.08607363507223,
+            "V_analytical": 8.2990587701513654,
+            "n": 1000,
+            "n_treated": 250
+          }
+        ],
+        [
+          {
+            "group": 2,
+            "t": 2,
+            "att": 0.95878456703230042,
+            "V_analytical": 1.3655081558525908,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 3,
+            "t": 2,
+            "att": -0.015274372004598082,
+            "V_analytical": 1.5622705737317992,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 4,
+            "t": 2,
+            "att": 0.035214863324030996,
+            "V_analytical": 2.5509999717603313,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 2,
+            "t": 3,
+            "att": 1.6389645731476969,
+            "V_analytical": 2.5207590004166121,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 3,
+            "t": 3,
+            "att": 1.1310910636531855,
+            "V_analytical": 1.7698321414254057,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 4,
+            "t": 3,
+            "att": -0.081344898977579572,
+            "V_analytical": 26.528116971418864,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 2,
+            "t": 4,
+            "att": 2.3806992397579885,
+            "V_analytical": 4.9158278439084047,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 3,
+            "t": 4,
+            "att": 1.7409605255070677,
+            "V_analytical": 7.0422779440394203,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 4,
+            "t": 4,
+            "att": 1.0955285948184277,
+            "V_analytical": 7.2540845558824589,
+            "n": 1000,
+            "n_treated": 250
+          }
+        ],
+        [
+          {
+            "group": 2,
+            "t": 2,
+            "att": 0.95760410519632622,
+            "V_analytical": 1.3592734312419661,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 3,
+            "t": 2,
+            "att": -0.016656387132396887,
+            "V_analytical": 1.5435862564208345,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 4,
+            "t": 2,
+            "att": 0.029544668614879491,
+            "V_analytical": 2.652215014899812,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 2,
+            "t": 3,
+            "att": 1.6360302491574186,
+            "V_analytical": 2.5233382404686435,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 3,
+            "t": 3,
+            "att": 1.1249002219908324,
+            "V_analytical": 1.7614072438907478,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 4,
+            "t": 3,
+            "att": -0.11645091845934755,
+            "V_analytical": 36.050830322016701,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 2,
+            "t": 4,
+            "att": 2.383190101028053,
+            "V_analytical": 4.5839458057180709,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 3,
+            "t": 4,
+            "att": 1.7362245388521977,
+            "V_analytical": 6.9677877892463167,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 4,
+            "t": 4,
+            "att": 1.0938438871495724,
+            "V_analytical": 6.8271441904143151,
+            "n": 1000,
+            "n_treated": 250
+          }
+        ],
+        [
+          {
+            "group": 2,
+            "t": 2,
+            "att": 0.95747321340889302,
+            "V_analytical": 1.3674586811317191,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 3,
+            "t": 2,
+            "att": -0.020232817704762499,
+            "V_analytical": 1.5647614171836552,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 4,
+            "t": 2,
+            "att": 0.025428399292493964,
+            "V_analytical": 2.6824243071791298,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 2,
+            "t": 3,
+            "att": 1.6261932117311431,
+            "V_analytical": 2.5409288877541987,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 3,
+            "t": 3,
+            "att": 1.1268622224241256,
+            "V_analytical": 1.7404520967940971,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 4,
+            "t": 3,
+            "att": -0.1388535890015439,
+            "V_analytical": 43.428478620085293,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 2,
+            "t": 4,
+            "att": 2.3913257025103003,
+            "V_analytical": 4.8333592823539711,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 3,
+            "t": 4,
+            "att": 1.7173867636420188,
+            "V_analytical": 9.1513757498100574,
+            "n": 1000,
+            "n_treated": 250
+          },
+          {
+            "group": 4,
+            "t": 4,
+            "att": 1.1185830227603852,
+            "V_analytical": 7.1119181688502682,
+            "n": 1000,
+            "n_treated": 250
+          }
+        ],
+        [
+          {
+            "group": 2,
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diff --git a/benchmarks/data/badcontrols_panel.csv b/benchmarks/data/badcontrols_panel.csv
new file mode 100644
index 000000000..ac3da9076
--- /dev/null
+++ b/benchmarks/data/badcontrols_panel.csv
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+997,1,2,0,-0.288979202755548,-0.44411900619678,1.20007473194059,0.0623296518929975
+997,2,2,1,1.93435747251544,0.643220145445648,1.20007473194059,0.0623296518929975
+997,3,2,1,3.52021954089933,1.31771423181432,1.20007473194059,0.0623296518929975
+997,4,2,1,5.03943692321187,2.11537512093276,1.20007473194059,0.0623296518929975
+998,1,4,0,1.77198585936234,0.773781628630291,0.335616714125819,0.877284191480645
+998,2,4,0,2.0552901878143,0.714456766596474,0.335616714125819,0.877284191480645
+998,3,4,0,2.62439405099623,0.912284687555365,0.335616714125819,0.877284191480645
+998,4,4,1,5.30002042850296,1.99052311888206,0.335616714125819,0.877284191480645
+999,1,0,0,-1.6041654907381,-1.07036639486553,-0.295971362977924,-1.84693999823918
+999,2,0,0,-1.46250490285658,-1.13596664850949,-0.295971362977924,-1.84693999823918
+999,3,0,0,-1.89581976146399,-1.04544887411505,-0.295971362977924,-1.84693999823918
+999,4,0,0,-0.635813479421222,-0.448983875186788,-0.295971362977924,-1.84693999823918
+1000,1,4,0,2.26380887283942,1.05779033043567,0.967022410218707,1.34504922017797
+1000,2,4,0,3.27649610475249,1.47565930092796,0.967022410218707,1.34504922017797
+1000,3,4,0,3.43529820368263,1.37488658240799,0.967022410218707,1.34504922017797
+1000,4,4,1,6.68405943925373,2.73613412420361,0.967022410218707,1.34504922017797
diff --git a/changelog.d/20260905-bad-controls-dml.md b/changelog.d/20260905-bad-controls-dml.md
new file mode 100644
index 000000000..78bea7657
--- /dev/null
+++ b/changelog.d/20260905-bad-controls-dml.md
@@ -0,0 +1,56 @@
+### Added
+- **`DMLDiD` bad-control lane (Caetano, Callaway, Payne & Sant'Anna 2026, "Difference-in-differences with 'bad controls'", arXiv:2608.03881; PR-B of the bad-controls initiative).**
+  `DMLDiD(...).fit(..., bad_control="x", bad_control_covariates=[...])` swaps the per-cell
+  Chang (2020) score for the paper's Neyman-orthogonal doubly-robust score (Eq. 10 / 11,
+  Algorithm 1; `ccps_panel_score` / `ccps_panel_score_augmented` in `_dr_scores.py`):
+  parallel trends conditional on the bad control's UNTREATED path, with its untreated
+  evolution identified by covariate unconfoundedness given its base-period value, the
+  optional `W` covariates (`[outcome]` = the base-period outcome, the paper's Remark 5
+  recommendation; default no `W`) and the covariates `Z`. Four cross-fitted nuisances
+  per cell, including the two NESTED second stages (`nu`, `omega`): in-sample fold-k
+  targets for the parametric `linear`/`logit` built-ins (the paper's Assumption-8
+  plug-in), split-half swap-and-average for `ridge` / `sieve` / user learners
+  (footnote 9); `omega` clipped to `[0, (1-trim)/trim]` with a warning. Every cell also
+  reports the paper's Remark 6 pre-test `ATT_X(g,t)` (the effect of treatment on the bad
+  control itself, an AIPW mean-effect diagnostic with its own analytical SE, sharing the
+  ATT's cluster / df branch; pre-period rows pre-test MP-5 / MP-8 and should be zero,
+  post-period rows check that treatment affects the covariate) via `results.bad_control_summary()` /
+  `results.bad_control_diagnostics`, with `att_x` / `se_x` joined into
+  `to_dataframe()` and new `summary()` header lines. Panel lane only, bare `cluster=`
+  only (`survey_design=` raises), `anticipation=0` and `base_period="varying"` only;
+  the bad control may not appear in `covariates`; `bad_control=None` is the untouched
+  pre-existing code path (bit-identical). The headline `att` keeps the CS "simple"
+  weighting (not the paper's Remark 4 overall; TODO row). Validation: score-level
+  paired double robustness + four-direction Neyman orthogonality + reduction to
+  `chang_panel_score` at 1e-14; a numpy oracle of Eq. 11 / Algorithm 1 at 1e-12
+  (ATT, SE, ATT_X); oracle user learners on the split-half branch; the Supplementary
+  Appendix's DGP 1 / DGP 4 recovery (`ATT = 1.00`, `ATT_X = 0.50`) with slow MC
+  coverage; and tolerance-based black-box goldens against the authors' GPL-3 R package
+  `badcontrols` 1.0.0 (executed only, never read; 10-seed means on both sides,
+  `|Δatt| < 0.5 SE` per cell) in `tests/test_dml_did_bad_controls_parity.py` with the
+  generator `benchmarks/R/generate_badcontrols_golden.R` and commit-pinned installer
+  in `benchmarks/R/requirements.R`. `BusinessReport` / target-parameter /
+  `practitioner_next_steps` carry the bad-control identification text, the second
+  citation and the refit snippet arguments.
+
+### Changed
+- **`_crossfit.py` deep-copy fallback warning** now reads `"_crossfit: could not
+  deep-copy ..."` (was `"cross_fit_predict: ..."`) and is attributed to the frame that
+  advances the fold generator; the module gains the per-fold generator
+  `iter_fold_fits` / `FoldFit` that `cross_fit_predict` is now a consumer of
+  (behavior-preserving refactor; every existing pin unchanged).
+
+### Documentation
+- REGISTRY `DMLDiD` "Bad-control extension (CCPS 2026)" block (equations as
+  implemented, nested-stage / omega-clip / W-default / base-period / anticipation /
+  fail-closed / complete-case / aggregation-weight / ATT_X / validation-scope Notes),
+  the CallawaySantAnna Approach-1 Note (a pre-treatment bad control in `covariates`
+  computes Proposition 3 on the panel lane), the infrastructure section's fourth score
+  family and `iter_fold_fits` contract; `docs/api/dml_did.rst` methodology sub-block,
+  restrictions and a runnable snippet; `docs/api/staggered.rst` "Covariates and bad
+  controls"; the paper review's requirements checklist flipped with library
+  annotations; guides (`llms.txt` signature + Diagnostics entry, `llms-full.txt`,
+  practitioner pitfall 3 rewrite, autonomous matrix); `choosing_estimator.rst`,
+  `practitioner_decision_tree.rst`, `docs/index.rst`, README one-liners; survey
+  roadmap / survey theory carve-outs; `docs/references.rst`; the regenerated
+  variance-conventions table (`dml_did_bad_control` row); `benchmarks/R/README.md`.
diff --git a/diff_diff/_crossfit.py b/diff_diff/_crossfit.py
index a2bca67d0..6f1c96c7e 100644
--- a/diff_diff/_crossfit.py
+++ b/diff_diff/_crossfit.py
@@ -35,7 +35,7 @@
 import pickle
 import warnings
 from dataclasses import dataclass, field
-from typing import Any, Dict, Iterator, Literal, Optional, Tuple, cast, overload
+from typing import Any, Dict, Iterator, Literal, NamedTuple, Optional, Tuple, cast, overload
 
 import numpy as np
 import pandas as pd
@@ -53,12 +53,14 @@
     "CrossFitResult",
     "assign_folds",
     "cross_fit_predict",
+    "FoldFit",
+    "iter_fold_fits",
 ]
 
 _LOG_LOSS_CLIP = 1e-15
 
 
-def _fresh_learner(learner: Any) -> Any:
+def _fresh_learner(learner: Any, *, stacklevel: int) -> Any:
     """Per-fold learner isolation: a deep copy of the (never-fit) template.
 
     ``copy.deepcopy`` of the user's template gives every fold a fully
@@ -70,7 +72,10 @@ def _fresh_learner(learner: Any) -> Any:
     a container parameter). The template itself is never fit. A copy FAILURE
     is never silent: the instance is reused with a loud ``UserWarning`` naming
     the learner and the fit-reset assumption now being relied on
-    (no-silent-failures rule).
+    (no-silent-failures rule). ``stacklevel`` is supplied by the caller so the
+    warning is attributed to the entry point's own caller (``cross_fit_predict``
+    passes the level that lands on the user's call site; internal consumers
+    of ``iter_fold_fits`` pass the level that lands on themselves).
     """
     try:
         return copy.deepcopy(learner)
@@ -80,14 +85,14 @@ def _fresh_learner(learner: Any) -> Any:
         # and this warning lands in notebook/CI logs (the same boundary as
         # DMLDiD's persisted-diagnostics sanitization).
         warnings.warn(
-            f"cross_fit_predict: could not deep-copy the "
+            f"_crossfit: could not deep-copy the "
             f"{type(learner).__name__} template for this fold "
             f"({type(exc).__name__}); "
             "REUSING the same instance and relying on its fit-reset behavior. "
             "A warm-start/stateful learner in this situation can leak data "
             "across folds.",
             UserWarning,
-            stacklevel=3,
+            stacklevel=stacklevel,
         )
         return learner
 
@@ -404,55 +409,45 @@ def assign_folds(
     )
 
 
-@overload
-def cross_fit_predict(
-    learner: RegressorLearner,
-    X: np.ndarray,
-    y: np.ndarray,
-    folds: FoldAssignment,
-    *,
-    fit_mask: Optional[np.ndarray] = ...,
-    predict_method: Literal["predict"] = ...,
-    sample_weight: Optional[np.ndarray] = ...,
-    context_label: str = ...,
-) -> CrossFitResult: ...
-
-
-@overload
-def cross_fit_predict(
-    learner: ClassifierLearner,
-    X: np.ndarray,
-    y: np.ndarray,
-    folds: FoldAssignment,
-    *,
-    fit_mask: Optional[np.ndarray] = ...,
-    predict_method: Literal["predict_proba"],
-    sample_weight: Optional[np.ndarray] = ...,
-    context_label: str = ...,
-) -> CrossFitResult: ...
+class FoldFit(NamedTuple):
+    """One fold's fitted learner plus the index sets it was built from.
 
+    Yielded by :func:`iter_fold_fits`. ``X`` / ``y`` / ``sample_weight`` are the
+    validated, float64-coerced arrays (so consumers index them positionally
+    exactly as :func:`cross_fit_predict` does); ``learner`` is the per-fold
+    deep copy already fit on ``fit_idx``; ``train_idx`` is fold ``k``'s full
+    training complement and ``test_idx`` the held-out fold.
+    """
 
-def cross_fit_predict(
+    k: int
+    learner: Any
+    fit_idx: np.ndarray
+    train_idx: np.ndarray
+    test_idx: np.ndarray
+    n_fit: int
+    w_fit: Optional[np.ndarray]
+    kind: str
+    label: str
+    X: np.ndarray
+    y: np.ndarray
+    sample_weight: Optional[np.ndarray]
+
+
+def _prepare_cross_fit_inputs(
     learner: object,
     X: np.ndarray,
     y: np.ndarray,
     folds: FoldAssignment,
     *,
-    fit_mask: Optional[np.ndarray] = None,
-    predict_method: str = "predict",
-    sample_weight: Optional[np.ndarray] = None,
-    context_label: str = "",
-) -> CrossFitResult:
-    """Out-of-fold predictions for every unit.
+    fit_mask: Optional[np.ndarray],
+    predict_method: str,
+    sample_weight: Optional[np.ndarray],
+) -> Tuple[np.ndarray, np.ndarray, np.ndarray, Optional[np.ndarray], str]:
+    """Argument validation shared by every cross-fit entry point.
 
-    Per fold k: fit the learner on ``train_mask(k) & fit_mask`` (e.g. the
-    untreated units), predict ALL units in fold k. ``context_label``
-    (e.g. the nuisance name or (g,t) cell) is prefixed into every
-    ``DegenerateFoldError`` message to identify WHICH cross-fit failed.
+    Own-argument failures raise plain ``ValueError`` (the module contract).
     """
     n_units = folds.n_units
-    label = f"{context_label}: " if context_label else ""
-
     if predict_method not in ("predict", "predict_proba"):
         raise ValueError(
             f"predict_method must be 'predict' or 'predict_proba', got {predict_method!r}"
@@ -491,20 +486,19 @@ def cross_fit_predict(
             )
         fit_mask_arr = raw_mask
 
+    sw: Optional[np.ndarray] = None
     if sample_weight is not None:
-        sample_weight = np.asarray(sample_weight, dtype=np.float64)
-        if sample_weight.ndim != 1:
+        sw = np.asarray(sample_weight, dtype=np.float64)
+        if sw.ndim != 1:
             raise ValueError(
-                f"sample_weight must be 1-dimensional, got ndim={sample_weight.ndim} "
+                f"sample_weight must be 1-dimensional, got ndim={sw.ndim} "
                 "(a column vector like (n, 1) is not accepted)"
             )
-        if sample_weight.shape[0] != n_units:
-            raise ValueError(
-                f"sample_weight has length {sample_weight.shape[0]}, expected {n_units}"
-            )
-        if not np.isfinite(sample_weight).all():
+        if sw.shape[0] != n_units:
+            raise ValueError(f"sample_weight has length {sw.shape[0]}, expected {n_units}")
+        if not np.isfinite(sw).all():
             raise ValueError("sample_weight contains NaN or Inf values")
-        if np.any(sample_weight < 0):
+        if np.any(sw < 0):
             raise ValueError("sample_weight must be non-negative")
 
     if predict_method == "predict_proba" and not np.all((y == 0.0) | (y == 1.0)):
@@ -512,91 +506,294 @@ def cross_fit_predict(
             "y must be strictly binary 0/1 for predict_method='predict_proba' "
             "(the logit solver silently saturates on other encodings)"
         )
+    return X, y, fit_mask_arr, sw, kind
 
-    oof = np.empty(n_units, dtype=np.float64)
-    fold_losses = np.empty(folds.n_folds, dtype=np.float64)
-    n_fit_per_fold = np.empty(folds.n_folds, dtype=np.int64)
 
-    for k, train_idx, test_idx in folds.iter_folds():
-        fit_idx = train_idx[fit_mask_arr[train_idx]]
-        n_fit = fit_idx.shape[0]
-        n_fit_per_fold[k] = n_fit
-        w_fit = None if sample_weight is None else sample_weight[fit_idx]
+def _learner_error(
+    exc: ValueError, *, k: int, label: str, n_fit: int, w_fit: Optional[np.ndarray]
+) -> DegenerateFoldError:
+    return DegenerateFoldError(
+        f"{label}learner error in fold {k}: {exc}; the fold's fit subset "
+        f"has n={n_fit}"
+        + (f", n_pos_weight={int(np.sum(w_fit > 0))}" if w_fit is not None else "")
+        + ". Reduce n_folds, widen fit_mask, or check the fold's data."
+    )
 
-        # (a) Universal cheap pre-checks -> DegenerateFoldError directly.
-        if n_fit == 0:
-            raise DegenerateFoldError(
-                f"{label}fold {k}: the fit subset is empty (train size "
-                f"{train_idx.shape[0]}, fit_mask keeps 0). Reduce n_folds, widen "
-                "fit_mask, or check the stratify labels."
-            )
-        if w_fit is not None and not np.any(w_fit > 0):
+
+def _fit_subset(
+    learner: object,
+    X: np.ndarray,
+    y: np.ndarray,
+    fit_idx: np.ndarray,
+    *,
+    n_train: int,
+    kind: str,
+    sample_weight: Optional[np.ndarray],
+    k: int,
+    label: str,
+    warn_stacklevel: int,
+) -> Tuple[Any, int, Optional[np.ndarray]]:
+    """Fit a fresh deep copy of ``learner`` on ``fit_idx`` (fold ``k``).
+
+    Universal degeneracy pre-checks raise ``DegenerateFoldError`` directly; a
+    learner ``ValueError`` is re-raised as ``DegenerateFoldError`` chained via
+    ``raise ... from exc``; a learner-raised ``DegenerateFoldError`` passes
+    through unwrapped. Returns ``(fitted_learner, n_fit, w_fit)``.
+    """
+    n_fit = int(fit_idx.shape[0])
+    w_fit = None if sample_weight is None else sample_weight[fit_idx]
+
+    # (a) Universal cheap pre-checks -> DegenerateFoldError directly.
+    if n_fit == 0:
+        raise DegenerateFoldError(
+            f"{label}fold {k}: the fit subset is empty (train size "
+            f"{n_train}, fit_mask keeps 0). Reduce n_folds, widen "
+            "fit_mask, or check the stratify labels."
+        )
+    if w_fit is not None and not np.any(w_fit > 0):
+        raise DegenerateFoldError(
+            f"{label}fold {k}: all {n_fit} fit rows have zero sample_weight. "
+            "Reduce n_folds or check the weights."
+        )
+    if kind == "classifier":
+        labels = y[fit_idx] if w_fit is None else y[fit_idx][w_fit > 0]
+        if np.unique(labels).shape[0] < 2:
             raise DegenerateFoldError(
-                f"{label}fold {k}: all {n_fit} fit rows have zero sample_weight. "
-                "Reduce n_folds or check the weights."
+                f"{label}fold {k}: the fit subset has a single "
+                f"{'positive-weight ' if w_fit is not None else ''}class "
+                f"(n_fit={n_fit}). A classifier needs both classes in every "
+                "fold's complement; reduce n_folds or stratify by the label."
             )
-        if predict_method == "predict_proba":
-            labels = y[fit_idx] if w_fit is None else y[fit_idx][w_fit > 0]
-            if np.unique(labels).shape[0] < 2:
-                raise DegenerateFoldError(
-                    f"{label}fold {k}: the fit subset has a single "
-                    f"{'positive-weight ' if w_fit is not None else ''}class "
-                    f"(n_fit={n_fit}). A classifier needs both classes in every "
-                    "fold's complement; reduce n_folds or stratify by the label."
-                )
 
-        # (b) Learner errors during the fold -> DegenerateFoldError, chained.
-        try:
-            fold_learner = _fresh_learner(learner)
-            # Unweighted path calls fit(X, y) WITHOUT the keyword: the
-            # advertised duck-typed contract is fit/predict(_proba), so a
-            # learner whose fit signature is only (X, y) must work when no
-            # weights are in play. sample_weight= is passed only on
-            # genuinely weighted paths, where an unsupported signature
-            # raises TypeError — a caller protocol violation that PROPAGATES
-            # (the DegenerateFoldError wrapper below catches ValueError
-            # only; fold-data degeneracy, not signature bugs).
-            fit_kwargs = {} if w_fit is None else {"sample_weight": w_fit}
-            if kind == "regressor":
-                reg = cast(RegressorLearner, fold_learner)
-                reg.fit(X[fit_idx], y[fit_idx], **fit_kwargs)
-                raw_pred = reg.predict(X[test_idx])
-            else:
-                clf = cast(ClassifierLearner, fold_learner)
-                clf.fit(X[fit_idx], y[fit_idx], **fit_kwargs)
-                raw_pred = clf.predict_proba(X[test_idx])
-            pred = _validate_predictions(
-                raw_pred,
-                test_idx.shape[0],
-                kind=kind,
-                context=f"{label}fold {k}",
-                classes=(getattr(fold_learner, "classes_", None) if kind == "classifier" else None),
-            )
-        except DegenerateFoldError:
-            raise
-        except ValueError as exc:
-            raise DegenerateFoldError(
-                f"{label}learner error in fold {k}: {exc}; the fold's fit subset "
-                f"has n={n_fit}"
-                + (f", n_pos_weight={int(np.sum(w_fit > 0))}" if w_fit is not None else "")
-                + ". Reduce n_folds, widen fit_mask, or check the fold's data."
-            ) from exc
-
-        oof[test_idx] = pred
-
-        # Out-of-fold loss (diagnostic; NaN sentinel for zero-weight folds).
-        w_test = None if sample_weight is None else sample_weight[test_idx]
-        if predict_method == "predict":
-            errs = (y[test_idx] - pred) ** 2
+    # (b) Learner errors during the fold -> DegenerateFoldError, chained.
+    try:
+        fold_learner = _fresh_learner(learner, stacklevel=warn_stacklevel)
+        # Unweighted path calls fit(X, y) WITHOUT the keyword: the
+        # advertised duck-typed contract is fit/predict(_proba), so a
+        # learner whose fit signature is only (X, y) must work when no
+        # weights are in play. sample_weight= is passed only on
+        # genuinely weighted paths, where an unsupported signature
+        # raises TypeError — a caller protocol violation that PROPAGATES
+        # (the DegenerateFoldError wrapper below catches ValueError
+        # only; fold-data degeneracy, not signature bugs).
+        fit_kwargs = {} if w_fit is None else {"sample_weight": w_fit}
+        if kind == "regressor":
+            cast(RegressorLearner, fold_learner).fit(X[fit_idx], y[fit_idx], **fit_kwargs)
         else:
-            p_clip = np.clip(pred, _LOG_LOSS_CLIP, 1.0 - _LOG_LOSS_CLIP)
-            errs = -(y[test_idx] * np.log(p_clip) + (1.0 - y[test_idx]) * np.log(1.0 - p_clip))
-        if w_test is None:
-            fold_losses[k] = float(np.mean(errs))
-        elif np.sum(w_test) > 0:
-            fold_losses[k] = float(np.sum(w_test * errs) / np.sum(w_test))
+            cast(ClassifierLearner, fold_learner).fit(X[fit_idx], y[fit_idx], **fit_kwargs)
+    except DegenerateFoldError:
+        raise
+    except ValueError as exc:
+        raise _learner_error(exc, k=k, label=label, n_fit=n_fit, w_fit=w_fit) from exc
+    return fold_learner, n_fit, w_fit
+
+
+def _predict_subset(
+    fold_learner: Any,
+    X_rows: np.ndarray,
+    *,
+    kind: str,
+    k: int,
+    label: str,
+    n_fit: int,
+    w_fit: Optional[np.ndarray],
+) -> np.ndarray:
+    """Predict ``X_rows`` with a fitted fold learner and validate the output.
+
+    Same exception contract as :func:`_fit_subset` (chained
+    ``DegenerateFoldError`` on a learner ``ValueError``; pass-through of a
+    learner-raised ``DegenerateFoldError``).
+    """
+    try:
+        if kind == "regressor":
+            raw_pred = cast(RegressorLearner, fold_learner).predict(X_rows)
         else:
-            fold_losses[k] = np.nan
+            raw_pred = cast(ClassifierLearner, fold_learner).predict_proba(X_rows)
+        return _validate_predictions(
+            raw_pred,
+            X_rows.shape[0],
+            kind=kind,
+            context=f"{label}fold {k}",
+            classes=(getattr(fold_learner, "classes_", None) if kind == "classifier" else None),
+        )
+    except DegenerateFoldError:
+        raise
+    except ValueError as exc:
+        raise _learner_error(exc, k=k, label=label, n_fit=n_fit, w_fit=w_fit) from exc
+
+
+def _fold_loss(
+    kind: str, y_test: np.ndarray, pred: np.ndarray, w_test: Optional[np.ndarray]
+) -> float:
+    """Out-of-fold MSE (regressor) or log-loss (classifier); NaN for a zero-weight fold."""
+    if kind == "regressor":
+        errs = (y_test - pred) ** 2
+    else:
+        p_clip = np.clip(pred, _LOG_LOSS_CLIP, 1.0 - _LOG_LOSS_CLIP)
+        errs = -(y_test * np.log(p_clip) + (1.0 - y_test) * np.log(1.0 - p_clip))
+    if w_test is None:
+        return float(np.mean(errs))
+    if np.sum(w_test) > 0:
+        return float(np.sum(w_test * errs) / np.sum(w_test))
+    return float(np.nan)
+
+
+def _iter_fold_fits_impl(
+    learner: object,
+    X: np.ndarray,
+    y: np.ndarray,
+    folds: FoldAssignment,
+    fit_mask_arr: np.ndarray,
+    sample_weight: Optional[np.ndarray],
+    kind: str,
+    label: str,
+    warn_stacklevel: int,
+) -> Iterator[FoldFit]:
+    for k, train_idx, test_idx in folds.iter_folds():
+        fit_idx = train_idx[fit_mask_arr[train_idx]]
+        fitted, n_fit, w_fit = _fit_subset(
+            learner,
+            X,
+            y,
+            fit_idx,
+            n_train=int(train_idx.shape[0]),
+            kind=kind,
+            sample_weight=sample_weight,
+            k=k,
+            label=label,
+            warn_stacklevel=warn_stacklevel,
+        )
+        yield FoldFit(
+            k=k,
+            learner=fitted,
+            fit_idx=fit_idx,
+            train_idx=train_idx,
+            test_idx=test_idx,
+            n_fit=n_fit,
+            w_fit=w_fit,
+            kind=kind,
+            label=label,
+            X=X,
+            y=y,
+            sample_weight=sample_weight,
+        )
+
+
+def iter_fold_fits(
+    learner: object,
+    X: np.ndarray,
+    y: np.ndarray,
+    folds: FoldAssignment,
+    *,
+    fit_mask: Optional[np.ndarray] = None,
+    predict_method: str = "predict",
+    sample_weight: Optional[np.ndarray] = None,
+    context_label: str = "",
+    warn_stacklevel: int = 4,
+) -> Iterator[FoldFit]:
+    """Per-fold fitted learners (the building block under ``cross_fit_predict``).
+
+    Validation runs EAGERLY at the call (not at the first ``__next__``), then
+    the returned iterator yields one :class:`FoldFit` per fold in ascending
+    ``k``, each holding a fresh deep copy of ``learner`` fit on
+    ``train_mask(k) & fit_mask``. Predictions are the caller's job via
+    ``_predict_subset``; this is what lets a consumer fit a NESTED nuisance on
+    fold ``k``'s own training units. ``warn_stacklevel`` is the frame the
+    deep-copy-failure warning is attributed to (default: the frame advancing
+    the iterator).
+    """
+    X64, y64, fit_mask_arr, sw, kind = _prepare_cross_fit_inputs(
+        learner,
+        X,
+        y,
+        folds,
+        fit_mask=fit_mask,
+        predict_method=predict_method,
+        sample_weight=sample_weight,
+    )
+    label = f"{context_label}: " if context_label else ""
+    return _iter_fold_fits_impl(
+        learner, X64, y64, folds, fit_mask_arr, sw, kind, label, warn_stacklevel
+    )
+
+
+@overload
+def cross_fit_predict(
+    learner: RegressorLearner,
+    X: np.ndarray,
+    y: np.ndarray,
+    folds: FoldAssignment,
+    *,
+    fit_mask: Optional[np.ndarray] = ...,
+    predict_method: Literal["predict"] = ...,
+    sample_weight: Optional[np.ndarray] = ...,
+    context_label: str = ...,
+) -> CrossFitResult: ...
+
+
+@overload
+def cross_fit_predict(
+    learner: ClassifierLearner,
+    X: np.ndarray,
+    y: np.ndarray,
+    folds: FoldAssignment,
+    *,
+    fit_mask: Optional[np.ndarray] = ...,
+    predict_method: Literal["predict_proba"],
+    sample_weight: Optional[np.ndarray] = ...,
+    context_label: str = ...,
+) -> CrossFitResult: ...
+
+
+def cross_fit_predict(
+    learner: object,
+    X: np.ndarray,
+    y: np.ndarray,
+    folds: FoldAssignment,
+    *,
+    fit_mask: Optional[np.ndarray] = None,
+    predict_method: str = "predict",
+    sample_weight: Optional[np.ndarray] = None,
+    context_label: str = "",
+) -> CrossFitResult:
+    """Out-of-fold predictions for every unit.
+
+    Per fold k: fit the learner on ``train_mask(k) & fit_mask`` (e.g. the
+    untreated units), predict ALL units in fold k. ``context_label``
+    (e.g. the nuisance name or (g,t) cell) is prefixed into every
+    ``DegenerateFoldError`` message to identify WHICH cross-fit failed.
+    """
+    n_units = folds.n_units
+    oof = np.empty(n_units, dtype=np.float64)
+    fold_losses = np.empty(folds.n_folds, dtype=np.float64)
+    n_fit_per_fold = np.empty(folds.n_folds, dtype=np.int64)
+
+    # stacklevel 5: _fresh_learner -> _fit_subset -> generator frame ->
+    # cross_fit_predict -> the user's call site.
+    for ff in iter_fold_fits(
+        learner,
+        X,
+        y,
+        folds,
+        fit_mask=fit_mask,
+        predict_method=predict_method,
+        sample_weight=sample_weight,
+        context_label=context_label,
+        warn_stacklevel=5,
+    ):
+        n_fit_per_fold[ff.k] = ff.n_fit
+        pred = _predict_subset(
+            ff.learner,
+            ff.X[ff.test_idx],
+            kind=ff.kind,
+            k=ff.k,
+            label=ff.label,
+            n_fit=ff.n_fit,
+            w_fit=ff.w_fit,
+        )
+        oof[ff.test_idx] = pred
+        w_test = None if ff.sample_weight is None else ff.sample_weight[ff.test_idx]
+        fold_losses[ff.k] = _fold_loss(ff.kind, ff.y[ff.test_idx], pred, w_test)
 
     return CrossFitResult(
         oof_predictions=oof,
diff --git a/diff_diff/_dr_scores.py b/diff_diff/_dr_scores.py
index a9324baa3..179e4b446 100644
--- a/diff_diff/_dr_scores.py
+++ b/diff_diff/_dr_scores.py
@@ -1,6 +1,6 @@
 """Shared doubly-robust DiD scores (private DML infrastructure).
 
-Three distinct score families live here — the repo's methodology review
+Four distinct score families live here — the repo's methodology review
 (``docs/methodology/papers/chang-2020-review.md``) pins that they are NOT
 interchangeable:
 
@@ -25,6 +25,19 @@
   different from Sant'Anna-Zhao/DoubleML's four treatment-by-period outcome
   regressions, so ``doubleml.DoubleMLDIDCSBinary`` is a characterization
   anchor, not a parity oracle.
+- :func:`ccps_panel_score` / :func:`ccps_panel_score_augmented` — the
+  Caetano, Callaway, Payne & Sant'Anna (2026) Neyman-orthogonal bad-control
+  score (their Equation 10 / sample analog Equation 11; paper review at
+  ``docs/methodology/papers/caetano-2026-review.md``) with FOUR cross-fitted
+  nuisances: the outcome regression ``m_0`` on ``(X_t, X_base, Z)``, its
+  nested projection ``nu_0`` on ``(X_base, W, Z)``, the propensity ``p`` on
+  ``(X_base, W, Z)``, and the nested odds projection ``omega_0`` on
+  ``(X_t, X_base, Z)``. Every untreated term is normalized by the treated
+  share ``1/p_hat`` (not ``1/(1-p_hat)``); with ``nu_hat = m_hat`` and
+  ``omega_hat = ps/(1-ps)`` it collapses algebraically to
+  :func:`chang_panel_score`, and its augmented step IS
+  :func:`chang_panel_score_augmented` (``summand - theta - (theta/p_hat)(D -
+  p_hat) == summand - D theta / p_hat``).
 
 References
 ----------
@@ -33,6 +46,9 @@
 
 Chang, N.-C. (2020). Double/debiased machine learning for
 difference-in-differences models. The Econometrics Journal, 23(2), 177-191.
+
+Caetano, C., Callaway, B., Payne, S., & Sant'Anna, H. (2026).
+Difference-in-differences with "bad controls". arXiv:2608.03881.
 """
 
 from typing import Optional, Tuple
@@ -45,6 +61,8 @@
     "drdid_panel_inf_func",
     "chang_panel_score",
     "chang_panel_score_augmented",
+    "ccps_panel_score",
+    "ccps_panel_score_augmented",
     "chang_rcs_score",
     "chang_rcs_lambda_slope",
     "chang_rcs_score_augmented",
@@ -258,6 +276,126 @@ def chang_panel_score_augmented(
     return summand - D * theta / p_hat
 
 
+def _validate_ccps_inputs(
+    dY: np.ndarray,
+    D: np.ndarray,
+    m_hat: np.ndarray,
+    nu_hat: np.ndarray,
+    ps: np.ndarray,
+    omega_hat: np.ndarray,
+    p_hat: float,
+    context: str,
+) -> Tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
+    """Shared validation for the CCPS (2026) bad-control score functions."""
+    arrays = {
+        "dY": np.asarray(dY, dtype=np.float64),
+        "D": np.asarray(D, dtype=np.float64),
+        "m_hat": np.asarray(m_hat, dtype=np.float64),
+        "nu_hat": np.asarray(nu_hat, dtype=np.float64),
+        "ps": np.asarray(ps, dtype=np.float64),
+        "omega_hat": np.asarray(omega_hat, dtype=np.float64),
+    }
+    for name, arr in arrays.items():
+        if arr.ndim != 1:
+            raise ValueError(f"{context}: {name} must be 1-dimensional, got ndim={arr.ndim}")
+    n = arrays["dY"].shape[0]
+    if n == 0:
+        raise ValueError(f"{context}: inputs are empty (n=0); the score is undefined")
+    for name, arr in arrays.items():
+        if arr.shape[0] != n:
+            raise ValueError(
+                f"{context}: {name} has length {arr.shape[0]}, expected {n} (length of dY)"
+            )
+        if not np.all(np.isfinite(arr)):
+            raise ValueError(f"{context}: {name} contains non-finite values")
+    D_arr = arrays["D"]
+    if not np.all((D_arr == 0.0) | (D_arr == 1.0)):
+        raise ValueError(f"{context}: D must be strictly binary 0/1")
+    if not np.isfinite(p_hat) or not (0.0 < p_hat < 1.0):
+        raise ValueError(
+            f"{context}: p_hat must satisfy 0 < p_hat < 1 strictly, got {p_hat!r} "
+            "(p_hat = 1 means no comparison population; the estimand is unidentified)"
+        )
+    ps_arr = arrays["ps"]
+    if np.any(ps_arr < 0.0) or np.any(ps_arr >= 1.0):
+        raise ValueError(
+            f"{context}: ps must lie in [0, 1) strictly; clip/trim propensity "
+            "scores before calling (values >= 1 would divide by zero)"
+        )
+    if np.any(arrays["omega_hat"] < 0.0):
+        raise ValueError(
+            f"{context}: omega_hat must be non-negative (it estimates a conditional "
+            "expectation of the odds p/(1-p)); clip the nested odds regression "
+            "before calling"
+        )
+    return (
+        arrays["dY"],
+        D_arr,
+        arrays["m_hat"],
+        arrays["nu_hat"],
+        ps_arr,
+        arrays["omega_hat"],
+    )
+
+
+def ccps_panel_score(
+    dY: np.ndarray,
+    D: np.ndarray,
+    m_hat: np.ndarray,
+    nu_hat: np.ndarray,
+    ps: np.ndarray,
+    omega_hat: np.ndarray,
+    p_hat: float,
+) -> np.ndarray:
+    """CCPS (2026) bad-control per-unit UNCENTERED score summand (their Equation 10).
+
+    Returns::
+
+        summand_i = (D_i/p_hat) dY_i - (D_i/p_hat) nu_hat_i
+                    - ((1-D_i)/p_hat) (m_hat_i - nu_hat_i) ps_i/(1-ps_i)
+                    - ((1-D_i)/p_hat) (dY_i - m_hat_i) omega_hat_i
+
+    whose sample mean is the ATT (Equation 11's ``ATT_dr``). The four
+    nuisances are cross-fitted plug-ins: ``m_hat`` = control outcome-change
+    regression on ``(X_t, X_base, Z)``; ``nu_hat`` = its nested control
+    projection on ``(X_base, W, Z)``; ``ps`` = propensity on ``(X_base, W, Z)``
+    (trimmed by the CALLER's policy, strictly below 1); ``omega_hat`` = nested
+    control projection of the odds ``p/(1-p)`` on ``(X_t, X_base, Z)``
+    (non-negative; bounded by the caller's policy). Every untreated term is
+    normalized by the treated share ``1/p_hat`` (Lemma S2 change of measure),
+    never by ``1/(1-p_hat)``. Reduction: with ``nu_hat = m_hat`` and
+    ``omega_hat = ps/(1-ps)`` this equals :func:`chang_panel_score` exactly.
+    """
+    dY, D, m_hat, nu_hat, ps, omega_hat = _validate_ccps_inputs(
+        dY, D, m_hat, nu_hat, ps, omega_hat, p_hat, "ccps_panel_score"
+    )
+    treated = D / p_hat
+    control = (1.0 - D) / p_hat
+    return (
+        treated * dY
+        - treated * nu_hat
+        - control * (m_hat - nu_hat) * ps / (1.0 - ps)
+        - control * (dY - m_hat) * omega_hat
+    )
+
+
+def ccps_panel_score_augmented(
+    summand: np.ndarray,
+    D: np.ndarray,
+    theta: float,
+    p_hat: float,
+) -> np.ndarray:
+    """CCPS (2026) Algorithm 1 step 4 influence-function summand.
+
+    The paper writes ``phi_i = phi_{1,i} - ATT - (ATT/pi)(D_i - pi)``; since
+    ``-theta - (theta/p_hat)(D_i - p_hat) == -D_i theta / p_hat``, this is
+    exactly :func:`chang_panel_score_augmented`, which is called verbatim (the
+    centering identity is what makes the two augmented steps interchangeable;
+    both are mean-zero and ``SE = sqrt(mean(psi_bar**2) / n)``).
+    """
+    return chang_panel_score_augmented(summand, D, theta, p_hat)
+
+
 def _validate_chang_rcs_inputs(
     y: np.ndarray,
     D: np.ndarray,
diff --git a/diff_diff/_reporting_helpers.py b/diff_diff/_reporting_helpers.py
index e0f102d1c..9bdc69b84 100644
--- a/diff_diff/_reporting_helpers.py
+++ b/diff_diff/_reporting_helpers.py
@@ -192,6 +192,22 @@ def describe_target_parameter(results: Any) -> Dict[str, Any]:
                 "the aggregation weight influence function; REGISTRY DMLDiD "
                 "complete-case Note)"
             )
+        _bad_control = getattr(results, "bad_control", None)
+        if _bad_control is not None:
+            _w = tuple(getattr(results, "bad_control_covariates", None) or ())
+            _w_clause = f" and the bad-control covariates W = {list(_w)!r}" if _w else ""
+            score_clause = (
+                "estimated by Caetano, Callaway, Payne & Sant'Anna (2026)'s "
+                "cross-fitted Neyman-orthogonal bad-control score (Eq. 10) "
+                f"with the pre-treatment bad control {_bad_control!r}"
+                f"{_w_clause} in the propensity set"
+            )
+            reference = "Caetano et al. (2026); Chang (2020); REGISTRY.md Sec. DMLDiD"
+        else:
+            score_clause = (
+                "estimated by Chang (2020)'s cross-fitted Neyman-orthogonal " "score (DML2)"
+            )
+            reference = "Chang (2020); REGISTRY.md Sec. DMLDiD"
         return {
             "name": f"overall ATT ({weight_name} average of ATT(g,t))",
             "definition": (
@@ -200,14 +216,14 @@ def describe_target_parameter(results: Any) -> Dict[str, Any]:
                 "cells (``t >= g - anticipation``; ``t >= g`` when "
                 "anticipation=0) — " + weight_clause + " — "
                 "where each cell is a conditional-on-covariates ATT "
-                "estimated by Chang (2020)'s cross-fitted Neyman-orthogonal "
-                "score (DML2). ``overall_att`` is the simple-aggregation "
+                + score_clause
+                + ". ``overall_att`` is the simple-aggregation "
                 "headline; event-study and group tables are produced "
                 "post-fit via ``results.aggregate('event_study'/'group')``."
             ),
             "aggregation": "simple",
             "headline_attribute": "overall_att",
-            "reference": "Chang (2020); REGISTRY.md Sec. DMLDiD",
+            "reference": reference,
         }
 
     if name == "SunAbrahamResults":
diff --git a/diff_diff/business_report.py b/diff_diff/business_report.py
index c08e4f6c8..845ea4285 100644
--- a/diff_diff/business_report.py
+++ b/diff_diff/business_report.py
@@ -560,7 +560,7 @@ def _build_schema(self) -> Dict[str, Any]:
         )
         next_steps = (dr_schema or {}).get("next_steps", [])
         caveats = _build_caveats(self._results, headline, sample, dr_schema)
-        references = _references_for(estimator_name)
+        references = _references_for(estimator_name, self._results)
 
         if diagnostics_results is None:
             diagnostics_block: Dict[str, Any] = {
@@ -1604,6 +1604,37 @@ def _describe_assumption(estimator_name: str, results: Any = None) -> Dict[str,
                 "learners to satisfy Chang (2020)'s rate conditions "
                 "(Assumption 3.1(f))." + _survey_caveat
             )
+        if getattr(results, "bad_control", None) is not None:
+            # CCPS (2026) bad-control lane: the identifying restriction is
+            # NOT plain conditional parallel trends on the supplied
+            # covariates - it conditions on the bad control's untreated
+            # potential path as well (MP-4, reduced by MP-7), whose
+            # untreated evolution is identified by covariate
+            # unconfoundedness (Assumption 6 / MP-5).
+            return {
+                "parallel_trends_variant": "conditional_on_covariates",
+                "no_anticipation": True,
+                "description": (
+                    "Identification relies on CONDITIONAL parallel trends "
+                    "(Caetano, Callaway, Payne & Sant'Anna 2026, MP-4): untreated "
+                    "potential-outcome trends are parallel only after "
+                    "conditioning on the supplied covariates AND the untreated "
+                    "potential path of the bad control (reduced to its "
+                    "base-period and current values by MP-7), per treatment "
+                    "cohort and period (group-time ATT), plus no anticipation "
+                    "for the outcome and the bad control (MP-2). The bad "
+                    "control's untreated evolution is identified by covariate "
+                    "unconfoundedness given its pre-treatment value, the "
+                    "bad-control covariates W, and the supplied covariates "
+                    "(Assumption 6 / MP-5) with overlap (MP-6). Panel data only. "
+                    "The Neyman-orthogonal score makes the estimate first-order "
+                    "insensitive to machine-learning regularization bias, with "
+                    "cross-fitting (DML2) removing own-observation overfitting; "
+                    "valid normal inference additionally requires the four "
+                    "nuisance learners to satisfy the paper's product-rate "
+                    "conditions (Assumption 9)."
+                ),
+            }
         return {
             "parallel_trends_variant": "conditional_on_covariates",
             "no_anticipation": True,
@@ -1952,8 +1983,13 @@ def _pt_method_stat_label(method: Optional[str]) -> Optional[str]:
     return "joint p"
 
 
-def _references_for(estimator_name: str) -> List[Dict[str, str]]:
-    """Map the estimator to the appropriate citation references."""
+def _references_for(estimator_name: str, results: Any = None) -> List[Dict[str, str]]:
+    """Map the estimator to the appropriate citation references.
+
+    ``results`` (optional) lets estimator-specific lanes add a second
+    citation entry - a DMLDiD bad-control fit cites Caetano et al. (2026)
+    alongside Chang (2020).
+    """
     base = [
         {
             "role": "sensitivity",
@@ -2033,7 +2069,18 @@ def _references_for(estimator_name: str) -> List[Dict[str, str]]:
         },
     }
     if estimator_name in estimator_refs:
-        return [estimator_refs[estimator_name]] + base
+        refs = [estimator_refs[estimator_name]]
+        if estimator_name == "DMLDiDResults" and getattr(results, "bad_control", None) is not None:
+            refs.append(
+                {
+                    "role": "estimator",
+                    "citation": (
+                        "Caetano, C., Callaway, B., Payne, S., & Sant'Anna, H. (2026). "
+                        'Difference-in-differences with "bad controls". arXiv:2608.03881.'
+                    ),
+                }
+            )
+        return refs + base
     return base
 
 
diff --git a/diff_diff/dml_did.py b/diff_diff/dml_did.py
index aa0e15a2f..16e6f4bdf 100644
--- a/diff_diff/dml_did.py
+++ b/diff_diff/dml_did.py
@@ -41,9 +41,19 @@
 import pandas as pd
 
 from diff_diff._base import BaseEstimator
-from diff_diff._crossfit import DegenerateFoldError, assign_folds, cross_fit_predict
+from diff_diff._crossfit import (
+    DegenerateFoldError,
+    _fit_subset,
+    _fold_loss,
+    _predict_subset,
+    assign_folds,
+    cross_fit_predict,
+    iter_fold_fits,
+)
 from diff_diff._dr_scores import (
     _chang_rcs_score_augmented_with_slope,
+    ccps_panel_score,
+    ccps_panel_score_augmented,
     chang_panel_score,
     chang_panel_score_augmented,
     chang_rcs_score,
@@ -233,6 +243,30 @@ def _is_native_learner_spec(spec: Any) -> bool:
     )
 
 
+def _is_parametric_learner_spec(spec: Any) -> bool:
+    """True for the PARAMETRIC built-in learners only: ``"linear"`` / ``"logit"``.
+
+    The CCPS (2026) nested second stage may use in-sample fold-k first-stage
+    predictions as its pseudo-outcomes ONLY when the first stage is the
+    paper's own linear/logit working model (Assumption 8's plug-in identity:
+    OLS of ``R'beta`` on ``S`` is exactly ``beta_1 * OLS(xt ~ S) + beta_2 xb +
+    beta_3 Z``). ``ridge``, ``sieve``, native SUBCLASSES and every foreign
+    learner take the split-half branch (footnote 9). The string check runs
+    FIRST so a foreign object's ``__eq__`` is never invoked; objects need the
+    exact native type plus primitive config (the ``_is_native_learner_spec``
+    trust boundary).
+    """
+    from diff_diff._learners import LinearLearner, LogitLearner
+
+    if isinstance(spec, str):
+        return spec in ("linear", "logit")
+    if type(spec) not in (LinearLearner, LogitLearner):
+        return False
+    return all(
+        _config_value_is_primitive(getattr(spec, attr, None)) for attr in type(spec)._CONFIG_ATTRS
+    )
+
+
 def _learner_spec_label(spec: Any) -> str:
     """Results-facing label for a learner spec (repr-of-spec contract).
 
@@ -475,14 +509,59 @@ def _validate_and_prepare(
         time: str,
         first_treat: str,
         covariates: Optional[Iterable[str]],
-    ) -> Tuple[pd.DataFrame, List[str]]:
-        """Validate inputs; return the numeric working frame + covariate list."""
+        bad_control: Optional[str] = None,
+        bad_control_covariates: Optional[Iterable[str]] = None,
+        has_survey_design: bool = False,
+    ) -> Tuple[pd.DataFrame, List[str], Optional[List[str]]]:
+        """Validate inputs; return the numeric working frame, covariate list,
+        and the materialized bad-control covariate list (``None`` when no bad
+        control is declared)."""
         # FULL config re-validation FIRST (mutation defense; anticipation
         # leads inside _revalidate_config — the ordering is load-bearing for
         # the anticipation-policy suite, which fits a bare DataFrame and
         # requires the config error to precede column checks).
         self._revalidate_config()
 
+        # Bad-control lane (CCPS 2026): unsupported-combination gates right
+        # after the config validation (config errors first), then the
+        # argument-NAME checks below once ``covariates`` is materialized.
+        if bad_control is None and bad_control_covariates is not None:
+            raise ValueError(
+                "bad_control_covariates requires bad_control: the W covariates "
+                "model the bad control's untreated evolution (Caetano, Callaway, "
+                "Payne & Sant'Anna 2026, Assumption 6) and have no role without "
+                "a bad control."
+            )
+        if bad_control is not None:
+            if not self.panel:
+                raise NotImplementedError(
+                    "bad_control is not available with panel=False: the bad-control "
+                    "identification strategies need the same unit's bad control at "
+                    "the base period and at t (Caetano et al. 2026, Remark 1: not "
+                    "available with repeated cross sections 'to a large extent')."
+                )
+            if has_survey_design:
+                raise NotImplementedError(
+                    "bad_control with survey_design= is not supported yet: the "
+                    "nested second-stage nuisances under design weights and "
+                    "replicate variances are unvalidated. cluster= is supported."
+                )
+            if self.anticipation != 0:
+                raise NotImplementedError(
+                    "bad_control requires anticipation=0: the paper's no-anticipation "
+                    "assumption (MP-2) covers the bad control as well as the outcome "
+                    "and the limited-anticipation relaxation is not developed "
+                    "(DEFERRED.md)."
+                )
+            if self.base_period != "varying":
+                raise NotImplementedError(
+                    "bad_control requires base_period='varying': under a universal "
+                    "base a pre-period cell would read the bad control at t BEFORE "
+                    "its base-period value, inverting the X_t / X_{t-1} ordering "
+                    "that covariate unconfoundedness (MP-5) conditions on "
+                    "(DEFERRED.md)."
+                )
+
         # covariates are REQUIRED (Chang's estimator exists for the
         # high-dimensional-X setting).
         if isinstance(covariates, (str, bytes)):
@@ -526,7 +605,18 @@ def _validate_and_prepare(
                 )
             seen[col] = role
 
+        # Bad-control NAME-level checks: names only, never ``data`` (so a
+        # malformed name reaches a targeted ValueError, not pandas).
+        w_names: Optional[List[str]] = None
+        if bad_control is not None:
+            w_names = self._validate_bad_control_names(
+                bad_control, bad_control_covariates, covariates, roles
+            )
+
         required_cols = [outcome, unit, time, first_treat, *covariates]
+        if bad_control is not None:
+            required_cols.append(bad_control)
+            required_cols.extend(w for w in (w_names or []) if w != outcome)
         missing = [c for c in required_cols if c not in data.columns]
         if missing:
             raise ValueError(f"Missing columns: {missing}")
@@ -619,7 +709,11 @@ def _validate_and_prepare(
         # (load-bearing: pd.to_numeric preserves int64/bool, where a bool
         # outcome TypeErrors in the subtraction and int64 overflow WRAPS to a
         # finite wrong value invisible to errstate/isfinite).
-        for col in [outcome, *covariates]:
+        numeric_cols = [outcome, *covariates]
+        if bad_control is not None:
+            numeric_cols.append(bad_control)
+            numeric_cols.extend(w for w in (w_names or []) if w != outcome)
+        for col in numeric_cols:
             try:
                 converted = pd.to_numeric(df[col])
             except (ValueError, TypeError) as exc:
@@ -663,7 +757,7 @@ def _validate_and_prepare(
                 UserWarning,
                 stacklevel=3,
             )
-            return df, covariates
+            return df, covariates, w_names
 
         # Duplicate (unit, time) rows.
         dup_mask = df.duplicated(subset=[unit, time], keep=False)
@@ -685,7 +779,76 @@ def _validate_and_prepare(
 
         self._check_control_group_availability(df, unit, first_treat)
 
-        return df, covariates
+        return df, covariates, w_names
+
+    @staticmethod
+    def _validate_bad_control_names(
+        bad_control: Any,
+        bad_control_covariates: Optional[Iterable[str]],
+        covariates: List[str],
+        roles: Dict[str, str],
+    ) -> List[str]:
+        """Name-level validation of the bad-control arguments (no data access).
+
+        Returns the materialized ``W`` list (``[]`` for ``None``). The outcome
+        name is allowed inside ``W`` and means the outcome at the cell's base
+        period (Remark 5's ``W = Y_{g-1}``).
+        """
+        if not isinstance(bad_control, str):
+            raise ValueError(
+                f"bad_control must be a single column name (str), got {bad_control!r}; "
+                "the paper's notation and the R reference implementation carry ONE "
+                "bad control."
+            )
+        if bad_control in roles.values():
+            role = next(r for r, c in roles.items() if c == bad_control)
+            raise ValueError(f"bad_control={bad_control!r} collides with {role}={bad_control!r}")
+        if bad_control in covariates:
+            raise ValueError(
+                f"bad_control={bad_control!r} also appears in covariates. A bad control "
+                "must not be conditioned on at period t (the 'include the bad "
+                "control' bias, Caetano et al. 2026 Section 3.1). Pass it ONLY as "
+                "bad_control (covariate-unconfoundedness lane), or - for the "
+                "pre-treatment-conditioning lane of Theorem 1 / Proposition 3 - "
+                "drop bad_control and pass it in covariates alone, where "
+                "DMLDiD/CallawaySantAnna read it at the cell's base period."
+            )
+        if bad_control_covariates is None:
+            return []
+        if isinstance(bad_control_covariates, (str, bytes)):
+            raise ValueError(
+                "bad_control_covariates must be a sequence of column names, not a "
+                f"bare string ({bad_control_covariates!r}); wrap it in a list."
+            )
+        # Materialize EXACTLY ONCE (one-shot iterables; same rule as covariates).
+        w_list = list(bad_control_covariates)
+        for w in w_list:
+            if not isinstance(w, str):
+                raise ValueError(
+                    f"bad_control_covariates entries must be column names (str), got {w!r}"
+                )
+        dupes = sorted({w for w in w_list if w_list.count(w) > 1})
+        if dupes:
+            raise ValueError(f"bad_control_covariates contains duplicate names: {dupes}")
+        for w in w_list:
+            if w in (roles["unit"], roles["time"], roles["first_treat"]):
+                raise ValueError(
+                    f"bad_control_covariates entry {w!r} names a role column "
+                    "(unit/time/first_treat); only the outcome name is allowed there "
+                    "(meaning the outcome at the cell's base period)."
+                )
+            if w == bad_control:
+                raise ValueError(
+                    f"bad_control_covariates entry {w!r} is the bad control itself; "
+                    "its pre-treatment value is already conditioned on."
+                )
+            if w in covariates:
+                raise ValueError(
+                    f"bad_control_covariates entry {w!r} also appears in covariates; a "
+                    "column plays one role (Z enters parallel trends, W enters only "
+                    "the bad control's unconfoundedness model)."
+                )
+        return w_list
 
     def _check_control_group_availability(
         self, df: pd.DataFrame, unit: str, first_treat: str
@@ -932,6 +1095,8 @@ def _precompute(
         first_treat: str,
         covariates: List[str],
         resolved_survey: Optional["ResolvedSurveyDesign"] = None,
+        bad_control: Optional[str] = None,
+        bad_control_covariates: Optional[List[str]] = None,
     ) -> Dict[str, Any]:
         # CS groupby form — NOT sorted(unique): sorted() raises a bare
         # TypeError on mixed-type unit labels that CS accepts.
@@ -982,6 +1147,34 @@ def _precompute(
             "canonical_size": n_units,
             "n_units": n_units,
         }
+        if bad_control is not None:
+            # CCPS (2026) lane: the bad control at EVERY period (read at t and
+            # at the base period per cell) and the W block at every period
+            # (read at the base period), in the user's listed order with the
+            # outcome name resolving to the outcome itself at that position.
+            w_names = list(bad_control_covariates or [])
+            bc_wide = df.pivot(index=unit, columns=time, values=bad_control).reindex(all_units)
+            w_wide = {
+                c: (
+                    outcome_wide
+                    if c == outcome
+                    else df.pivot(index=unit, columns=time, values=c).reindex(all_units)
+                )
+                for c in w_names
+            }
+            out["bad_control_by_period"] = {
+                t: bc_wide[t].to_numpy(dtype=np.float64) for t in time_periods
+            }
+            out["w_by_period"] = {
+                t: (
+                    np.column_stack([w_wide[c][t].to_numpy(dtype=np.float64) for c in w_names])
+                    if w_names
+                    else np.empty((n_units, 0))
+                )
+                for t in time_periods
+            }
+            out["bad_control"] = bad_control
+            out["bad_control_covariates"] = tuple(w_names)
         if resolved_survey is not None:
             from diff_diff.survey import collapse_survey_to_unit_level
 
@@ -1110,6 +1303,10 @@ def _compute_dml_gt(
         dropped_units_out: Optional[set] = None,
     ) -> Tuple[Dict[str, Any], Optional[Dict[str, Any]], Optional[Dict[str, Any]]]:
         """One (g, t) cell. Returns (gt_entry, if_entry|None, diagnostics|None)."""
+        if precomputed.get("bad_control") is not None:
+            return self._compute_ccps_gt(
+                precomputed, g, t, g_idx, t_idx, root_entropy, dropped_units_out
+            )
         observed_sorted = precomputed["observed_sorted"]
         period_to_col = precomputed["period_to_col"]
         base = _select_base_period_impl(self.base_period, self.anticipation, g, t, observed_sorted)
@@ -1341,40 +1538,47 @@ def _compute_dml_gt(
                 diagnostics,
             )
 
-        # Payload BEFORE the SE/inference block: the design-based per-cell SE
-        # consumes it. No-survey payload: per-unit entries psi_bar_i /
-        # n_cell, so sqrt(sum(if^2)) IS the cell SE (the CS
-        # influence_func_info contract). Weighted payload: w_i * psi_bar_i /
-        # sum(w) — the Hajek analogue (reduces to psi_bar/n at w == 1).
-        n_units = precomputed["n_units"]
-        inf_full = np.zeros(n_units)
-        if w_cell is not None:
-            inf_full[cell_idx] = w_cell * psi_bar / float(np.sum(w_cell))
-        else:
-            inf_full[cell_idx] = psi_bar / n_cell
-        treated_idx = np.flatnonzero(treated_valid).astype(np.int64)
-        # Nonzero-derivation unchanged under weighting: a zero-weight control
-        # dropping from the payload is inert — the per-cell CR1 helper
-        # rebuilds the full-length psi vector over the complete design.
-        control_idx = np.flatnonzero((inf_full != 0.0) & ~treated_valid).astype(np.int64)
-        if_entry = {
-            "treated_idx": treated_idx,
-            "control_idx": control_idx,
-            "treated_inf": inf_full[treated_idx],
-            "control_inf": inf_full[control_idx],
-        }
+        return self._finish_panel_cell(
+            precomputed=precomputed,
+            cell_idx=cell_idx,
+            treated_valid=treated_valid,
+            D_cell=D_cell,
+            w_cell=w_cell,
+            psi_bar=psi_bar,
+            theta=theta,
+            n_treated=n_treated,
+            n_control=n_control,
+            resolved_survey_unit=resolved_survey_unit,
+            df_survey=df_survey,
+            diagnostics=diagnostics,
+        )
 
-        # Per-cell SE. Replicate designs use IF-reweighting on the Hajek
-        # payload (compute_replicate_if_variance; the same psi the aggregate
-        # _se_from_psi call consumes) — a zero or non-finite replicate
-        # variance is degenerate and fails closed to NaN (stricter than the
-        # shared aggregate clamp; REGISTRY DMLDiD Note). PSU designs
-        # (declared OR bare cluster=) route through the CS per-cell CR1
-        # helper (3-valued contract: float = use it, NaN = unidentified
-        # clustered variance and MUST propagate, None = malformed -> fall
-        # back). Non-PSU survey designs use the weighted sqrt-sum (CS
-        # mirror: the full design enters aggregate SEs only); the no-survey
-        # branch is verbatim.
+    def _cell_se_from_payload(
+        self,
+        *,
+        inf_full: np.ndarray,
+        if_entry: Dict[str, Any],
+        psi_bar: np.ndarray,
+        n_cell: int,
+        w_cell: Optional[np.ndarray],
+        resolved_survey_unit: Any,
+        df_survey: Optional[float],
+    ) -> Tuple[float, Optional[float]]:
+        """Per-cell SE from a scattered influence payload; returns ``(se, df)``.
+
+        Replicate designs use IF-reweighting on the Hajek payload
+        (compute_replicate_if_variance; the same psi the aggregate
+        _se_from_psi call consumes) — a zero or non-finite replicate variance
+        is degenerate and fails closed to NaN (stricter than the shared
+        aggregate clamp; REGISTRY DMLDiD Note). PSU designs (declared OR bare
+        cluster=) route through the CS per-cell CR1 helper (3-valued
+        contract: float = use it, NaN = unidentified clustered variance and
+        MUST propagate, None = malformed -> fall back). Non-PSU survey designs
+        use the weighted sqrt-sum (CS mirror: the full design enters
+        aggregate SEs only); the no-survey branch is verbatim. The returned
+        ``df`` is the CELL-LOCAL replicate-design rebind (never written back
+        to ``precomputed["df_survey"]``, which feeds the aggregation kit).
+        """
         se: float
         with np.errstate(over="ignore", invalid="ignore"):
             if resolved_survey_unit is not None and resolved_survey_unit.uses_replicate_variance:
@@ -1390,10 +1594,7 @@ def _compute_dml_gt(
                 # Per-cell df: min(design df, n_valid - 1) — the dCDH
                 # _effective_df_survey rule, inlined. n_valid is computed
                 # over the WHOLE replicate columns, so it equals R for every
-                # cell in practice (defensive; REGISTRY Note). df_survey is
-                # a CELL-LOCAL binding — never mutate
-                # precomputed["df_survey"], which feeds the post-fit
-                # aggregation kit.
+                # cell in practice (defensive; REGISTRY Note).
                 if df_survey is not None:
                     df_survey = min(int(df_survey), int(n_valid_rep) - 1)
                 else:
@@ -1413,6 +1614,81 @@ def _compute_dml_gt(
                 se = float(np.sqrt(np.sum(inf_full**2)))
             else:
                 se = float(np.sqrt(np.mean(psi_bar**2) / n_cell))
+        return se, df_survey
+
+    def _scatter_if_payload(
+        self,
+        *,
+        n_units: int,
+        cell_idx: np.ndarray,
+        treated_valid: np.ndarray,
+        psi_bar: np.ndarray,
+        w_cell: Optional[np.ndarray],
+    ) -> Tuple[np.ndarray, Dict[str, Any]]:
+        """Scatter a cell's per-unit IF summands into the all-units index space.
+
+        No-survey payload: per-unit entries psi_bar_i / n_cell, so
+        sqrt(sum(if^2)) IS the cell SE (the CS influence_func_info contract).
+        Weighted payload: w_i * psi_bar_i / sum(w) — the Hajek analogue
+        (reduces to psi_bar/n at w == 1). Control members derive from
+        NONZERO-ness: a zero-weight control dropping from the payload is inert
+        (the per-cell CR1 helper rebuilds the full-length psi vector over the
+        complete design).
+        """
+        n_cell = psi_bar.shape[0]
+        inf_full = np.zeros(n_units)
+        if w_cell is not None:
+            inf_full[cell_idx] = w_cell * psi_bar / float(np.sum(w_cell))
+        else:
+            inf_full[cell_idx] = psi_bar / n_cell
+        treated_idx = np.flatnonzero(treated_valid).astype(np.int64)
+        control_idx = np.flatnonzero((inf_full != 0.0) & ~treated_valid).astype(np.int64)
+        if_entry = {
+            "treated_idx": treated_idx,
+            "control_idx": control_idx,
+            "treated_inf": inf_full[treated_idx],
+            "control_inf": inf_full[control_idx],
+        }
+        return inf_full, if_entry
+
+    def _finish_panel_cell(
+        self,
+        *,
+        precomputed: Dict[str, Any],
+        cell_idx: np.ndarray,
+        treated_valid: np.ndarray,
+        D_cell: np.ndarray,
+        w_cell: Optional[np.ndarray],
+        psi_bar: np.ndarray,
+        theta: float,
+        n_treated: int,
+        n_control: int,
+        resolved_survey_unit: Any,
+        df_survey: Optional[float],
+        diagnostics: Dict[str, Any],
+    ) -> Tuple[Dict[str, Any], Optional[Dict[str, Any]], Optional[Dict[str, Any]]]:
+        """Shared panel-cell tail: IF payload, per-cell SE, inference, gt_entry.
+
+        Used verbatim by the Chang lane and the CCPS bad-control lane (the
+        payload schema is what the CS bootstrap/aggregation mixins consume).
+        """
+        n_cell = psi_bar.shape[0]
+        inf_full, if_entry = self._scatter_if_payload(
+            n_units=precomputed["n_units"],
+            cell_idx=cell_idx,
+            treated_valid=treated_valid,
+            psi_bar=psi_bar,
+            w_cell=w_cell,
+        )
+        se, df_survey = self._cell_se_from_payload(
+            inf_full=inf_full,
+            if_entry=if_entry,
+            psi_bar=psi_bar,
+            n_cell=n_cell,
+            w_cell=w_cell,
+            resolved_survey_unit=resolved_survey_unit,
+            df_survey=df_survey,
+        )
         # NOTE: `se` is deliberately OUTSIDE the non_finite_score gate on the
         # design-based branches — a NaN from the CR1 helper (or a degenerate
         # replicate variance) is the unidentified-variance signal and must
@@ -1446,6 +1722,614 @@ def _compute_dml_gt(
             gt_entry["survey_weight_sum"] = float(np.sum(w_cell[D_cell == 1.0]))
         return gt_entry, if_entry, diagnostics
 
+    def _compute_ccps_gt(
+        self,
+        precomputed: Dict[str, Any],
+        g: Any,
+        t: Any,
+        g_idx: int,
+        t_idx: int,
+        root_entropy: int,
+        dropped_units_out: Optional[set] = None,
+    ) -> Tuple[Dict[str, Any], Optional[Dict[str, Any]], Optional[Dict[str, Any]]]:
+        """One (g, t) cell under the CCPS (2026) bad-control score (Eq. 10).
+
+        Same return contract as :meth:`_compute_dml_gt`. Panel lane only,
+        ``anticipation=0`` and ``base_period="varying"`` (fit-time gates), no
+        survey design (``cluster=`` allowed), so ``w_cell`` is always ``None``
+        here and the nuisances are unweighted.
+        """
+        observed_sorted = precomputed["observed_sorted"]
+        period_to_col = precomputed["period_to_col"]
+        base = _select_base_period_impl(self.base_period, self.anticipation, g, t, observed_sorted)
+        if base is None or base not in period_to_col or t not in period_to_col:
+            return _nan_gt_entry(skip_reason="missing_period"), None, None
+
+        unit_cohorts = precomputed["unit_cohorts"]
+        outcome_matrix = precomputed["outcome_matrix"]
+        treated_mask = precomputed["cohort_masks"][g]
+        if self.control_group == "never_treated":
+            control_mask = precomputed["never_treated_mask"]
+        else:  # not_yet_treated (CS semantics: untreated at max(t, base) + k)
+            nyt_threshold = max(t, base) + self.anticipation
+            control_mask = precomputed["never_treated_mask"] | (
+                (unit_cohorts > nyt_threshold) & (unit_cohorts != g)
+            )
+
+        Z_by_period = precomputed["covariate_by_period"]
+        bc_by_period = precomputed["bad_control_by_period"]
+        w_by_period = precomputed["w_by_period"]
+        base_col = period_to_col[base]
+        t_col = period_to_col[t]
+        with np.errstate(over="ignore", invalid="ignore"):
+            y_base = outcome_matrix[:, base_col]
+            y_post = outcome_matrix[:, t_col]
+            dY = y_post - y_base
+            Z_base = Z_by_period[base]
+            xt_all = bc_by_period[t]
+            xb_all = bc_by_period[base]
+            W_base = w_by_period[base]
+            # ONE complete-case policy for both groups: every design column of
+            # R = [xt, xb, Z] and S = [xb, W, Z] must be finite (the score
+            # needs m_hat/omega_hat on every unit, treated included).
+            valid = (
+                np.isfinite(y_base)
+                & np.isfinite(y_post)
+                & np.isfinite(dY)
+                & np.all(np.isfinite(Z_base), axis=1)
+                & np.isfinite(xt_all)
+                & np.isfinite(xb_all)
+                & np.all(np.isfinite(W_base), axis=1)
+            )
+
+        treated_valid = treated_mask & valid
+        control_valid = control_mask & valid
+        if dropped_units_out is not None:
+            dropped_units_out.update(
+                np.flatnonzero((treated_mask | control_mask) & ~valid).tolist()
+            )
+        n_treated = int(np.sum(treated_valid))
+        n_control = int(np.sum(control_valid))
+        if n_treated == 0 or n_control == 0:
+            return (
+                _nan_gt_entry(
+                    n_treated=n_treated,
+                    n_control=n_control,
+                    skip_reason="zero_treated_control",
+                ),
+                None,
+                None,
+            )
+
+        cell_mask = treated_valid | control_valid
+        cell_idx = np.flatnonzero(cell_mask)
+        n_cell = cell_idx.shape[0]
+        D_cell = treated_valid[cell_idx].astype(np.float64)
+        dY_cell = dY[cell_idx]
+        xt = xt_all[cell_idx]
+        xb = xb_all[cell_idx]
+        # Fixed column orders (the numpy oracle and the plug-in identity test
+        # reproduce them): R = [xt, xb, Z]; S = [xb, W (user order), Z].
+        R = np.column_stack([xt, xb, Z_base[cell_idx]])
+        S = np.column_stack([xb, W_base[cell_idx], Z_base[cell_idx]])
+
+        # Survey state: survey_design fails closed on this lane, so
+        # weighted_moments is False and w_cell is None; bare cluster= still
+        # supplies a resolved PSU design for folds and the CR1 SE.
+        use_psu_folds = bool(precomputed.get("use_psu_folds", False))
+        resolved_survey_unit = precomputed.get("resolved_survey_unit")
+        df_survey = precomputed.get("df_survey")
+        w_cell: Optional[np.ndarray] = None
+        p_hat = n_treated / n_cell
+        if min(p_hat, 1.0 - p_hat) < self.pscore_trim:
+            warnings.warn(
+                f"DMLDiD cell (g={g}, t={t}): empirical treated share "
+                f"p_hat={p_hat:.4f} ({n_treated} treated / {n_control} control) is "
+                f"extreme (min(p, 1-p) < pscore_trim={self.pscore_trim}); the CCPS "
+                "score and variance scale with powers of 1/p_hat, so this cell's "
+                "estimate may be unstable.",
+                UserWarning,
+                stacklevel=3,
+            )
+
+        seed_seq = np.random.SeedSequence(entropy=root_entropy, spawn_key=(g_idx, t_idx))
+        rng = np.random.default_rng(seed_seq)
+        diagnostics: Dict[str, Any] = {
+            "propensity": None,
+            "outcome": None,
+            "nu": None,
+            "omega": None,
+            "bad_control_outcome": None,
+            "p_hat": float(p_hat),
+            "n_clipped_ps": None,
+            "n_clipped_omega": None,
+            "nested_stage": None,
+            "fold_seed": {"entropy": int(root_entropy), "spawn_key": [int(g_idx), int(t_idx)]},
+            "psu_folds": use_psu_folds,
+        }
+
+        psu_cell: Optional[np.ndarray] = None
+        try:
+            if use_psu_folds and resolved_survey_unit is not None:
+                psu_cell = np.asarray(resolved_survey_unit.psu)[cell_idx]
+                folds = assign_folds(
+                    n_cell,
+                    int(precomputed.get("effective_n_folds", self.n_folds)),
+                    rng=rng,
+                    cluster_ids=psu_cell,
+                )
+            else:
+                folds = assign_folds(n_cell, self.n_folds, rng=rng, stratify=D_cell)
+        except ValueError as exc:
+            diagnostics["skip_reason"] = "cross_fit_degenerate"
+            diagnostics["error"] = str(exc)
+            return (
+                _nan_gt_entry(
+                    n_treated=n_treated,
+                    n_control=n_control,
+                    skip_reason="cross_fit_degenerate",
+                ),
+                None,
+                diagnostics,
+            )
+
+        context = f"DMLDiD (g={g}, t={t})"
+        try:
+            with np.errstate(over="ignore", invalid="ignore"):
+                m_hat, ps_raw, nu_hat, omega_raw, stage = self._ccps_nuisances(
+                    R, S, dY_cell, D_cell, folds, rng, psu_cell, use_psu_folds, context
+                )
+        except DegenerateFoldError as exc:
+            diagnostics["skip_reason"] = "cross_fit_degenerate"
+            diagnostics["error"] = self._sanitize_learner_error(exc)
+            return (
+                _nan_gt_entry(
+                    n_treated=n_treated,
+                    n_control=n_control,
+                    skip_reason="cross_fit_degenerate",
+                ),
+                None,
+                diagnostics,
+            )
+
+        _check_propensity_diagnostics(ps_raw, self.pscore_trim)
+        ps = np.clip(ps_raw, self.pscore_trim, 1.0 - self.pscore_trim)
+        n_clipped = int(np.sum((ps_raw < self.pscore_trim) | (ps_raw > 1.0 - self.pscore_trim)))
+        omega_cap = (1.0 - self.pscore_trim) / self.pscore_trim
+        omega_hat = np.clip(omega_raw, 0.0, omega_cap)
+        n_clipped_omega = int(np.sum((omega_raw < 0.0) | (omega_raw > omega_cap)))
+        if n_clipped_omega > 0:
+            warnings.warn(
+                f"DMLDiD cell (g={g}, t={t}): {n_clipped_omega} of {n_cell} nested "
+                f"odds-projection predictions (omega_hat) fell outside [0, "
+                f"{omega_cap:.4g}] and were clipped (Assumption S2(iv) boundedness; "
+                "the paper gives no rule - REGISTRY DMLDiD Note).",
+                UserWarning,
+                stacklevel=3,
+            )
+        diagnostics.update(stage)
+        diagnostics["n_clipped_ps"] = n_clipped
+        diagnostics["n_clipped_omega"] = n_clipped_omega
+
+        try:
+            with np.errstate(over="ignore", invalid="ignore"):
+                summand = ccps_panel_score(dY_cell, D_cell, m_hat, nu_hat, ps, omega_hat, p_hat)
+                theta = float(np.mean(summand))
+                psi_bar = ccps_panel_score_augmented(summand, D_cell, theta, p_hat)
+        except ValueError as exc:
+            diagnostics["skip_reason"] = "non_finite_score"
+            diagnostics["error"] = self._sanitize_learner_error(exc)
+            return (
+                _nan_gt_entry(
+                    n_treated=n_treated,
+                    n_control=n_control,
+                    skip_reason="non_finite_score",
+                ),
+                None,
+                diagnostics,
+            )
+        if not (np.isfinite(theta) and np.all(np.isfinite(psi_bar))):
+            diagnostics["skip_reason"] = "non_finite_score"
+            return (
+                _nan_gt_entry(
+                    n_treated=n_treated,
+                    n_control=n_control,
+                    skip_reason="non_finite_score",
+                ),
+                None,
+                diagnostics,
+            )
+
+        gt_entry, if_entry, diagnostics_out = self._finish_panel_cell(
+            precomputed=precomputed,
+            cell_idx=cell_idx,
+            treated_valid=treated_valid,
+            D_cell=D_cell,
+            w_cell=w_cell,
+            psi_bar=psi_bar,
+            theta=theta,
+            n_treated=n_treated,
+            n_control=n_control,
+            resolved_survey_unit=resolved_survey_unit,
+            df_survey=df_survey,
+            diagnostics=diagnostics,
+        )
+        if gt_entry.get("skip_reason") is not None or diagnostics_out is None:
+            return gt_entry, if_entry, diagnostics_out
+
+        # ATT_X(g, t) diagnostic (Remark 6): AIPW ATT with the bad control at t
+        # as the outcome, mu_X = cross-fitted control regression of xt on S,
+        # the same clipped propensity, and its OWN influence payload. It never
+        # affects cell retention: a degenerate mu_X cross-fit or a non-finite
+        # score leaves every ATT_X inference field NaN.
+        att_x = float("nan")
+        se_x = float("nan")
+        df_x = df_survey
+        mu_diag: Optional[Dict[str, Any]] = None
+        try:
+            with np.errstate(over="ignore", invalid="ignore"):
+                mu_res = cross_fit_predict(
+                    make_learner(self.outcome_learner, kind="regressor"),
+                    S,
+                    xt,
+                    folds,
+                    predict_method="predict",
+                    fit_mask=(D_cell == 0.0),
+                    context_label=f"{context} bad-control outcome",
+                )
+            mu_diag = {
+                "fold_losses": [float(v) for v in mu_res.fold_losses],
+                "n_fit_per_fold": [int(v) for v in mu_res.n_fit_per_fold],
+            }
+            mu_x = mu_res.oof_predictions
+            try:
+                with np.errstate(over="ignore", invalid="ignore"):
+                    sx = chang_panel_score(xt, D_cell, mu_x, ps, p_hat)
+                    att_x_val = float(np.mean(sx))
+                    psi_x = chang_panel_score_augmented(sx, D_cell, att_x_val, p_hat)
+            except ValueError:
+                att_x_val = float("nan")
+                psi_x = None
+            if psi_x is not None and np.isfinite(att_x_val) and np.all(np.isfinite(psi_x)):
+                att_x = att_x_val
+                inf_x, if_x = self._scatter_if_payload(
+                    n_units=precomputed["n_units"],
+                    cell_idx=cell_idx,
+                    treated_valid=treated_valid,
+                    psi_bar=psi_x,
+                    w_cell=None,
+                )
+                se_x, df_x = self._cell_se_from_payload(
+                    inf_full=inf_x,
+                    if_entry=if_x,
+                    psi_bar=psi_x,
+                    n_cell=n_cell,
+                    w_cell=None,
+                    resolved_survey_unit=resolved_survey_unit,
+                    df_survey=df_survey,
+                )
+        except DegenerateFoldError as exc:
+            mu_diag = {"error": self._sanitize_learner_error(exc)}
+        t_x, p_x, ci_x = safe_inference(att_x, se_x, alpha=self.alpha, df=df_x)
+        diagnostics_out["bad_control_outcome"] = mu_diag
+        diagnostics_out["att_x"] = {
+            "effect": att_x,
+            "se": se_x,
+            "t_stat": t_x,
+            "p_value": p_x,
+            "conf_int": ci_x,
+            "n_treated": n_treated,
+            "n_control": n_control,
+        }
+        return gt_entry, if_entry, diagnostics_out
+
+    def _ccps_nuisances(
+        self,
+        R: np.ndarray,
+        S: np.ndarray,
+        dY: np.ndarray,
+        D: np.ndarray,
+        folds: Any,
+        rng: np.random.Generator,
+        psu_cell: Optional[np.ndarray],
+        use_psu_folds: bool,
+        context: str,
+    ) -> Tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray, Dict[str, Any]]:
+        """The four cross-fitted CCPS nuisances on one cell's folds.
+
+        First stage per fold k (fit on the training complement I_{-k}):
+        ``m0`` = outcome regression of dY on R among controls; ``p`` =
+        propensity of D on S on all units. Second stage per fold k, fit on
+        TRAINING controls only: ``nu0`` = regression on S of the fold-k m0
+        model's predictions; ``omega0`` = regression on R of the fold-k
+        propensity odds (propensity clipped by ``pscore_trim`` first). The
+        nested TARGETS come from the fold-k first-stage model's predictions on
+        its own training units when BOTH learners are the parametric built-ins
+        (Assumption 8's plug-in), and from a split-half of the training
+        complement otherwise (footnote 9: fit the first stage on half A,
+        targets on half B's controls, nested fit on B; swap; average the two
+        nested models' held-out predictions). The score's m_hat / ps on the
+        held-out fold ALWAYS come from the full-training-complement fits.
+        Returns ``(m_hat, ps_raw, nu_hat, omega_raw, stage_diagnostics)``.
+        """
+        controls = D == 0.0
+        n = D.shape[0]
+        n_folds = folds.n_folds
+        trim = self.pscore_trim
+        prop = make_learner(self.propensity_learner, kind="classifier")
+        outc = make_learner(self.outcome_learner, kind="regressor")
+        parametric = _is_parametric_learner_spec(self.propensity_learner) and (
+            _is_parametric_learner_spec(self.outcome_learner)
+        )
+
+        m_hat = np.empty(n)
+        ps_raw = np.empty(n)
+        nu_hat = np.empty(n)
+        omega_raw = np.empty(n)
+        m_losses = np.empty(n_folds)
+        p_losses = np.empty(n_folds)
+        m_nfit = np.empty(n_folds, dtype=np.int64)
+        p_nfit = np.empty(n_folds, dtype=np.int64)
+        nu_nfit = np.empty(n_folds, dtype=np.int64)
+        om_nfit = np.empty(n_folds, dtype=np.int64)
+        nu_label = f"{context} nu: "
+        om_label = f"{context} omega: "
+
+        gen_m = iter_fold_fits(
+            outc,
+            R,
+            dY,
+            folds,
+            fit_mask=controls,
+            predict_method="predict",
+            context_label=f"{context} outcome",
+        )
+        gen_p = iter_fold_fits(
+            prop,
+            S,
+            D,
+            folds,
+            predict_method="predict_proba",
+            context_label=f"{context} propensity",
+        )
+        for ff_m, ff_p in zip(gen_m, gen_p):
+            k = ff_m.k
+            test = ff_m.test_idx
+            train = ff_m.train_idx
+            m_test = _predict_subset(
+                ff_m.learner,
+                R[test],
+                kind="regressor",
+                k=k,
+                label=ff_m.label,
+                n_fit=ff_m.n_fit,
+                w_fit=None,
+            )
+            p_test = _predict_subset(
+                ff_p.learner,
+                S[test],
+                kind="classifier",
+                k=k,
+                label=ff_p.label,
+                n_fit=ff_p.n_fit,
+                w_fit=None,
+            )
+            m_hat[test] = m_test
+            ps_raw[test] = p_test
+            m_losses[k] = _fold_loss("regressor", dY[test], m_test, None)
+            p_losses[k] = _fold_loss("classifier", D[test], p_test, None)
+            m_nfit[k] = ff_m.n_fit
+            p_nfit[k] = ff_p.n_fit
+
+            if parametric:
+                fit_idx = ff_m.fit_idx  # training controls
+                m_tr = _predict_subset(
+                    ff_m.learner,
+                    R[fit_idx],
+                    kind="regressor",
+                    k=k,
+                    label=ff_m.label,
+                    n_fit=ff_m.n_fit,
+                    w_fit=None,
+                )
+                p_tr = np.clip(
+                    _predict_subset(
+                        ff_p.learner,
+                        S[fit_idx],
+                        kind="classifier",
+                        k=k,
+                        label=ff_p.label,
+                        n_fit=ff_p.n_fit,
+                        w_fit=None,
+                    ),
+                    trim,
+                    1.0 - trim,
+                )
+                y_nu = np.zeros(n)
+                y_nu[fit_idx] = m_tr
+                nu_learner, n_nu, _ = _fit_subset(
+                    outc,
+                    S,
+                    y_nu,
+                    fit_idx,
+                    n_train=int(train.shape[0]),
+                    kind="regressor",
+                    sample_weight=None,
+                    k=k,
+                    label=nu_label,
+                    warn_stacklevel=3,
+                )
+                nu_hat[test] = _predict_subset(
+                    nu_learner,
+                    S[test],
+                    kind="regressor",
+                    k=k,
+                    label=nu_label,
+                    n_fit=n_nu,
+                    w_fit=None,
+                )
+                y_om = np.zeros(n)
+                y_om[fit_idx] = p_tr / (1.0 - p_tr)
+                om_learner, n_om, _ = _fit_subset(
+                    outc,
+                    R,
+                    y_om,
+                    fit_idx,
+                    n_train=int(train.shape[0]),
+                    kind="regressor",
+                    sample_weight=None,
+                    k=k,
+                    label=om_label,
+                    warn_stacklevel=3,
+                )
+                omega_raw[test] = _predict_subset(
+                    om_learner,
+                    R[test],
+                    kind="regressor",
+                    k=k,
+                    label=om_label,
+                    n_fit=n_om,
+                    w_fit=None,
+                )
+                nu_nfit[k] = n_nu
+                om_nfit[k] = n_om
+                continue
+
+            # Split-half branch: ONE draw per outer fold, ascending k, on the
+            # shared cell rng, using the outer folds' own mechanism.
+            try:
+                if use_psu_folds and psu_cell is not None:
+                    halves = assign_folds(
+                        int(train.shape[0]), 2, rng=rng, cluster_ids=psu_cell[train]
+                    )
+                else:
+                    halves = assign_folds(int(train.shape[0]), 2, rng=rng, stratify=D[train])
+            except ValueError as exc:
+                raise DegenerateFoldError(f"{context} split-half fold {k}: {exc}") from exc
+            nu_pred = np.zeros(test.shape[0])
+            om_pred = np.zeros(test.shape[0])
+            n_nu_total = 0
+            n_om_total = 0
+            for h in (0, 1):
+                a_idx = train[halves.fold_ids == h]
+                b_idx = train[halves.fold_ids != h]
+                a_ctrl = a_idx[controls[a_idx]]
+                b_ctrl = b_idx[controls[b_idx]]
+                m_a, n_ma, _ = _fit_subset(
+                    outc,
+                    R,
+                    dY,
+                    a_ctrl,
+                    n_train=int(a_idx.shape[0]),
+                    kind="regressor",
+                    sample_weight=None,
+                    k=k,
+                    label=f"{context} split-half m: ",
+                    warn_stacklevel=3,
+                )
+                p_a, n_pa, _ = _fit_subset(
+                    prop,
+                    S,
+                    D,
+                    a_idx,
+                    n_train=int(a_idx.shape[0]),
+                    kind="classifier",
+                    sample_weight=None,
+                    k=k,
+                    label=f"{context} split-half p: ",
+                    warn_stacklevel=3,
+                )
+                m_b = _predict_subset(
+                    m_a,
+                    R[b_ctrl],
+                    kind="regressor",
+                    k=k,
+                    label=f"{context} split-half m: ",
+                    n_fit=n_ma,
+                    w_fit=None,
+                )
+                p_b = np.clip(
+                    _predict_subset(
+                        p_a,
+                        S[b_ctrl],
+                        kind="classifier",
+                        k=k,
+                        label=f"{context} split-half p: ",
+                        n_fit=n_pa,
+                        w_fit=None,
+                    ),
+                    trim,
+                    1.0 - trim,
+                )
+                y_nu = np.zeros(n)
+                y_nu[b_ctrl] = m_b
+                nu_h, n_nu_h, _ = _fit_subset(
+                    outc,
+                    S,
+                    y_nu,
+                    b_ctrl,
+                    n_train=int(b_idx.shape[0]),
+                    kind="regressor",
+                    sample_weight=None,
+                    k=k,
+                    label=nu_label,
+                    warn_stacklevel=3,
+                )
+                y_om = np.zeros(n)
+                y_om[b_ctrl] = p_b / (1.0 - p_b)
+                om_h, n_om_h, _ = _fit_subset(
+                    outc,
+                    R,
+                    y_om,
+                    b_ctrl,
+                    n_train=int(b_idx.shape[0]),
+                    kind="regressor",
+                    sample_weight=None,
+                    k=k,
+                    label=om_label,
+                    warn_stacklevel=3,
+                )
+                nu_pred += 0.5 * _predict_subset(
+                    nu_h,
+                    S[test],
+                    kind="regressor",
+                    k=k,
+                    label=nu_label,
+                    n_fit=n_nu_h,
+                    w_fit=None,
+                )
+                om_pred += 0.5 * _predict_subset(
+                    om_h,
+                    R[test],
+                    kind="regressor",
+                    k=k,
+                    label=om_label,
+                    n_fit=n_om_h,
+                    w_fit=None,
+                )
+                n_nu_total += n_nu_h
+                n_om_total += n_om_h
+            nu_hat[test] = nu_pred
+            omega_raw[test] = om_pred
+            nu_nfit[k] = n_nu_total
+            om_nfit[k] = n_om_total
+
+        nan_losses = [float("nan")] * n_folds
+        stage: Dict[str, Any] = {
+            "propensity": {
+                "fold_losses": [float(v) for v in p_losses],
+                "n_fit_per_fold": [int(v) for v in p_nfit],
+            },
+            "outcome": {
+                "fold_losses": [float(v) for v in m_losses],
+                "n_fit_per_fold": [int(v) for v in m_nfit],
+            },
+            "nu": {"fold_losses": nan_losses, "n_fit_per_fold": [int(v) for v in nu_nfit]},
+            "omega": {"fold_losses": nan_losses, "n_fit_per_fold": [int(v) for v in om_nfit]},
+            "nested_stage": "in_sample" if parametric else "split_half",
+        }
+        return m_hat, ps_raw, nu_hat, omega_raw, stage
+
     def _compute_dml_rcs_gt(
         self,
         precomputed: Dict[str, Any],
@@ -1870,6 +2754,8 @@ def fit(
         first_treat: str,
         covariates: Optional[Iterable[str]] = None,
         survey_design: Optional["SurveyDesign"] = None,
+        bad_control: Optional[str] = None,
+        bad_control_covariates: Optional[Iterable[str]] = None,
     ) -> DMLDiDResults:
         """Estimate staggered ATT(g,t) via per-cell cross-fitted Chang scores.
 
@@ -1894,9 +2780,49 @@ def fit(
             documented library extension of Chang (2020), which assumes
             i.i.d. sampling — Theorem 2's coverage claim does not carry
             over (REGISTRY DMLDiD Notes).
+        bad_control : str, optional
+            Column name of a "bad control" (Caetano, Callaway, Payne &
+            Sant'Anna 2026): a time-varying covariate that treatment can
+            affect. When set, each panel cell runs the paper's
+            Neyman-orthogonal doubly-robust score (Equation 10 / Algorithm 1)
+            instead of the Chang score - parallel trends conditional on the
+            bad control's UNTREATED path, with its untreated evolution
+            identified by covariate unconfoundedness given its base-period
+            value, ``bad_control_covariates`` and ``covariates`` - and stores
+            the per-cell ``ATT_X(g, t)`` pre-test (Remark 6) on
+            ``results.bad_control_diagnostics`` /
+            ``results.bad_control_summary()``. The column is read at the
+            cell's base period AND at ``t`` (both must be finite for a unit
+            to join the cell) and must NOT also appear in ``covariates``
+            (the "include the bad control" bias; to condition only on its
+            pre-treatment value - the paper's Approach 1 - pass it in
+            ``covariates`` alone instead). Requires ``panel=True``,
+            ``anticipation=0``, ``base_period="varying"`` and no
+            ``survey_design`` (each raises ``NotImplementedError``; bare
+            ``cluster=`` is supported). ``covariates`` stays required.
+            Default ``None`` = the plain Chang lane (unchanged).
+        bad_control_covariates : iterable of str, optional
+            Extra pre-treatment covariates ``W`` for the bad control's
+            unconfoundedness model (the propensity design is
+            ``[X_base, W, Z]``; the outcome regressions use
+            ``[X_t, X_base, Z]``). Every entry is read at the cell's base
+            period; the ``outcome`` name is allowed and means the
+            base-period outcome (``Y_{g-1}``, the paper's Remark 5
+            recommendation: ``bad_control_covariates=[outcome]``). Names
+            may not overlap ``covariates`` or ``bad_control``. Default
+            ``None`` = no ``W`` (matches the R ``badcontrols`` default);
+            results store ``()``. Requires ``bad_control``.
         """
-        df, covariates = self._validate_and_prepare(
-            data, outcome, unit, time, first_treat, covariates
+        df, covariates, w_names = self._validate_and_prepare(
+            data,
+            outcome,
+            unit,
+            time,
+            first_treat,
+            covariates,
+            bad_control=bad_control,
+            bad_control_covariates=bad_control_covariates,
+            has_survey_design=survey_design is not None,
         )
 
         # --- Survey/cluster resolution (CS transliteration, staggered.py) ---
@@ -2028,7 +2954,15 @@ def fit(
 
         if self.panel:
             precomputed = self._precompute(
-                df, outcome, unit, time, first_treat, covariates, resolved_survey=resolved_survey
+                df,
+                outcome,
+                unit,
+                time,
+                first_treat,
+                covariates,
+                resolved_survey=resolved_survey,
+                bad_control=bad_control,
+                bad_control_covariates=w_names,
             )
             cell_fn = self._compute_dml_gt
         else:
@@ -2099,6 +3033,7 @@ def fit(
         group_time_effects: Dict[Tuple[Any, Any], Dict[str, Any]] = {}
         influence_func_info: Dict[Tuple[Any, Any], Dict[str, Any]] = {}
         cross_fit_diagnostics: Dict[Tuple[Any, Any], Dict[str, Any]] = {}
+        bad_control_diagnostics: Dict[Tuple[Any, Any], Dict[str, Any]] = {}
         skipped: Dict[str, List[Tuple[Any, Any]]] = {}
         skip_errors: List[str] = []
         dropped_units: set = set()
@@ -2115,6 +3050,12 @@ def fit(
                 if if_entry is not None:
                     influence_func_info[(g, t)] = if_entry
                 if diagnostics is not None:
+                    # MOVE the ATT_X block out of the cross-fit diagnostics so
+                    # the per-cell inference dict is stored (and serialized)
+                    # exactly once; skipped cells carry no ATT_X.
+                    att_x_entry = diagnostics.pop("att_x", None)
+                    if att_x_entry is not None:
+                        bad_control_diagnostics[(g, t)] = att_x_entry
                     cross_fit_diagnostics[(g, t)] = diagnostics
                 reason = gt_entry.get("skip_reason")
                 if reason is not None:
@@ -2166,11 +3107,18 @@ def fit(
                     else "(point weights use per-cell valid counts; aggregation "
                     "cohort masses use full cohorts — see REGISTRY.md)"
                 )
+                _bc_note = (
+                    ", a non-finite bad control at the cell's base period or at t, "
+                    "a non-finite bad-control covariate at the base period"
+                    if bad_control is not None
+                    else ""
+                )
                 warnings.warn(
                     f"{len(dropped_units)} unit(s) were excluded from at least one "
                     "(group, time) cell they would otherwise join, due to a "
                     "missing or NON-FINITE outcome, a non-finite covariate at the "
-                    "cell's base period, or an outcome difference overflowing to "
+                    f"cell's base period{_bc_note}, or an outcome difference "
+                    "overflowing to "
                     f"non-finite. DMLDiD estimates each cell on its complete cases "
                     f"{_weighting_note}.",
                     UserWarning,
@@ -2400,6 +3348,9 @@ def fit(
             cluster_name=cluster_name,
             n_clusters=n_clusters,
             df_inference=df_inference,
+            bad_control=bad_control,
+            bad_control_covariates=(tuple(w_names) if w_names is not None else None),
+            bad_control_diagnostics=(bad_control_diagnostics if bad_control_diagnostics else None),
         )
         results._aggregation_kit = _build_aggregation_kit(
             cast(Any, self),  # duck-typed host contract (alpha/anticipation/cband)
diff --git a/diff_diff/dml_did_results.py b/diff_diff/dml_did_results.py
index cce685a0f..a0c4daa5d 100644
--- a/diff_diff/dml_did_results.py
+++ b/diff_diff/dml_did_results.py
@@ -24,9 +24,10 @@
 """
 
 from dataclasses import dataclass, field
-from typing import Any, Dict, Optional
+from typing import Any, Dict, Optional, Tuple
 
 import numpy as np
+import pandas as pd
 
 from diff_diff.results_base import _json_safe_label
 from diff_diff.staggered_results import CallawaySantAnnaResults
@@ -109,6 +110,22 @@ class DMLDiDResults(CallawaySantAnnaResults):
         from OS randomness.
     n_bootstrap, bootstrap_weights, cband
         Multiplier-bootstrap configuration used at fit.
+    bad_control : str, optional
+        The bad-control column of a Caetano, Callaway, Payne & Sant'Anna
+        (2026) fit (``fit(bad_control=...)``); ``None`` on plain Chang fits.
+    bad_control_covariates : tuple of str, optional
+        The ``W`` columns (user order; the outcome name means the outcome
+        at the cell's base period); ``()`` when a bad control was declared
+        without ``W``; ``None`` on plain fits.
+    bad_control_diagnostics : dict, optional
+        Per-``(g, t)`` ``ATT_X(g, t)`` pre-test (Remark 6): the AIPW
+        mean-effect of treatment on the bad control at ``t`` (pre-period
+        cells assess MP-5 / MP-8 and should be zero; post-period cells check
+        that treatment affects the covariate) with keys
+        ``effect``/``se``/``t_stat``/``p_value``/``conf_int``/``n_treated``/
+        ``n_control``. Analytical SE only (never bootstrapped or
+        aggregated). Retained cells only; ``None`` on plain fits. Read
+        through ``bad_control_summary()``.
     """
 
     propensity_learner: Any = "logit"
@@ -120,6 +137,10 @@ class DMLDiDResults(CallawaySantAnnaResults):
     n_bootstrap: int = 0
     bootstrap_weights: Optional[str] = None
     cband: bool = True
+    # CCPS (2026) bad-control lane (None / None / None on plain fits).
+    bad_control: Optional[str] = None
+    bad_control_covariates: Optional[Tuple[str, ...]] = None
+    bad_control_diagnostics: Optional[Dict[Any, Dict[str, Any]]] = field(default=None, repr=False)
 
     def __repr__(self) -> str:
         folds = f"n_folds={self.n_folds}"
@@ -182,6 +203,12 @@ def summary(self, alpha: Optional[float] = None) -> str:
             # (df=df_survey / df_inference) — the parent's t labels are
             # CORRECT there and must not be relabeled.
             base = base.replace("t-stat", "z-stat").replace("P>|t|", "P>|z|")
+        bad_control = getattr(self, "bad_control", None)
+        if bad_control is not None:
+            # 81 characters: fits inside the 85-wide '=' rules.
+            dml_banner = (
+                "DML DiD (CCPS 2026 bad-control score) Staggered Difference-in-Differences Results"
+            )
         lines = base.split("\n")
         for i, line in enumerate(lines):
             if cs_banner in line:
@@ -217,6 +244,23 @@ def summary(self, alpha: Optional[float] = None) -> str:
         ]
         if n_degenerate:
             header.append(f"{'Degenerate cells skipped:':<30} {n_degenerate:>10}")
+        if bad_control is not None:
+            w_names = getattr(self, "bad_control_covariates", None) or ()
+            w_label = ", ".join(w_names) if w_names else "(none)"
+            diag = getattr(self, "bad_control_diagnostics", None) or {}
+            n_post = sum(1 for (g, t) in diag if t >= g - self.anticipation)
+            n_pre = len(diag) - n_post
+            header += [
+                f"{'Bad control:':<30} {bad_control:>10}",
+                f"{'Bad-control covariates (W):':<30} {w_label:>10}",
+                f"{'ATT_X cells (post / pre):':<30} {f'{n_post} / {n_pre}':>10}",
+            ]
+            if self.n_bootstrap > 0:
+                header.append("ATT_X SE: analytical (not bootstrapped).")
+            header += [
+                "Overall ATT weighting: CS simple (not Remark 4; REGISTRY DMLDiD Note).",
+                "Call results.bad_control_summary() for the ATT_X pre-test table.",
+            ]
         if self.n_bootstrap > 0:
             header.append(f"{'Bootstrap iterations:':<30} {self.n_bootstrap:>10}")
             header.append(f"{'Bootstrap weights:':<30} {str(self.bootstrap_weights):>10}")
@@ -232,6 +276,61 @@ def summary(self, alpha: Optional[float] = None) -> str:
         insert_at = 4
         return "\n".join(lines[:insert_at] + header + [""] + lines[insert_at:])
 
+    def bad_control_summary(self) -> pd.DataFrame:
+        """Per-cell ``ATT_X(g, t)`` pre-test table (Caetano et al. 2026, Remark 6).
+
+        One row per RETAINED cell of a bad-control fit: the AIPW mean effect
+        of treatment on the bad control at ``t`` (``att_x``), its analytical
+        SE and inference, and ``post`` (``t >= g - anticipation``). Pre-period
+        rows assess covariate unconfoundedness (MP-5); post-period rows are a
+        mean-effect check of Condition 2 (a nonzero value is evidence the
+        treatment moves the bad control; a zero value does not establish the
+        converse). Typed-empty on plain fits.
+        """
+        cols = [
+            "group",
+            "time",
+            "post",
+            "att_x",
+            "se_x",
+            "t_stat",
+            "p_value",
+            "conf_int_lower",
+            "conf_int_upper",
+        ]
+        diag = getattr(self, "bad_control_diagnostics", None)
+        if not diag:
+            return pd.DataFrame(columns=cols)
+        rows = []
+        for (g, t), entry in sorted(diag.items()):
+            ci = entry.get("conf_int", (float("nan"), float("nan")))
+            rows.append(
+                {
+                    "group": g,
+                    "time": t,
+                    "post": bool(t >= g - self.anticipation),
+                    "att_x": entry.get("effect"),
+                    "se_x": entry.get("se"),
+                    "t_stat": entry.get("t_stat"),
+                    "p_value": entry.get("p_value"),
+                    "conf_int_lower": ci[0],
+                    "conf_int_upper": ci[1],
+                }
+            )
+        return pd.DataFrame(rows, columns=cols)
+
+    def to_dataframe(self, level: str = "group_time") -> pd.DataFrame:
+        """Parent DataFrame; on bad-control fits the ``group_time`` level gains
+        ``att_x`` / ``se_x`` (analytical, unlike a bootstrapped ``se``)."""
+        frame = super().to_dataframe(level=level)
+        diag = getattr(self, "bad_control_diagnostics", None)
+        if level != "group_time" or not diag:
+            return frame
+        keys = list(zip(frame["group"], frame["time"]))
+        frame["att_x"] = [diag.get(k, {}).get("effect", float("nan")) for k in keys]
+        frame["se_x"] = [diag.get(k, {}).get("se", float("nan")) for k in keys]
+        return frame
+
     def to_dict(self) -> Dict[str, Any]:
         """Headline dict extended with DML provenance (JSON-serializable)."""
         result = super().to_dict()
@@ -257,4 +356,15 @@ def to_dict(self) -> Dict[str, Any]:
         result["cross_fit_diagnostics"] = _serialize_cross_fit_diagnostics(
             self.cross_fit_diagnostics
         )
+        bad_control = getattr(self, "bad_control", None)
+        if bad_control is not None:
+            # Conditional emission (the reference_event_times precedent):
+            # plain fits keep today's exact key set.
+            result["bad_control"] = str(bad_control)
+            result["bad_control_covariates"] = list(
+                getattr(self, "bad_control_covariates", None) or ()
+            )
+            result["bad_control_diagnostics"] = _serialize_cross_fit_diagnostics(
+                getattr(self, "bad_control_diagnostics", None)
+            )
         return result
diff --git a/diff_diff/guides/llms-autonomous.txt b/diff_diff/guides/llms-autonomous.txt
index 07ac6624e..b87729b8a 100644
--- a/diff_diff/guides/llms-autonomous.txt
+++ b/diff_diff/guides/llms-autonomous.txt
@@ -349,7 +349,7 @@ supported / out of scope; `warn` supported but with documented caveats;
 | `StackedDiD` | ✓ | ✓ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✓ |
 | `WooldridgeDiD` (ETWFE) | ✓ | ✓ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✓ |
 | `LWDiD` | ✓ | ✓ | ✗ | ✗ | ✓ | warn | partial | ✗ | ✓ |
-| `DMLDiD` | ✓ | ✓ | ✗ | ✗ | partial | ✓ (REQUIRED) | ✗ | ✗ | ✓ (pweight full-design TSL + replicate weights + coarser cluster=; PSU-cohesive folds; panel=False = declared RCS) |
+| `DMLDiD` | ✓ | ✓ | ✗ | ✗ | partial | ✓ (REQUIRED) | ✗ | ✗ | ✓ (pweight full-design TSL + replicate weights + coarser cluster=; PSU-cohesive folds; panel=False = declared RCS; bad-control lane `fit(bad_control=)`: panel only, `cluster=` only) |
 | `EfficientDiD` | ✓ | ✓ | ✗ | ✗ | partial | ✓ | ✗ | ✗ | ✓ |
 | `SyntheticDiD` | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✓ | ✗ | partial |
 | `TROP` | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | partial |
@@ -522,7 +522,13 @@ estimators:
   never-treated: same CS rule (not_yet_treated needs never-treated units
   or >= 2 cohorts). Aggregation is post-fit
   (`results.aggregate('event_study'/...)`); with `seed=None` point
-  estimates vary across fits (random folds) - set `seed`.
+  estimates vary across fits (random folds) - set `seed`. Bad controls
+  (Caetano, Callaway, Payne & Sant'Anna 2026): `fit(..., bad_control=,
+  bad_control_covariates=)` runs the paper's orthogonal DR score and
+  stores the per-cell `ATT_X(g,t)` pre-test
+  (`results.bad_control_summary()`); panel only, `cluster=` only,
+  `anticipation=0` + varying base only; never put the bad control in
+  `covariates`.
 
 Diagnostic: `BaconDecomposition().fit(df, ...)` shows the weight allocation of a
 TWFE fit to 2×2 comparison types. Forbidden-comparison weight > 10% is a
@@ -765,8 +771,9 @@ Explicit RCS support in this library:
   REGISTRY.md §CallawaySantAnna; use this variant on RCS data.
 - `DMLDiD(panel=False)` - Chang (2020) Case 2 declared-RCS mode
   (row-unique unit IDs; level-outcome orthogonal scores with the
-  lambda-corrected variance; REGISTRY.md §DMLDiD). Survey/cluster
-  support on both designs: `survey_design=` (pweight full-design TSL
+  lambda-corrected variance; REGISTRY.md §DMLDiD). The bad-control
+  lane (`fit(bad_control=)`) is panel only (Remark 1) and `cluster=`
+  only. Survey/cluster support on both designs: `survey_design=` (pweight full-design TSL
   or replicate weights — per-cell AND aggregate IF-reweighting, df =
   rank-1; replicate + cluster=/bootstrap rejected; the weighted-lambda
   plug-in is a library extension - Theorem 2's coverage claim does not
diff --git a/diff_diff/guides/llms-full.txt b/diff_diff/guides/llms-full.txt
index 39e3cb9f5..8195c2e19 100644
--- a/diff_diff/guides/llms-full.txt
+++ b/diff_diff/guides/llms-full.txt
@@ -1415,7 +1415,10 @@ DMLDiD(
     pscore_trim=0.01,             # clip fitted propensities (never drop)
     panel=True,                   # False = declared repeated cross sections (Chang Case 2)
     cluster=None,                 # coarser-than-unit clustering (variance/folds only)
-).fit(data, outcome, unit, time, first_treat, covariates, survey_design=None) -> DMLDiDResults
+).fit(data, outcome, unit, time, first_treat, covariates, survey_design=None,
+     bad_control=None,              # Caetano et al. (2026) bad-control lane: a covariate treatment can affect (NOT in covariates)
+     bad_control_covariates=None,   # W for the bad control's unconfoundedness model; [outcome] = base-period outcome (Remark 5)
+) -> DMLDiDResults
 ```
 
 Key contracts:
@@ -1423,7 +1426,8 @@ Key contracts:
 - HonestDiD / PreTrendsPower consume the aggregate('event_study') container (admitted source); the native `compute_honest_did(results)` route raises with the container instruction. Varying-base containers warn; use base_period='universal' for clean Rambachan-Roth interpretation.
 - `SieveLearner(k_max=None, criterion="bic")` is the exported configurable learner (adaptive polynomial degree by IC); any sklearn-style estimator object also plugs in (seed stochastic learners yourself — the library seed pins folds, not learner internals).
 - Per-cell complete cases (one consolidated unbalanced-input warning); degenerate cells (fewer members than folds, singleton treated stratum, fail-closed learner) become NaN cells with machine-readable skip_reason and a consolidated warning; surviving cells still aggregate.
-- Survey/cluster support on BOTH designs. `survey_design=` (pweight-only): weighted moment kernels (Hajek p-hat/lambda-hat/theta), sample_weight into the nuisance learners (user learner objects must accept sample_weight by keyword — rejected up front otherwise); two variance lanes. Full-design TSL (weights/strata/PSU/FPC): PSU-cohesive cross-fitting folds when the PSU is strictly coarser than the sampling unit, design-based per-cell/aggregate variance with df = n_PSU - n_strata t-inference. Replicate weights (BRR/Fay/JK1/JKn/SDR): per-cell AND aggregate IF-reweighting variance on the augmented cross-fitted scores with df = rank(replicate matrix) - 1 t-inference (nuisances not re-estimated per replicate; replicate + cluster= and replicate + bootstrap rejected). A documented library EXTENSION of Chang's i.i.d. theory (Theorem 2's coverage claim does not carry over on the weighted-lambda RCS lane — REGISTRY DMLDiD Notes). Bare cluster= keeps the kernels unweighted (variance/folds/df only). aggregate('total') fails closed on declared-survey fits. panel=False requires row-unique unit IDs and assumes stationary cross-sectional sampling (Assumption 2.3, warned, not data-checkable). Reproducibility: set seed (fold draws move point estimates; PSU folds consume the RNG differently than stratified folds).
+- Bad controls (Caetano, Callaway, Payne & Sant'Anna 2026): `fit(..., bad_control='x', bad_control_covariates=[outcome])` swaps the cell score for the paper's Neyman-orthogonal doubly-robust score (Eq. 10; parallel trends conditional on the bad control's UNTREATED path, its untreated evolution identified by covariate unconfoundedness given the base-period bad control, W and Z; four cross-fitted nuisances incl. two nested second stages) and stores the per-cell `ATT_X(g,t)` pre-test (`results.bad_control_summary()`, `results.bad_control_diagnostics`; analytical SE only, never bootstrapped/aggregated). Panel lane only, bare `cluster=` only (`survey_design=` raises), `anticipation=0` and `base_period='varying'` only; the bad control may not appear in `covariates`; `bad_control_covariates=None` means no W. Headline `att` keeps the CS simple weighting (not the paper's Remark 4 overall). Approach 1 (condition on the PRE-treatment bad control) = pass it in `covariates` on the panel lane instead.
+- Survey/cluster support on BOTH designs (bad-control lane: panel only, `cluster=` only). `survey_design=` (pweight-only): weighted moment kernels (Hajek p-hat/lambda-hat/theta), sample_weight into the nuisance learners (user learner objects must accept sample_weight by keyword — rejected up front otherwise); two variance lanes. Full-design TSL (weights/strata/PSU/FPC): PSU-cohesive cross-fitting folds when the PSU is strictly coarser than the sampling unit, design-based per-cell/aggregate variance with df = n_PSU - n_strata t-inference. Replicate weights (BRR/Fay/JK1/JKn/SDR): per-cell AND aggregate IF-reweighting variance on the augmented cross-fitted scores with df = rank(replicate matrix) - 1 t-inference (nuisances not re-estimated per replicate; replicate + cluster= and replicate + bootstrap rejected). A documented library EXTENSION of Chang's i.i.d. theory (Theorem 2's coverage claim does not carry over on the weighted-lambda RCS lane — REGISTRY DMLDiD Notes). Bare cluster= keeps the kernels unweighted (variance/folds/df only). aggregate('total') fails closed on declared-survey fits. panel=False requires row-unique unit IDs and assumes stationary cross-sectional sampling (Assumption 2.3, warned, not data-checkable). Reproducibility: set seed (fold draws move point estimates; PSU folds consume the RNG differently than stratified folds).
 
 ### TROP
 
diff --git a/diff_diff/guides/llms-practitioner.txt b/diff_diff/guides/llms-practitioner.txt
index 3ab24ef67..bd67bcaa9 100644
--- a/diff_diff/guides/llms-practitioner.txt
+++ b/diff_diff/guides/llms-practitioner.txt
@@ -228,6 +228,8 @@ Is treatment adoption staggered (multiple cohorts, different timing)?
 |   |                             cell; covariates REQUIRED, aggregation
 |   |                             post-fit, set seed= for reproducible
 |   |                             fold draws; panel=False = declared
+|   |                             RCS; fit(bad_control=) = Caetano
+|   |                             et al. (2026) bad-control lane
 |   |                             repeated cross sections (Case 2,
 |   |                             lambda-corrected variance);
 |   |                             survey_design=/cluster= supported on
@@ -658,8 +660,23 @@ Executed end-to-end examples: tutorials 29 (PyMC-Marketing lift test) and
    to reject a pre-trends test does NOT prove parallel trends holds. Use
    HonestDiD to bound how large a violation could be.
 
-3. **Including "bad controls"**: Covariates affected by treatment will bias
-   estimates. Only include pre-treatment or time-invariant covariates.
+3. **Including "bad controls"**: A covariate that treatment can affect
+   (Caetano, Callaway, Payne & Sant'Anna 2026) must NEVER enter at period t
+   - that is the "include the bad control" bias. Two valid routes: (a)
+   condition only on its PRE-treatment value under parallel trends given
+   the pre-treatment bad control (Assumption 4/5, MP-8/MP-9) - on the
+   panel lane `CallawaySantAnna` / `DMLDiD` read `covariates` at each
+   cell's base period, so passing the column there does this; (b) the
+   paper's covariate-unconfoundedness approach, which allows treatment to
+   affect the control's path: `DMLDiD(...).fit(..., bad_control="x",
+   bad_control_covariates=[outcome])` (a `fit()` argument, never a
+   constructor argument), then read `results.bad_control_summary()` by
+   period: nonzero PRE-period ATT_X (t < g) indicates a possible MP-5 /
+   MP-8 violation (the identifying assumptions for the bad control's
+   untreated evolution; these rows should be zero), while nonzero
+   POST-period ATT_X (t >= g) is evidence that treatment affects the
+   covariate (Condition 2) - a zero value does not establish the
+   converse. Time-invariant covariates are always safe.
 
 4. **Ignoring sensitivity analysis**: Without HonestDiD or placebo tests,
    you cannot assess how robust your results are to assumption violations.
diff --git a/diff_diff/guides/llms.txt b/diff_diff/guides/llms.txt
index f9220d90c..2ffd140af 100644
--- a/diff_diff/guides/llms.txt
+++ b/diff_diff/guides/llms.txt
@@ -81,11 +81,12 @@ The site is organized into 5 sections, each with a landing page:
 - [ChangesInChanges](https://diff-diff.readthedocs.io/en/stable/api/changes_in_changes.html): Athey & Imbens (2006) nonlinear/distributional DiD for the 2x2 design: recovers the treated group's full counterfactual outcome distribution and quantile treatment effects (ATT + QTE grid) via the CDF transformation `F_10(F_00^{-1}(F_01(y)))`; invariant to monotone outcome transformations (unconditional fits; the covariate QR branch is not); bootstrap inference (panel or repeated cross-section resampling); point parity with R `qte::CiC()`, including its covariate branch (`covariates=` -> per-cell linear quantile regression, Melly-Santangelo-style conditional CiC). Continuous outcomes, numeric covariates. Alias `CiC`.
 - [QDiD](https://diff-diff.readthedocs.io/en/stable/api/changes_in_changes.html): **Deprecated 3.9, removed 4.0 - use `ChangesInChanges(method="qdid")`.** Athey & Imbens (2006) quantile DiD comparison estimator (additive quantile-by-quantile DiD, matching R `qte::QDiD()` including its covariate branch via `covariates=`); same bootstrap machinery as ChangesInChanges. The paper recommends CiC over QDiD (scale-dependent model with testable restrictions; a non-monotonicity warning fires when violated - unconditional fits only, the covariate-path counterfactual quantile curve is monotone by construction).
 - [LWDiD](https://diff-diff.readthedocs.io/en/stable/api/lwdid.html): Lee & Wooldridge (2025, 2026) rolling-transformation DiD — unit-specific demean/detrend converts panel to cross-section, supports staggered adoption with flexible control groups. Signature: `LWDiD(rolling='demean', estimation_method='reg', vcov_type='hc1', cluster=None, control_group='not_yet_treated', alpha=0.05, n_bootstrap=0, seed=None, pscore_trim=0.01, n_neighbors=1, caliper=None, with_replacement=True, n_jobs=1).fit(data, outcome, unit, time, treatment, first_treat=None, covariates=None)`. `estimation_method` values: `reg` (papers' RA), `ipw`, `dr` (papers' IPWRA, doubly robust), `psm`; `vcov_type` values: `classical`/`hc1`/`hc2`/`hc3` for `reg`; `ipw`/`dr` accept `hc1` only (influence-function variance); `psm` accepts `hc1` as configuration only - PSM inference is unavailable (NaN) pending an Abadie-Imbens matching variance; cluster-robust inference via the constructor's `cluster=` column (hc1/CR1 only, not a `vcov_type` value; rejected for `psm`). Per-period effects: post-fit `results.aggregate('event_study')`.
-- [DMLDiD](https://diff-diff.readthedocs.io/en/stable/api/dml_did.html): Chang (2020) double/debiased machine learning DiD — staggered ATT(g,t) with cross-fitted ML nuisances (DML2) and Neyman-orthogonal scores; covariates REQUIRED (conditional parallel trends). Signature: `DMLDiD(propensity_learner='logit', outcome_learner='linear', n_folds=5, control_group='never_treated', anticipation=0, alpha=0.05, n_bootstrap=0, bootstrap_weights=None, seed=None, base_period='varying', cband=True, pscore_trim=0.01, panel=True, cluster=None).fit(data, outcome, unit, time, first_treat, covariates, survey_design=None)`. `panel=False` = declared repeated cross sections (Chang Case 2: level outcomes, row-unique unit IDs, lambda-corrected variance). Survey/cluster support on BOTH designs: `survey_design=` (pweight full-design TSL — weighted moments, PSU-cohesive folds, design-based variance with t-inference; a library extension of Chang's i.i.d. theory), replicate-weight designs (BRR/Fay/JK1/JKn/SDR — per-cell AND aggregate IF-reweighting variance, df = rank-1; cluster= and bootstrap combinations rejected), and coarser-than-unit `cluster=` (variance/folds only, kernels stay unweighted). Learners: string names (`linear`/`ridge`/`sieve` regressors, `logit` classifier) or any object with fit/predict(_proba) (sklearn-compatible); `SieveLearner(k_max, criterion)` is exported for adaptive polynomial nuisances. Aggregation is POST-FIT: `results.aggregate('event_study'/'group'/'simple')`, plus `'total'` on panel non-survey fits (RCS and declared-survey fits fail 'total' closed); sup-t bands via bootstrap replay. With seed=None point estimates vary across fits (random folds); set seed for reproducibility.
+- [DMLDiD](https://diff-diff.readthedocs.io/en/stable/api/dml_did.html): Chang (2020) double/debiased machine learning DiD — staggered ATT(g,t) with cross-fitted ML nuisances (DML2) and Neyman-orthogonal scores; covariates REQUIRED (conditional parallel trends). Signature: `DMLDiD(propensity_learner='logit', outcome_learner='linear', n_folds=5, control_group='never_treated', anticipation=0, alpha=0.05, n_bootstrap=0, bootstrap_weights=None, seed=None, base_period='varying', cband=True, pscore_trim=0.01, panel=True, cluster=None).fit(data, outcome, unit, time, first_treat, covariates, survey_design=None, bad_control=None, bad_control_covariates=None)`. `panel=False` = declared repeated cross sections (Chang Case 2: level outcomes, row-unique unit IDs, lambda-corrected variance). Survey/cluster support on BOTH designs (bad-control lane: panel only, `cluster=` only): `survey_design=` (pweight full-design TSL — weighted moments, PSU-cohesive folds, design-based variance with t-inference; a library extension of Chang's i.i.d. theory), replicate-weight designs (BRR/Fay/JK1/JKn/SDR — per-cell AND aggregate IF-reweighting variance, df = rank-1; cluster= and bootstrap combinations rejected), and coarser-than-unit `cluster=` (variance/folds only, kernels stay unweighted). Bad controls (Caetano, Callaway, Payne & Sant'Anna 2026): `fit(..., bad_control='x', bad_control_covariates=[outcome])` runs the paper's Neyman-orthogonal doubly-robust score (Eq. 10) - parallel trends conditional on the bad control's untreated path plus covariate unconfoundedness given its base-period value, W and Z - and stores the per-cell `ATT_X(g,t)` pre-test (`results.bad_control_summary()`); a bad control must NOT be in `covariates`. Learners: string names (`linear`/`ridge`/`sieve` regressors, `logit` classifier) or any object with fit/predict(_proba) (sklearn-compatible); `SieveLearner(k_max, criterion)` is exported for adaptive polynomial nuisances. Aggregation is POST-FIT: `results.aggregate('event_study'/'group'/'simple')`, plus `'total'` on panel non-survey fits (RCS and declared-survey fits fail 'total' closed); sup-t bands via bootstrap replay. With seed=None point estimates vary across fits (random folds); set seed for reproducibility.
 - [BaconDecomposition](https://diff-diff.readthedocs.io/en/stable/api/bacon.html): Goodman-Bacon (2021) decomposition for diagnosing TWFE bias in staggered settings
 
 ## Diagnostics and Sensitivity Analysis
 
+- [Bad-control pre-test](https://diff-diff.readthedocs.io/en/stable/api/dml_did.html): Caetano, Callaway, Payne & Sant'Anna (2026) Remark 6 `ATT_X(g,t)` — the effect of treatment on the bad control itself, per (g,t) cell (AIPW mean-effect diagnostic with analytical SE; pre-period rows (t < g) assess the identifying assumptions MP-5 / MP-8 and should be zero - a nonzero pre-period ATT_X flags a possible violation, NOT a bad control; post-period rows (t >= g) are the Condition-2 check - a nonzero post-period ATT_X is evidence treatment affects the covariate, while a zero value does not establish the converse). `DMLDiD(...).fit(..., bad_control=, bad_control_covariates=)` then `results.bad_control_summary()` / `results.bad_control_diagnostics`.
 - [RD Plots](https://diff-diff.readthedocs.io/en/stable/api/regression_discontinuity.html): Calonico, Cattaneo & Titiunik (2015) optimal data-driven RD plots (`RDPlot`), parity with R rdrobust 4.0.0's `rdplot()` - all 8 `binselect` bin-count selectors (evenly/quantile spaced x IMSE-optimal/mimicking-variance x spacings/polynomial-regression), implied scale + WIMSE weights per Supplement S.1, optional covariate adjustment reusing the RD estimator's pipeline, optional lazy-matplotlib rendering (matplotlib not a dependency)
 - [Manipulation Testing](https://diff-diff.readthedocs.io/en/stable/api/regression_discontinuity.html): Cattaneo, Jansson & Ma (2020) density-discontinuity manipulation test (`RDDensityTest`), parity with R rddensity 3.0 - boundary-adaptive local polynomial density estimation at the cutoff, robust bias-corrected inference, unrestricted/restricted models, jackknife/plugin variances, data-driven bandwidths, mass-point adjustment
 - [Parallel Trends Testing](https://diff-diff.readthedocs.io/en/stable/api/diagnostics.html): Simple and Wasserstein-robust parallel trends tests, equivalence testing (TOST)
diff --git a/diff_diff/practitioner.py b/diff_diff/practitioner.py
index 15b4ca119..546aa9b86 100644
--- a/diff_diff/practitioner.py
+++ b/diff_diff/practitioner.py
@@ -543,6 +543,14 @@ def _handle_dml_did(results: Any):
                 "# design forward so the comparison isolates the learner):\n"
                 "alt = DMLDiD(outcome_learner='sieve', seed=0"
                 + (", panel=False" if getattr(results, "panel", True) is False else "")
+                + (
+                    # Bad-control fits carry the comparison group forward: a
+                    # Proposition 2 not-yet-treated fit must not silently
+                    # revert to the never-treated constructor default.
+                    f", control_group={getattr(results, 'control_group', None)!r}"
+                    if getattr(results, "bad_control", None) is not None
+                    else ""
+                )
                 + (
                     # cluster_name covers bare cluster=, a design-injected
                     # cluster (survey_design without PSU + cluster=), and a
@@ -561,6 +569,15 @@ def _handle_dml_did(results: Any):
                     if getattr(results, "survey_metadata", None) is not None
                     else ""
                 )
+                + (
+                    # Carry the bad-control specification forward so the
+                    # refit targets the same (Caetano et al. 2026) estimand.
+                    f",\n    bad_control={getattr(results, 'bad_control', None)!r},"
+                    f"\n    bad_control_covariates="
+                    f"{list(getattr(results, 'bad_control_covariates', None) or ())!r}"
+                    if getattr(results, "bad_control", None) is not None
+                    else ""
+                )
                 + ")\n"
                 "print(alt.att, results.att)  # should be close"
             ),
diff --git a/docs/api/_autosummary/diff_diff.dml_did_results.DMLDiDResults.rst b/docs/api/_autosummary/diff_diff.dml_did_results.DMLDiDResults.rst
index befccb05c..6a6697c7f 100644
--- a/docs/api/_autosummary/diff_diff.dml_did_results.DMLDiDResults.rst
+++ b/docs/api/_autosummary/diff_diff.dml_did_results.DMLDiDResults.rst
@@ -13,6 +13,7 @@
 
       ~DMLDiDResults.__init__
       ~DMLDiDResults.aggregate
+      ~DMLDiDResults.bad_control_summary
       ~DMLDiDResults.epv_summary
       ~DMLDiDResults.print_summary
       ~DMLDiDResults.summary
@@ -30,6 +31,9 @@
       ~DMLDiDResults.alpha
       ~DMLDiDResults.anticipation
       ~DMLDiDResults.att
+      ~DMLDiDResults.bad_control
+      ~DMLDiDResults.bad_control_covariates
+      ~DMLDiDResults.bad_control_diagnostics
       ~DMLDiDResults.base_period
       ~DMLDiDResults.bootstrap_results
       ~DMLDiDResults.bootstrap_weights
diff --git a/docs/api/dml_did.rst b/docs/api/dml_did.rst
index 38c0c61b4..fed2d3ce8 100644
--- a/docs/api/dml_did.rst
+++ b/docs/api/dml_did.rst
@@ -85,6 +85,52 @@ both periods. RCS aggregation weights are FIXED cohort row masses (the
 CS-RCS convention, keeping the variance the influence function of the
 reported aggregate); ``aggregate('total')`` is unavailable on RCS fits.
 
+**Bad controls (Caetano, Callaway, Payne & Sant'Anna 2026;**
+``fit(..., bad_control=, bad_control_covariates=)``\ **).** A "bad control"
+is a time-varying covariate :math:`X_t` that treatment can affect.
+Conditioning on it at :math:`t` biases DiD; conditioning only on its
+pre-treatment value (pass it in ``covariates`` - the panel lane reads
+covariates at the cell's base period) is the paper's Approach 1. This
+lane implements the paper's covariate-unconfoundedness approach: parallel
+trends conditional on the bad control's UNTREATED path, with the bad
+control's untreated evolution identified given its base-period value, the
+optional ``bad_control_covariates`` :math:`W` (the outcome name means the
+base-period outcome, the paper's Remark 5 recommendation), and the
+covariates :math:`Z`. Per cell, with :math:`R = [X_t, X_b, Z]` and
+:math:`S = [X_b, W, Z]`, the Neyman-orthogonal doubly-robust score
+(paper Equation 10) is
+
+.. math::
+
+   \text{summand}_i = \frac{D_i}{\hat\pi}\bigl(\Delta Y_i - \hat\nu(S_i)\bigr)
+   - \frac{1 - D_i}{\hat\pi}\Bigl[\bigl(\hat m(R_i) - \hat\nu(S_i)\bigr)\frac{\hat p(S_i)}{1 - \hat p(S_i)}
+   + \bigl(\Delta Y_i - \hat m(R_i)\bigr)\hat\omega(R_i)\Bigr]
+
+with four cross-fitted nuisances: the control outcome-change regression
+:math:`\hat m` on :math:`R`, the propensity :math:`\hat p` on :math:`S`, and
+two NESTED second-stage regressions - :math:`\hat\nu` (the first-stage
+predictions regressed on :math:`S` among training controls) and
+:math:`\hat\omega` (the propensity odds regressed on :math:`R`, clipped to
+:math:`[0, (1-\text{trim})/\text{trim}]` with a warning). With the parametric
+built-in learners the nested targets are the paper's own plug-in; with
+``ridge`` / ``sieve`` / user learners the training complement is split in
+half (footnote 9). The variance is the same augmented-score plug-in as the
+plain lane. Each cell also reports :math:`\widehat{ATT}_X(g,t)`, the
+paper's Remark 6 pre-test (the effect of treatment on the bad control
+itself, an AIPW mean-effect diagnostic with its own analytical SE), via
+``results.bad_control_summary()``: pre-period rows (:math:`t < g`) assess
+the identifying assumptions MP-5 / MP-8 and should be zero (a nonzero
+value flags a possible violation), post-period rows (:math:`t \ge g`) are
+the Condition-2 check (a nonzero value is evidence treatment affects the
+covariate; a zero value does not establish the converse). Restrictions: panel lane only, bare
+``cluster=`` only (``survey_design=`` raises), ``anticipation=0`` and
+``base_period='varying'`` only. The headline ``att`` keeps the CS
+"simple" weighting, not the paper's Remark 4 overall. Validated against
+the authors' R package ``badcontrols`` as a tolerance-based black box
+(``tests/test_dml_did_bad_controls_parity.py``) plus the paper's
+Supplementary DGPs 1 and 4; see ``docs/methodology/REGISTRY.md`` "DMLDiD"
+> "Bad-control extension (CCPS 2026)" for every convention.
+
 **Aggregation.** ``DMLDiD`` writes the CallawaySantAnna per-cell
 influence-function payload and inherits the CS aggregation and
 multiplier-bootstrap machinery: event-study / group / simple aggregations
@@ -124,6 +170,34 @@ Basic usage
    es = results.aggregate("event_study")
    print(es.to_dataframe())
 
+Bad control (Caetano et al. 2026): a covariate treatment can affect, such
+as an occupation or earnings measure, is passed as ``bad_control`` rather
+than in ``covariates``; ``bad_control_covariates=[outcome]`` conditions the
+bad control's evolution on the base-period outcome (Remark 5), and the
+explicit ``control_group="not_yet_treated"`` is the paper's Proposition 2
+comparison group:
+
+.. code-block:: python
+
+   from diff_diff import DMLDiD
+
+   data = data.assign(
+       occupation=lambda d: 0.7 * d["x1"] + 0.3 * d["x2"] + 0.5 * d["treated"] * d["post"]
+   )
+   bc = DMLDiD(control_group="not_yet_treated", seed=0).fit(
+       data,
+       outcome="y",
+       unit="unit",
+       time="time",
+       first_treat="first_treat",
+       covariates=["x3"],
+       bad_control="occupation",
+       bad_control_covariates=["y"],
+   )
+   print(bc.summary())
+   print(bc.bad_control_summary())   # per-cell ATT_X(g, t): pre-period rows should be ~0 (MP-5 / MP-8);
+                                     # nonzero post-period rows = treatment moves the covariate
+
 Learner configuration
 ---------------------
 
@@ -154,7 +228,7 @@ API Reference
 
 .. autoclass:: diff_diff.dml_did_results.DMLDiDResults
    :no-index:
-   :members: aggregate, summary, to_dict, to_dataframe
+   :members: aggregate, bad_control_summary, summary, to_dict, to_dataframe
 
 .. autoclass:: diff_diff.SieveLearner
    :no-index:
@@ -217,6 +291,15 @@ Restrictions
 - **Event-study surface is post-fit only** — fit-time
   ``event_study_effects`` is never populated; call
   ``results.aggregate('event_study')``.
+- **Bad-control lane** — ``fit(bad_control=...)`` requires
+  ``panel=True``, ``anticipation=0`` and ``base_period='varying'``, and
+  no ``survey_design`` (each raises ``NotImplementedError``; bare
+  ``cluster=`` is supported). The bad control may not appear in
+  ``covariates`` (the "include the bad control" bias); ``covariates``
+  stays required. Units with a non-finite bad control at the base period
+  or at ``t``, or a non-finite bad-control covariate at the base period,
+  leave that cell (complete cases). ``ATT_X`` is analytical only: never
+  bootstrapped or aggregated.
 
 .. seealso::
 
diff --git a/docs/api/staggered.rst b/docs/api/staggered.rst
index 771d56e11..45e13db1a 100644
--- a/docs/api/staggered.rst
+++ b/docs/api/staggered.rst
@@ -18,6 +18,21 @@ CallawaySantAnna
 
 Callaway & Sant'Anna (2021) estimator for heterogeneous treatment timing.
 
+**Covariates and bad controls.** On the panel lane a covariate is read at
+each cell's base period (the observed period preceding the cohort's first
+treatment for post-treatment cells), never at :math:`t`. A time-varying
+covariate that treatment can affect (a "bad control", Caetano, Callaway,
+Payne & Sant'Anna 2026) conditioned this way therefore computes the
+paper's Proposition 3 estimand - parallel trends given the PRE-treatment
+bad control (Approach 1) - not the biased "include the bad control"
+contrast; passing the pre-treatment value is the user's responsibility.
+On the repeated-cross-section lane covariates are read on the
+observation's own row, so a time-varying bad control there IS
+:math:`X_t` and Approach 1 does not apply. For the paper's
+covariate-unconfoundedness approach with extra covariates :math:`W`, use
+:class:`~diff_diff.DMLDiD` with ``fit(..., bad_control=,
+bad_control_covariates=)``.
+
 .. autoclass:: diff_diff.CallawaySantAnna
    :no-index:
    :members:
diff --git a/docs/choosing_estimator.rst b/docs/choosing_estimator.rst
index 2bbd7cdfa..3268eaf7c 100644
--- a/docs/choosing_estimator.rst
+++ b/docs/choosing_estimator.rst
@@ -683,6 +683,15 @@ insensitive to the nuisance learners' regularization bias.
   DoubleML at machine precision (committed parity spikes); the RCS lane
   has no DoubleML oracle (different score) and is validated by equation
   fixtures + a committed characterization spike
+- Bad controls (Caetano, Callaway, Payne & Sant'Anna 2026): a covariate
+  treatment can affect goes in ``fit(bad_control=...)`` (never in
+  ``covariates``), optionally with ``bad_control_covariates=[outcome]``;
+  the cell score becomes the paper's orthogonal doubly-robust score and
+  ``results.bad_control_summary()`` reports the per-cell ``ATT_X(g,t)``
+  pre-test (pre-period rows should be zero - they assess MP-5 / MP-8;
+  nonzero post-period rows show treatment affects the covariate). Panel
+  only, bare ``cluster=`` only, ``anticipation=0`` and the varying base
+  only.
 
 **vs Callaway-Sant'Anna**: same cell architecture and aggregation surface;
 DMLDiD replaces CS's parametric nuisances with cross-fitted ML learners —
@@ -1016,7 +1025,7 @@ estimation. The depth of support varies by estimator and variance method:
      - --
      - --
    * - ``DMLDiD``
-     - Full (pweight only)
+     - Full (pweight only; bad-control lane: ``cluster=`` only)
      - Full (TSL; df = ``n_PSU - n_strata``)
      - Full (IF-reweighting; per-cell + aggregate)
      - Multiplier (PSU)
diff --git a/docs/doc-deps.yaml b/docs/doc-deps.yaml
index 7beb3e6c3..66047f445 100644
--- a/docs/doc-deps.yaml
+++ b/docs/doc-deps.yaml
@@ -977,13 +977,20 @@ sources:
         section: "Current Limitations"
         type: user_guide
       - path: docs/methodology/REGISTRY.md
-        section: "DMLDiD"
+        section: "DMLDiD (incl. the 'Bad-control extension (CCPS 2026)' block) + CallawaySantAnna Approach-1 Note"
+        type: methodology
+      - path: docs/methodology/papers/caetano-2026-review.md
+        section: "Requirements checklist annotations + Implementation Notes '(library: ...)' parentheticals"
         type: methodology
+        note: "Bad-control lane: fit(bad_control=, bad_control_covariates=), nested nu/omega stages, ATT_X diagnostic; R badcontrols black-box goldens (benchmarks/R/generate_badcontrols_golden.R, tests/test_dml_did_bad_controls_parity.py)."
+      - path: docs/api/staggered.rst
+        section: "CallawaySantAnna 'Covariates and bad controls' paragraph (Approach 1)"
+        type: api_reference
       - path: docs/methodology/survey-theory.md
         section: "IF-based TSL roster / variance-dispatch table / PSU-multiplier-bootstrap roster"
         type: methodology
       - path: docs/methodology/variance-conventions.md
-        section: "dml_did / dml_did_rcs inventory rows (CI-pinned to tests/test_variance_conventions.py)"
+        section: "dml_did / dml_did_rcs / dml_did_bad_control inventory rows (CI-pinned to tests/test_variance_conventions.py)"
         type: methodology
       - path: docs/index.rst
         section: "Supported Estimators (one-line catalog row)"
@@ -999,7 +1006,10 @@ sources:
       - path: docs/methodology/REGISTRY.md
         section: "DMLDiD"
         type: methodology
-        note: "DMLDiDResults subclasses CallawaySantAnnaResults (kit-based post-fit aggregate(), bootstrap replay); adds learner/fold/cross-fit provenance and the seed/n_bootstrap/bootstrap_weights/cband inference-provenance fields."
+        note: "DMLDiDResults subclasses CallawaySantAnnaResults (kit-based post-fit aggregate(), bootstrap replay); adds learner/fold/cross-fit provenance, the seed/n_bootstrap/bootstrap_weights/cband inference-provenance fields, and the bad-control surface (bad_control / bad_control_covariates / bad_control_diagnostics fields, bad_control_summary(), the att_x / se_x to_dataframe join, summary() header lines)."
+      - path: docs/methodology/REPORTING.md
+        section: "DMLDiD bad-control identification / citation Note"
+        type: methodology
       - path: docs/tutorials/32_dml_did.ipynb
         type: tutorial
 
@@ -1446,7 +1456,7 @@ sources:
       - path: docs/methodology/REGISTRY.md
         section: "Cross-fitting, DR-score, and ridge infrastructure (DML)"
         type: methodology
-        note: "Unit/cluster-level replayable K-fold assignment (assign_folds/FoldAssignment: state captured by value pre-draw, BootstrapReplaySpec discipline; global fold cursor across sorted strata) + out-of-fold nuisance prediction (cross_fit_predict: fit on complement & fit_mask, predict every unit; DegenerateFoldError contract; loss-only log-loss clip, oof predictions unclipped)."
+        note: "Unit/cluster-level replayable K-fold assignment (assign_folds/FoldAssignment: state captured by value pre-draw, BootstrapReplaySpec discipline; global fold cursor across sorted strata) + out-of-fold nuisance prediction (cross_fit_predict: fit on complement & fit_mask, predict every unit; DegenerateFoldError contract; loss-only log-loss clip, oof predictions unclipped) + the per-fold generator iter_fold_fits / FoldFit (eager validation; fitted per-fold deep copies; _predict_subset is the caller's job) that cross_fit_predict and the DMLDiD bad-control nested stages consume; deep-copy warning prefix '_crossfit: could not deep-copy'."
 
   diff_diff/_learners.py:
     drift_risk: low
@@ -1467,7 +1477,10 @@ sources:
       - path: docs/methodology/REGISTRY.md
         section: "Cross-fitting, DR-score, and ridge infrastructure (DML)"
         type: methodology
-        note: "Shared DR panel scores: drdid_panel_inf_func (Sant'Anna-Zhao locally efficient IF, relocated verbatim from ContinuousDiD._dr_cell_inf_func, oracle-pinned in tests/test_dr_scores.py) and the Chang (2020) Case 1 orthogonal score pair (chang_panel_score / chang_panel_score_augmented) and Case 2 RCS family (chang_rcs_score / chang_rcs_lambda_slope / chang_rcs_score_augmented, lambda-corrected Theorem 2 variance) consumed by the DMLDiD estimator (panel=True/False). The two families are NOT interchangeable (Chang normalizes by the unconditional treated share; SZ is self-normalized)."
+        note: "Shared DR panel scores: drdid_panel_inf_func (Sant'Anna-Zhao locally efficient IF, relocated verbatim from ContinuousDiD._dr_cell_inf_func, oracle-pinned in tests/test_dr_scores.py), the Chang (2020) Case 1 orthogonal score pair (chang_panel_score / chang_panel_score_augmented), the Case 2 RCS family (chang_rcs_score / chang_rcs_lambda_slope / chang_rcs_score_augmented, lambda-corrected Theorem 2 variance), and the Caetano et al. (2026) bad-control family (ccps_panel_score / ccps_panel_score_augmented, Eq. 10-11; reduces to chang_panel_score with nu=m, omega=ps/(1-ps)) consumed by the DMLDiD estimator (panel=True/False; bad-control lane). The families are NOT interchangeable (Chang/CCPS normalize by the unconditional treated share; SZ is self-normalized)."
+      - path: docs/methodology/papers/caetano-2026-review.md
+        type: methodology
+        note: "The paper review's Relation section and requirements checklist name ccps_panel_score / ccps_panel_score_augmented as the Eq. 10 score location; keep the cross-reference and the checklist annotations current if functions move."
       - path: docs/methodology/papers/chang-2020-review.md
         type: methodology
         note: "The paper review's 'Relation to Existing diff-diff Estimators' section names drdid_panel_inf_func as the DRDID-parity score location; keep the cross-reference current if functions move."
diff --git a/docs/index.rst b/docs/index.rst
index 5df12e3b8..c561e490c 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -186,7 +186,7 @@ Supported Estimators
    * - :class:`~diff_diff.LWDiD`
      - Lee & Wooldridge (2025, 2026) rolling-transformation DiD; ``rolling='detrend'`` handles heterogeneous linear trends
    * - :class:`~diff_diff.DMLDiD`
-     - Chang (2020) double/debiased ML DiD; staggered ATT(g,t) with cross-fitted nuisance learners (panel or declared repeated cross sections; survey/cluster support)
+     - Chang (2020) double/debiased ML DiD; staggered ATT(g,t) with cross-fitted nuisance learners (panel or declared repeated cross sections; survey/cluster support); Caetano et al. (2026) bad-control score via ``fit(bad_control=)`` (bad-control lane: panel only, ``cluster=`` only)
    * - :class:`~diff_diff.QDiD`
      - Quantile DiD comparison estimator applying DiD quantile-by-quantile (deprecated 3.9 - use :class:`~diff_diff.ChangesInChanges` with ``method="qdid"``)
    * - :class:`~diff_diff.RegressionDiscontinuity`
diff --git a/docs/methodology/REGISTRY.md b/docs/methodology/REGISTRY.md
index e19c8601c..a2718955f 100644
--- a/docs/methodology/REGISTRY.md
+++ b/docs/methodology/REGISTRY.md
@@ -752,7 +752,7 @@ Private infrastructure modules (`diff_diff/_crossfit.py`,
 "DMLDiD" section). `SieveLearner` is publicly exported for DMLDiD nuisance
 configuration; the other learners and modules stay private.
 
-**Two DISTINCT doubly-robust panel score families** (per the Chang review:
+**Four DISTINCT doubly-robust score families** (per the Chang review:
 "Chang's Case-1 score normalizes by the unconditional `p_0` … whereas the SZ
 DR score is self-normalized; the two are not interchangeable"):
 
@@ -776,6 +776,17 @@ DR score is self-normalized; the two are not interchangeable"):
   `ps ∈ [0,1)`, `0 < p̂ < 1` strictly — `p̂ = 1` means no comparison
   population and is rejected as unidentified — finiteness) and never emit
   silent inf.
+- `ccps_panel_score(dY, D, m_hat, nu_hat, ps, omega_hat, p_hat)` — Caetano,
+  Callaway, Payne & Sant'Anna (2026) Equation 10's Neyman-orthogonal
+  bad-control score as the per-unit UNCENTERED summand
+  `(D/π)dY − (D/π)ν − ((1−D)/π)(m − ν)ps/(1−ps) − ((1−D)/π)(dY − m)ω`, whose
+  mean is the ATT; the untreated terms are normalized by `1/π` (not
+  `1/(1−π)`). `ccps_panel_score_augmented(summand, D, theta, p_hat)` is the
+  same centering identity as `chang_panel_score_augmented` (`ψ̄ = summand −
+  D θ/π̂` equals the paper's `ψ − θ − (θ/π)(D − π)`). With `ν = m` and
+  `ω = ps/(1−ps)` the score reduces to `chang_panel_score` (pinned at 1e-14).
+  Validation adds `omega_hat ≥ 0`; see the DMLDiD "Bad-control extension"
+  block for the estimator-level conventions.
 
 - **Note:** p̂ convention (documented deviation). Chang's arXiv text is
   internally contradictory about the fold-level scalar nuisance: the printed
@@ -833,7 +844,17 @@ fold-time degeneracy raises `DegenerateFoldError` (pre-checks plus chained
 wrapping of learner `ValueError`s with the fold index and the original message
 quoted); log-loss diagnostics clip probabilities to `[1e-15, 1−1e-15]` for the
 LOSS ONLY — out-of-fold predictions are returned unclipped (nuisance trimming
-is estimator policy, applied by the consuming estimator).
+is estimator policy, applied by the consuming estimator). `iter_fold_fits`
+is the per-fold building block under `cross_fit_predict` (its sole consumer
+besides the DMLDiD bad-control lane): validation runs eagerly at the call,
+then it yields one `FoldFit` per fold in ascending `k` (the fitted per-fold
+deep copy, `fit_idx == train_idx[fit_mask[train_idx]]`, `train_idx`,
+`test_idx`, the coerced arrays); predictions are the caller's job via
+`_predict_subset`, which is what lets a consumer fit a NESTED nuisance on a
+fold's training complement before predicting the held-out fold. The
+deep-copy fallback warning is attributed to the frame that advances the
+generator (the user's `cross_fit_predict` call site, or `dml_did.py` for the
+internal routes) and reads `"_crossfit: could not deep-copy ..."`.
 
 **Learner contract (`_learners.py`)** — duck-typed `RegressorLearner` /
 `ClassifierLearner` Protocols (sklearn-compatible `fit`/`predict`/
@@ -936,6 +957,23 @@ With covariates (doubly robust):
 ATT(g,t) = E[((G_g - p̂_g(X))/(1-p̂_g(X))) × (Y_t - Y_{g-1} - m̂_{0,g,t}(X) + m̂_{0,g,g-1}(X))] / E[G_g]
 ```
 
+- **Note:** Bad controls, Approach 1 (Caetano, Callaway, Payne & Sant'Anna
+  2026, Theorem 1 / Proposition 3). ON THE PANEL LANE a time-varying covariate
+  passed in `covariates` is read at the cell's base period (the observed
+  period preceding `g` for post cells), never at `t`, so a bad control (a
+  covariate that treatment can affect) conditioned this way computes the
+  paper's Proposition 3 estimand under Assumption 4 or 5 (MP-8 / MP-9:
+  parallel trends conditional on the PRE-treatment bad control), not the
+  Section 3.1 `τ^use` "include the bad control" bias. Passing the
+  pre-treatment value is the user's responsibility; no library guard can
+  detect a post-treatment column there. The repeated-cross-section lanes of
+  CallawaySantAnna and DMLDiD read covariates on the observation's own row,
+  so a time-varying bad control there IS `X_t` and Approach 1 does not apply
+  (Remark 1). For the paper's covariate-unconfoundedness approach (parallel
+  trends given the bad control's untreated path, with extra covariates `W`)
+  use `DMLDiD(...).fit(..., bad_control=, bad_control_covariates=)` - see the
+  DMLDiD "Bad-control extension (CCPS 2026)" block.
+
 Aggregations:
 - Simple: `ATT = Σ_{g,t} w_{g,t} × ATT(g,t)` weighted by group size
 - Event-study: `ATT(e) = Σ_g w_g × ATT(g, g+e)` for event-time e
@@ -2862,7 +2900,7 @@ closed-form `∂λψ₂` (`chang_rcs_lambda_slope`).
 **Key implementation requirements:**
 
 *Assumption checks / warnings:*
-- **Conditional parallel trends (Assumption 2.1, Abadie 2005):** `E[Y^0(1) - Y^0(0) | X, D = 1] = E[Y^0(1) - Y^0(0) | X, D = 0]` per cell. Untestable; the estimator adds **no identification assumptions beyond Abadie (2005)** (Section 2, p. 8).
+- **Conditional parallel trends (Assumption 2.1, Abadie 2005):** `E[Y^0(1) - Y^0(0) | X, D = 1] = E[Y^0(1) - Y^0(0) | X, D = 0]` per cell. Untestable; the estimator adds **no identification assumptions beyond Abadie (2005)** (Section 2, p. 8) on the plain lane; the bad-control lane (`fit(..., bad_control=)`) adds MP-4 / MP-5 / MP-6 / MP-7 of Caetano et al. (2026) - see the "Bad-control extension (CCPS 2026)" block below.
 - **Overlap (Assumption 2.2):** `P(D = 1) > 0` and `P(D = 1 | X) < 1` a.s. Regularity Assumptions 3.1(a) (Case 1) / 3.2(a) (Case 2) strengthen this to **strict overlap**: `Pr(κ ≤ g_0(X) ≤ 1 - κ) = 1` for some fixed `κ > 0`, imposed on the **estimated** propensity too (pp. 28, 37). The theory does not cover fitted propensities approaching 0 or 1 — see the trimming Note below.
 - **Stationary RCS sampling (Assumption 2.3, `panel=False` only):** conditional on `T = 0` (resp. `T = 1`), rows are i.i.d. draws from the distribution of `(Y(0), D, X)` (resp. `(Y(1), D, X)`) — each wave samples the same target population, so the composition of `(D, X)` is stable across waves while outcomes are the period-specific potential outcomes (trends and treatment effects are expected, not violations). Not data-checkable; surfaced as a fit-time `UserWarning` after the declared-RCS structure validates.
 - **First-stage rate condition (Assumptions 3.1(f) (Case 1) / 3.2(h) (Case 2) + Theorem 1):** BOTH conditions hold jointly — the bundle envelope `‖η̂_k - η_0‖_{P,2} ≤ ε_N` with `ε_N = o(N^{-1/4})` (each nuisance component must meet the rate; a fast learner cannot compensate a slow one), AND the product bound `‖ĝ - g_0‖²_{P,2} + ‖ĝ - g_0‖_{P,2}·‖ℓ̂ - ℓ_0‖_{P,2} ≤ ε_N²`. Not detectable at runtime; documented.
@@ -3209,6 +3247,206 @@ the finite-dimensional `p_0` is handled by the variance correction below.
 
 - **Note:** Chang §4.2 simulation-DGP replication scope (PR-B2). The §4.2.2 kernel-design RCS DGP (arXiv v3 p. 19) is replicated verbatim in `tests/test_methodology_dml_did.py`, estimated with the library's NATIVE learners rather than the paper's Gaussian-kernel first stages (no kernel first stage is bundled); the fixture is correctly specified on both nuisances (true propensity `sigmoid(X − 1/2)` by Bayes' rule; true `ℓ₂₀ = 0.25·X`), so it validates paper-DGP faithfulness — the discriminating assertion compares against the design's own confounded unadjusted contrast (→ θ₀ + 1), not against a misspecified learner. The design's unbounded X means the a.s. strict-overlap Assumption 3.2(a) holds for no fixed κ > 0 (mass outside [0.01, 0.99] ≈ 2.1e-5 — immaterial at the fixture Ns; the same quirk applies more strongly to §4.2.1, tail ≈ 0.06%). The §4.2.1 ML design is NOT replicable with the bundled unpenalized learners: at (N=500, p=100) the native logit+linear stack is order-of-magnitude noise across seeds (SE ~4-10; `solve_logit` EPV ~1.4-1.6 vs threshold 10; fitted out-of-fold clipping ~5-29% of rows — estimated propensities, not true ones, whose out-of-[0.01, 0.99] mass is ≈0.06%), and at (N=200, p=100) the linear outcome learner fails closed on control-fold rank deficiency even under an oracle propensity (ridge/sieve fit there) — tracked in TODO.md (penalized propensity learner + p-robust outcome learner).
 
+**Bad-control extension (CCPS 2026): `fit(..., bad_control=, bad_control_covariates=)`.**
+
+**Source:** Caetano, C., Callaway, B., Payne, S., & Sant'Anna, H. (2026).
+Difference-in-differences with "bad controls". arXiv:2608.03881v2 +
+Supplementary Appendix v1 (paper review on file:
+`docs/methodology/papers/caetano-2026-review.md`; a deliberate exception to
+the published-source rule, recorded there). The authors' GPL-3 R package
+`badcontrols` is used ONLY as an executed black-box oracle
+(`benchmarks/R/generate_badcontrols_golden.R`); the lane is derived from the
+paper alone.
+
+A "bad control" `X_t` is a time-varying covariate that treatment can affect.
+Conditioning on `X_t` biases DiD (the paper's Section 3.1 "include the bad
+control" bias); conditioning on the PRE-treatment value `X_{g-1}` alone is the
+paper's Approach 1 (Theorem 1 / Proposition 3), already available by passing
+the bad control in `covariates` on the panel lane (read at the cell's base
+period; see the CallawaySantAnna Note). This lane implements Approach 2:
+parallel trends conditional on the bad control's UNTREATED path (MP-4,
+reduced to `(X_{g-1}, X_t(0))` by MP-7) plus covariate unconfoundedness for
+the bad control's untreated evolution given `(X_{g-1}, W, Z)` (Assumption 6 /
+MP-5) and overlap (Assumption 7 / MP-6), estimated with the paper's
+Neyman-orthogonal doubly-robust score (Equation 10 / 11, Algorithm 1,
+Propositions 5-7), applied per CS `(g, t)` cell (Proposition 2 / SB.3).
+
+*Per-cell estimator (panel lane, as implemented - `ccps_panel_score`):* with
+`dY = Y_t − Y_base`, `xt` / `xb` the bad control at `t` / at the base period,
+`Z` = `covariates` at base, `W` = `bad_control_covariates` at base (the
+outcome name in `W` means `Y_base`), `R = [xt, xb, Z]`, `S = [xb, W, Z]`,
+`π̂ = p̂` = the cell's treated share::
+
+    m̂(R)   = cross-fitted E[dY | R, D=0]                       (outcome_learner, controls)
+    p̂(S)   = cross-fitted P(D=1 | S), clipped to [trim, 1−trim] (propensity_learner)
+    ν̂(S)   = nested: fold-k m̂ predictions on training controls, regressed on S
+    ω̂(R)   = nested: fold-k odds p̂/(1−p̂) (clipped by pscore_trim) on training controls,
+              regressed on R, then clipped to [0, (1−trim)/trim]
+    summand = (D/π̂) dY − (D/π̂) ν̂ − ((1−D)/π̂)(m̂ − ν̂) p̂/(1−p̂) − ((1−D)/π̂)(dY − m̂) ω̂
+    θ̂ = mean(summand);  ψ̄ = summand − D θ̂/π̂;  SE = sqrt(mean(ψ̄²)/n_cell)
+
+With `ν̂ = m̂` and `ω̂ = p̂/(1−p̂)` the summand is `chang_panel_score` verbatim
+(pinned at 1e-14 in `tests/test_methodology_dr_scores.py`); the centering is
+`chang_panel_score_augmented`, so the SE / cluster / t-inference tail is the
+plain lane's, unchanged.
+
+*ATT_X(g, t) diagnostic (Remark 6; `results.bad_control_summary()`,
+`results.bad_control_diagnostics`):* `E[X_t(g) − X_t(0) | G = g]` is identified
+by Assumption 6 / MP-5 plus overlap (Lemma 3 reduces the conditioning set to
+the cell base `X_{g-1}` for `t > g`) as an ATT on LEVELS of `X_t` with `S` as
+the conditioning set (the paper's p. 31 application form), and estimated as
+the AIPW `chang_panel_score(xt, D, μ̂_X, p̂, π̂)` with `μ̂_X` the cross-fitted
+control regression of `xt` on `S`; SE from its own augmented-score payload
+through the same branch (and the same `df`) as the ATT. It is a MEAN-effect
+diagnostic whose reading depends on the period (Remark 6, review lines
+100-103 and 126-130): POST-period cells (`t ≥ g`) are one-sided evidence for
+Condition 2 (a nonzero post-period ATT_X shows treatment affects the
+control), silent on Condition 1, and a zero value is not evidence that the
+control is good; PRE-period cells (`t < g`) are the pre-test of the
+identifying assumptions MP-5 / MP-8 (covariate unconfoundedness for the bad
+control's untreated evolution) and should be zero - a nonzero pre-period
+ATT_X flags a possible violation of those assumptions, NOT a bad control.
+Not the SC / S17 "parallel trends for X" estimand.
+
+- **Note:** Nested-stage convention. The paper's Algorithm 1 leaves the
+  nested pseudo-outcome construction to the practitioner (footnote 9 warns
+  against in-sample first-stage fits for ML learners). Library: when BOTH
+  learners are the parametric built-ins (`"linear"` / `"logit"` strings or the
+  exact `LinearLearner` / `LogitLearner` objects; `_is_parametric_learner_spec`)
+  the nested targets are the fold-k first-stage model's IN-SAMPLE predictions
+  on its training units - for `LinearLearner` this is exactly Assumption 8's
+  plug-in (OLS of `R'β` on `S` equals `β₁·OLS(xt ~ S) + β₂ xb + β₃ Z`, pinned
+  by `TestCCPSPlugInIdentity`), i.e. the paper's own parametric DR estimator.
+  Otherwise (`ridge`, `sieve`, native subclasses, any user learner) the
+  training complement of each outer fold is split in half
+  (`assign_folds(n_train, 2, ...)`, one RNG draw per outer fold in ascending
+  `k`, AFTER the cell's fold draw, using the cell's resolved fold mechanism -
+  PSU-cohesive under `cluster=`, else `D`-stratified); the first stage is fit
+  on half A, targets and nested fits on half B's controls, swapped, and the
+  two nested models' held-out predictions averaged (footnote 9). The score's
+  `m̂` / `p̂` on the held-out fold always come from the full-complement fits.
+  `cross_fit_diagnostics[(g,t)]["nested_stage"]` records `"in_sample"` /
+  `"split_half"`; the split-half branch needs ≥ 2 controls per stratum per
+  half (or ≥ 2 PSUs) and skips small cells as `cross_fit_degenerate` more
+  often than the plain lane.
+- **Note:** `ω̂` boundedness (documented deviation). Assumption S2(iv) bounds
+  `ω_0`; the paper gives no rule for the estimated odds projection, which a
+  linear regression on `R` can push negative or above the overlap bound.
+  Library: the nested target uses the fold-k propensity clipped by
+  `pscore_trim` (so the target lies in `[trim/(1−trim), (1−trim)/trim]`) and
+  `ω̂` is clipped to `[0, (1−trim)/trim]` with a `UserWarning` when any entry
+  is clipped; `n_clipped_omega` is recorded per cell.
+- **Note:** `W` default and Remark 5. `bad_control_covariates=None` (default)
+  means NO `W` (`S = [xb, Z]`, matching R `badcontrols`'s
+  `bad_control_cov_formula = NULL`); results store `()`. Remark 5's
+  `W = Y_{g-1}` is the recommended explicit choice via
+  `bad_control_covariates=[outcome]`. `W` names may not overlap `covariates`
+  or the bad control (one role per column).
+- **Note:** Base-period semantics (varying base only). Post cells (`t ≥ g`)
+  read `xb` / `W` at the observed period immediately preceding `g` - exactly
+  Remark 5's `X_{g-1}` / `Y_{g-1}`. Pre-period varying-base pseudo-cells
+  (`t < g`) read them at the period preceding `t`, so `W = Y_{t-1}` there by
+  construction of the CS pre-period pseudo-ATT (Remark 6 computes "the same
+  estimand as in Proposition 2 but for pre-treatment periods"; the paper's
+  own pre-period base is the immediately preceding period, Figures 6-7).
+  Remark 5 rejects `Y_{t-1}` only for POST cells: on a pre-period cell
+  `t − 1 < g`, so `Y_{t-1} = Y_{t-1}(0)` IS observed for group `g`, and its
+  second objection (feedback from treatment to the bad control through the
+  outcome) is inapplicable because no unit in the cell has been treated yet.
+  `base_period="universal"` fails closed (`NotImplementedError`): under a
+  universal base a pre cell with `t < g − 1` would read `xt` EARLIER than
+  `xb` / `W`, inverting the `X_t` / `X_{t-1}` ordering MP-5 conditions on
+  (DEFERRED.md, paper-gated).
+- **Note:** Anticipation fails closed (`anticipation != 0` →
+  `NotImplementedError`): MP-2 assumes no anticipation for `Y` AND `X`, and
+  the paper does not develop the limited-anticipation base-period convention
+  for `X` / `W` (DEFERRED.md, paper-gated).
+- **Note:** `π̂` = the cell's treated share `n_g / n_cell` (the plain lane's
+  `p̂` convention; the paper's global `π̂` in the two-period case - review Gap
+  11). Intercepts are the learners' own (review Gap 19).
+- **Note:** Repeated cross sections and survey designs fail closed.
+  `panel=False` + `bad_control` → `NotImplementedError` (Remark 1: the
+  approach is "to a large extent" unavailable with repeated cross sections
+  because `X_{g-1}` and `X_t` must be observed for the same unit; RCS lanes
+  read covariates on the observation's own row, so a time-varying bad
+  control there IS `X_t`). `survey_design=` + `bad_control` →
+  `NotImplementedError` (the nested stages under design weights and replicate
+  variances are unvalidated; DEFERRED.md). Bare `cluster=` IS supported
+  (PSU-cohesive folds and halves, CR1 per-cell SE, `df_survey` t-inference;
+  a single-PSU cluster column yields NaN inference for the ATT and ATT_X of
+  every retained cell, the lonely-PSU carve-out).
+- **Note:** Complete-case policy. A unit joins a cell only if `dY`, `Z_base`,
+  `xt`, `xb` and `W_base` are all finite - ONE rule for both groups. Treated
+  `xt` is load-bearing for the ATT itself (`m̂` and `ω̂` are evaluated on
+  `R = [xt, xb, Z]` for every unit and the score validator rejects
+  non-finite entries), not only for ATT_X. The unbalanced-input warning
+  names the bad-control columns. Under bare `cluster=` a treated unit dropped
+  for a non-finite `xt` makes `aggregate("total")` raise the existing
+  "incomplete treated support" `NotImplementedError` (the `_cs_total_mass`
+  coincidence guard).
+- **Note:** Time-invariant bad control. If `xt − xb` is constant within a
+  cell (including `xt == xb`), `R = [xt, xb, Z]` is rank-deficient once the
+  learner prepends its intercept; no up-front skip - the learners' own rank
+  guards decide (`LinearLearner` fails closed → `cross_fit_degenerate`;
+  `RidgeLearner` / user learners proceed). A zero `ATT_X` from such a column
+  is not evidence against Condition 2.
+- **Note:** Value collinearity between `W = Y_base` and a lagged-outcome
+  column in `Z` (names are rejected; values are not) fails the cell closed on
+  the native lane because `S` is the PROPENSITY design and the only native
+  classifier is the unpenalized `LogitLearner`.
+- **Note:** Empty `Z` is not allowed (the paper's `Z` may be empty; DMLDiD's
+  pre-existing "covariates are REQUIRED" contract stands; TODO.md).
+- **Note:** Binary bad control: LPM regressions on `xt`; ATT_X is a risk
+  difference; no special handling (R's `bad_control_binary` is unused on its
+  DR path too).
+- **Note:** Aggregation weights (deviation: headline weighting differs from
+  Remark 4). The headline `att` is the CS "simple" post-treatment average
+  exactly as on the plain lane (each post cell weighted by its complete-case
+  `n_treated` on no-design fits, by fixed cohort mass under `cluster=`; every
+  post cell of a cohort enters, so early cohorts carry more total weight).
+  The paper's Remark 4 overall
+  `ATT^o = Σ_{g∈Ḡ} Σ_{t=g}^{T} [P(G=g | G∈Ḡ)/(T−g+1)] ATT(g,t)` (cohort mass
+  among the ever-treated divided by the cohort's number of post periods) is
+  NOT exposed by any current aggregation (`aggregate("group")` returns one
+  row per cohort and never forms a cross-cohort mass; TODO.md). ATT_X is
+  never aggregated or bootstrapped: on bootstrapped fits the cell `se` is the
+  bootstrap SE while `se_x` stays analytical (`summary()` says so;
+  `to_dataframe()` joins `att_x` / `se_x` at `level="group_time"` only).
+  Calendar-time aggregation is not supported (DEFERRED.md
+  "Calendar-time aggregation").
+- **Note:** ATT_X inference assumptions. The plug-in `mean(ψ_X²)` variance is
+  valid under the same cross-fitting and product-rate conditions as the ATT
+  (Assumption 9-type); under a misspecified parametric nuisance it is the
+  usual DR plug-in approximation, exactly as for the ATT. A degenerate `μ̂_X`
+  cross-fit or a non-finite ATT_X score leaves every ATT_X inference field
+  NaN and never skips the cell.
+- **Note:** Validation scope. (i) `tests/test_methodology_dr_scores.py::TestCCPSScore`:
+  oracle recovery, PAIRED double robustness (`(m, ν)` vs `(p, ω)`; single
+  swaps are not robust), four-direction Neyman orthogonality against
+  purpose-built non-orthogonal comparators, the reduction to
+  `chang_panel_score`, the augmented identity. (ii) `tests/test_methodology_dml_did.py`:
+  numpy oracle of Equation 11 / Algorithm 1 (folds re-derived from the same
+  spawned seed, in-sample nested targets; `rtol=1e-12` on ATT, SE and ATT_X),
+  oracle user learners on the split-half branch (closed-form score mean at
+  1e-12), the Assumption-8 plug-in identity, and the Supplementary Appendix's
+  DGP 1 / DGP 4 (the two the parametric DR is consistent on, Table S1)
+  with seed-pinned recovery of `ATT = 1.00` and `ATT_X = λ = 0.50`, a
+  discriminating naive include-`X_t` contrast, and slow MC coverage;
+  DGPs 2 / 3 / 5 need a flexible-learner fixture (TODO.md). (iii) R
+  `badcontrols` 1.0.0 (commit `651ccc92`; ptetools 1.0.0) black-box goldens
+  (`tests/test_dml_did_bad_controls_parity.py`): `didbc()` cross-fits with its
+  own fold draw (`nfolds=1` errors) and its single-seed fold noise is up to
+  ~0.5 analytical SE on the smallest cells, so both sides are averaged over
+  10 seeds and parity is TOLERANCE-based: `|Δatt| < 0.5 SE_R` per cell and
+  `|se_py/SE_R − 1| < 0.3` on the two `W=[W]` runs and the `W=[Y]` post
+  cells; `W=[Y]` pre cells and the no-bad-control run (R's `dr_ml` path is
+  not the plain Chang score) at 1.0 SE as characterizations. Observed
+  single-seed gaps are ≤ 0.63 SE (cell `(4,4)`, `W=[Y]`, n = 500; both
+  implementations' 10-seed means agree within 0.1 SE there) and SE ratios
+  within 1.25. (iv) `bad_control=None` is the pre-existing code path
+  (dispatch precedes all new code; `TestBadControlAPI` pins bit-identity of
+  every payload).
+
 **Requirements checklist (shipped Case 1 panel + Case 2 RCS staggered lanes):**
 - [x] Neyman-orthogonal Case 1 score (3.1) implemented exactly (Abadie score + mean-zero adjustment; `chang_panel_score`)
 - [x] DML2 cross-fitting: per-cell K-fold partition, nuisances fit on fold complements, never on the evaluation fold
@@ -3221,6 +3459,9 @@ the finite-dimensional `p_0` is handled by the variance correction below.
 - [x] Validation: 2-period DoubleMLDID + staggered per-cell DoubleMLDIDBinary parity spikes (version-pinned, committed, golden literals consumed in-tests) + oracle-nuisance closed-form equivalence + degenerate-cell hand-pipeline equivalence (rtol 1e-14 — BLAS reduces differently-laid-out inputs in platform-dependent order, so bit identity does not hold cross-platform) + Monte Carlo coverage sanity
 - [x] Case 2 (repeated cross sections): Equation 3.2 score + λ-corrected Theorem 2 variance — SHIPPED as `DMLDiD(panel=False)` (`chang_rcs_score` / `chang_rcs_lambda_slope` / `chang_rcs_score_augmented`; equation-level fixtures, oracle closed forms, derivative-identity checks, DR both directions, characterization spike, MC coverage). The paper's own §4.2.2 kernel-design RCS DGP is replicated (`tests/test_methodology_dml_did.py` "Chang Sec. 4.2.2" section: DGP-shape pin, seed-pinned recovery at both paper Ns with a discriminating comparison against the design's confounded unadjusted contrast, slow MC coverage — see the §4.2 replication Note below); the §4.2.1 ML design is not replicable with the bundled learners (narrowed TODO.md row).
 - [ ] Case 3 (multilevel treatment): deferred (`DEFERRED.md`; implementation-required overlap conditions per the paper review's Case 3 caution)
+- [x] Bad-control lane (Caetano et al. 2026 Eq. 10 / 11, Algorithm 1): `ccps_panel_score` / `ccps_panel_score_augmented`, nested `ν̂` / `ω̂` stages (parametric in-sample = Assumption-8 plug-in; split-half otherwise), `ω̂` clip, per-cell `ATT_X(g,t)` diagnostic, panel + `cluster=` only, varying base + `anticipation=0` only (Notes above)
+- [x] Bad-control validation: score-level DR / orthogonality / reduction, numpy Eq. 11 oracle, split-half oracle learners, SA DGP 1 / 4 recovery + MC coverage, R `badcontrols` black-box goldens (tolerance-based; Validation-scope Note)
+- [ ] Bad-control imputation estimator (Section 6.1, Eqs. 5-7, S8 IF), SC "PT for X" variant, Remark-4 overall weighting, ATT_X event study, RCS / anticipation / universal-base / survey lanes: TODO.md / DEFERRED.md rows
 
 ---
 
diff --git a/docs/methodology/REPORTING.md b/docs/methodology/REPORTING.md
index 71bcf94f1..bf11dc8d5 100644
--- a/docs/methodology/REPORTING.md
+++ b/docs/methodology/REPORTING.md
@@ -290,6 +290,23 @@ a library setting.
   identification narrative is likewise design-aware: RCS fits cite the
   stationary-sampling Assumption 2.3 and the Case 2 rate package.
 
+- **Note:** DMLDiD bad-control fits (`results.bad_control` set; Caetano,
+  Callaway, Payne & Sant'Anna 2026) take a separate identification branch
+  in `business_report.py`: the description names parallel trends
+  conditional on the covariates AND the bad control's untreated path
+  (MP-4, reduced by MP-7) with the bad control's untreated evolution
+  identified by covariate unconfoundedness given its pre-treatment value,
+  `W` and `Z` (Assumption 6 / MP-5), the panel-only restriction, and
+  Assumption 9's product rates; `_references_for(estimator_name, results)`
+  appends a second estimator-role citation entry for Caetano et al.
+  (2026) after Chang (2020). The target-parameter block (`_reporting_helpers.py`)
+  names the Eq. 10 score with the pre-treatment bad control (and the `W`
+  list only when non-empty) and its reference string is
+  "Caetano et al. (2026); Chang (2020); REGISTRY.md Sec. DMLDiD". The
+  practitioner learner-sensitivity snippet carries `bad_control=` /
+  `bad_control_covariates=` inside `.fit(` and `control_group=` inside
+  `DMLDiD(...)` on such fits.
+
   The simple 2x2 parallel-trends helper (`utils.check_parallel_trends`)
   has no survey-aware variant. On a survey-backed `DiDResults` the
   check is skipped **unconditionally**, regardless of whether
diff --git a/docs/methodology/papers/caetano-2026-review.md b/docs/methodology/papers/caetano-2026-review.md
index 35173169c..12b25d2ed 100644
--- a/docs/methodology/papers/caetano-2026-review.md
+++ b/docs/methodology/papers/caetano-2026-review.md
@@ -1175,9 +1175,9 @@ Headline findings (authors' summary, SA pp. 16-17, with table facts):
 **Requirements checklist:**
 
 Approach 1 (Theorem 1 / Proposition 1 / Proposition 3 - docs + CallawaySantAnna):
-- [ ] Document that passing the PRE-treatment bad control (read at base period `g - 1`) plus `Z` as CallawaySantAnna covariates computes the Proposition 3 estimand (two-period: Theorem 1 / Proposition 1), and state Assumptions 4 / 5 (MP-8 / MP-9) explicitly
-- [ ] Guard: the post-treatment bad control must NOT be in the covariate set (`τ^use` bias); warn or refuse when a time-varying covariate is read at `t` rather than `g - 1`
-- [ ] Pre-test surface: pre-period pseudo-`ATT(g, t)` (existing CS pre-period cells) and `ATT_X(g, t)` (bad control as outcome)
+- [x] Document that passing the PRE-treatment bad control (read at base period `g - 1`) plus `Z` as CallawaySantAnna covariates computes the Proposition 3 estimand (two-period: Theorem 1 / Proposition 1), and state Assumptions 4 / 5 (MP-8 / MP-9) explicitly
+- [x] Guard: the post-treatment bad control must NOT be in the covariate set (`τ^use` bias); warn or refuse when a time-varying covariate is read at `t` rather than `g - 1` (DMLDiD refuses `bad_control` in `covariates`; on the PANEL lane CS/DMLDiD read `covariates` at the base period, so Approach 1 is the user's responsibility to pass the pre-treatment value and no library guard can detect a post-treatment column there; RCS lanes read covariates at `t` and are out of scope)
+- [x] Pre-test surface: pre-period pseudo-`ATT(g, t)` (existing CS pre-period cells) and `ATT_X(g, t)` (bad control as outcome) (per-cell ATT_X; no event study)
 
 Imputation estimator (Section 6.1):
 - [ ] Untreated-only OLS of `ΔY` on `(X_{t*}, X_{t*-1}, Z)` and of `X_{t*}` on `(X_{t*-1}, W, Z)`; `ν̂_0` by plug-in (Eq. 5 under Assumption 8); `ATT̂_ra = m̂_1 - τ̂_ra` (Eqs. 6-7)
@@ -1185,33 +1185,33 @@ Imputation estimator (Section 6.1):
 - [ ] Rank / positive-definiteness checks on the two untreated design matrices (Assumption S1(ii)); NaN inference via `safe_inference()` when violated
 
 DR estimator, parametric (Section 6.2):
-- [ ] Score `φ_1` (Eq. 10) exactly; sample analog Eq. 11; `π̂` global
-- [ ] Nuisances: `m_0` (untreated OLS), `ν_0` (nested plug-in), `p` (logit on ALL units, on `(X_{t*-1}, W, Z)`), `ω_0` (untreated OLS of fitted odds on `(X_{t*}, X_{t*-1}, Z)`)
-- [ ] Variance `V̂_dr` from `φ̂_i = φ̂_{1,i} - ATT̂_dr - (ATT̂_dr/π̂)(D_i - π̂)` (Algorithm 1 step 4); `se = √(V̂_dr/n)`; no DoF correction
-- [ ] Overlap enforcement on `p̂` (away from 1) and boundedness of `ω̂_0` - implementation-chosen rule, documented deviation
-- [ ] Double-robustness tests: correct `(m_0, ν_0)` with wrong `(p, ω_0)` and vice versa (Proposition 6 pairing)
+- [x] Score `φ_1` (Eq. 10) exactly; sample analog Eq. 11; `π̂` = the cell's treated share (`n_g/n_cell`; the paper's global `π̂` in the two-period case)
+- [x] Nuisances: `m_0` (untreated OLS), `ν_0` (nested plug-in), `p` (logit on ALL units, on `(X_{t*-1}, W, Z)`), `ω_0` (untreated OLS of fitted odds on `(X_{t*}, X_{t*-1}, Z)`)
+- [x] Variance `V̂_dr` from `φ̂_i = φ̂_{1,i} - ATT̂_dr - (ATT̂_dr/π̂)(D_i - π̂)` (Algorithm 1 step 4); `se = √(V̂_dr/n)`; no DoF correction
+- [x] Overlap enforcement on `p̂` (away from 1) and boundedness of `ω̂_0` - implementation-chosen rule, documented deviation (`pscore_trim` clip; `ω̂` clipped to `[0, (1-trim)/trim]` with a warning; REGISTRY Note)
+- [x] Double-robustness tests: correct `(m_0, ν_0)` with wrong `(p, ω_0)` and vice versa (Proposition 6 pairing)
 
 DR estimator, ML / cross-fitting (Algorithm 1):
-- [ ] K-fold partition; per-fold first stage (`m̂_0^{-k}` untreated, `p̂^{-k}` all) then nested second stage (`ν̂_0^{-k}`, `ω̂_0^{-k}` untreated) on `I_{-k}`; score on `I_k`
-- [ ] Pseudo-outcome overfitting control for the nested stage (OOB predictions or a further split of the training fold - footnote 9)
-- [ ] Pluggable regressor / classifier learners; document the `o_p(n^{-1/4})` requirement (Assumption 9)
-- [ ] Degenerate-fold guards (no untreated rows in a training complement; no treated rows)
+- [x] K-fold partition; per-fold first stage (`m̂_0^{-k}` untreated, `p̂^{-k}` all) then nested second stage (`ν̂_0^{-k}`, `ω̂_0^{-k}` untreated) on `I_{-k}`; score on `I_k`
+- [x] Pseudo-outcome overfitting control for the nested stage (OOB predictions or a further split of the training fold - footnote 9) (split-half for `ridge` / `sieve` / user learners; the parametric `linear`/`logit` branch uses in-sample fold-k targets = the paper's own parametric plug-in, REGISTRY Note)
+- [x] Pluggable regressor / classifier learners; document the `o_p(n^{-1/4})` requirement (Assumption 9)
+- [x] Degenerate-fold guards (no untreated rows in a training complement; no treated rows)
 
 Staggered cells + aggregation (Section 5, SB.3):
-- [ ] Per-(g,t) substitution: `Y_t - Y_{g-1}`, `X_t`, `X_{g-1}`, `W = Y_{g-1}` default (Remark 5), not-yet-treated (default) or never-treated comparison
-- [ ] Per-cell IFs `ψ_{g,t}` / `φ_{g,t}`; aggregation IF `ξ_θ` with estimated-weight terms `ξ^w_{g,t}` (CS 2021 conventions); simple / group / event-study / calendar aggregations
-- [ ] Drop already-treated group; require no group treated in period 1
+- [x] Per-(g,t) substitution: `Y_t - Y_{g-1}`, `X_t`, `X_{g-1}`, `W = Y_{g-1}` (Remark 5; library: opt-in via `bad_control_covariates=[outcome]`, default no `W`), not-yet-treated (the paper's Proposition 2 choice) or never-treated comparison (library default `control_group="never_treated"`; set `"not_yet_treated"` for Proposition 2) (anticipation fails closed)
+- [x] Per-cell IFs `ψ_{g,t}` / `φ_{g,t}`; aggregation IF `ξ_θ` with estimated-weight terms `ξ^w_{g,t}` (CS 2021 conventions); simple / group / event-study / calendar aggregations (simple / group / event-study; calendar not supported by CS/DMLDiD, DEFERRED.md 'Calendar-time aggregation' row; the headline `att` is CS simple, not Remark 4's overall - TODO.md)
+- [x] Drop already-treated group; require no group treated in period 1 (a first-period cohort has no base period and is skipped as `missing_period` with the consolidated warning; not a hard error)
 
 Pre-tests and guards:
-- [ ] Pre-period pseudo-`ATT(g, t)` with base = immediately preceding period (Figure 6/7 convention)
+- [x] Pre-period pseudo-`ATT(g, t)` with base = immediately preceding period (Figure 6/7 convention)
 - [ ] `ATT_X(g, t)` estimator (bad control as outcome) with event study; estimand convention documented (the paper writes none)
-- [ ] Panel-only: fail closed for repeated cross-sections (Remark 1)
-- [ ] Balanced-panel / missing-data policy (paper: complete cases only)
+- [x] Panel-only: fail closed for repeated cross-sections (Remark 1)
+- [x] Balanced-panel / missing-data policy (paper: complete cases only) (library: per-cell complete cases incl. treated `X_t`)
 
 Validation:
-- [ ] Recovery tests on the SD DGPs 1-5 (true ATT = 1.00) matching Tables S2-S6 qualitatively (bias, SE/SD, coverage)
-- [ ] Black-box parity against R `badcontrols` on a shared fixture (no source porting)
-- [ ] Reduction test: with no bad control and no `W`, the DR score reduces to the Chang (2020) panel DR score DMLDiD computes (see Relation section)
+- [x] Recovery tests on the SD DGPs 1-5 (true ATT = 1.00) matching Tables S2-S6 qualitatively (bias, SE/SD, coverage) (DGP 1 and DGP 4, parametric DR; DGPs 2/3/5 need a flexible-learner fixture, TODO row)
+- [x] Black-box parity against R `badcontrols` on a shared fixture (no source porting)
+- [x] Reduction test: with no bad control and no `W`, the DR score reduces to the Chang (2020) panel DR score DMLDiD computes (see Relation section)
 
 ---
 
@@ -1219,19 +1219,22 @@ Validation:
 
 ### Data Structure Requirements
 - **Balanced panel**, one row per unit-period (MP-3; the application requires non-missing
-  data in every period). Columns: outcome `Y_it`; unit id; time `t`; first-treatment group
+  data in every period) (library: per-cell complete cases). Columns: outcome `Y_it`; unit id; time `t`; first-treatment group
   `G_i` (never-treated coded `∞`, e.g. `0`/`NaN` in the library convention); bad control
   `X_it` (time-varying, scalar in the paper); `Z_i` (pre-treatment/baseline or exogenous
   time-varying covariates - the staggered notation carries a single `Z_i` per unit); `W_i`
-  (pre-treatment confounders of `X`, per unit; default `W = Y_{g-1}`).
+  (pre-treatment confounders of `X`, per unit; default `W = Y_{g-1}`) (library: opt-in via
+  `bad_control_covariates=[outcome]`; default no `W`).
 - **"Pre-treatment value" is cell-specific:** for cell `(g, t)` the bad control is read at
   `t` (inner nuisance only) and at the base period `g - 1` (both nuisances and the
   propensity); `W = Y_{g-1}` is the outcome at the group's base period, NOT `t - 1`
-  (Remark 5). Two-period case: `t* - 1` and `t*`.
+  (Remark 5) (library: varying-base pre-period pseudo-cells read `Y_{t-1}`, REGISTRY Note).
+  Two-period case: `t* - 1` and `t*`.
 - **Comparison units per cell:** not-yet-treated (`G > t`, includes never-treated) for
   Propositions 2-3; never-treated only for Theorem 3. Treated units in the cell: `G = g`.
 - Treatment must be absorbing (MP-1); no anticipation for `Y` AND `X` (MP-2); no group
-  treated in period 1; already-treated units dropped.
+  treated in period 1 (library: such a cohort is skipped as `missing_period` with a
+  warning); already-treated units dropped.
 - Panel only; repeated cross-sections must fail closed (Remark 1).
 
 ### Computational Considerations
@@ -1255,7 +1258,9 @@ Validation:
 - Aggregation: per-unit IF vectors across cells (`ψ_{g,t}` / `φ_{g,t}`) plus weight IFs
   `ξ^w_{g,t}`; memory `O(n x cells)` as in CallawaySantAnna.
 - Never fit a nuisance on the fold it is evaluated on; the nested-stage pseudo-outcome
-  should not be the in-sample first-stage fit (footnote 9).
+  should not be the in-sample first-stage fit (footnote 9) (library: split-half for
+  `ridge` / `sieve` / user learners; the parametric `linear`/`logit` branch uses the
+  in-sample plug-in, which is the paper's own parametric estimator, REGISTRY Note).
 
 ### Tuning Parameters
 
@@ -1281,7 +1286,7 @@ separate from the paper's claims.
   (positional; "varying" / "universal"); never-treated or not-yet-treated controls;
   covariates read at the cell's BASE PERIOD; estimation methods `reg` / `ipw` / `dr`
   (Sant'Anna and Zhao 2020); multiplier bootstrap; aggregations (simple, group, event
-  study, calendar). **Consequence:** Approach 1 (Theorem 1 / Proposition 1 / Proposition 3)
+  study; calendar is not supported, DEFERRED.md). **Consequence:** Approach 1 (Theorem 1 / Proposition 1 / Proposition 3)
   is ALREADY computable by passing the bad control in `covariates` (it is read at `g - 1`,
   exactly the paper's `X_{g-1}`); only documentation and the explicit assumptions
   (4 / 5 / MP-8 / MP-9 and the `τ^use` warning) are missing. The paper's Proposition 3
diff --git a/docs/methodology/survey-theory.md b/docs/methodology/survey-theory.md
index 9001b5fd4..bfe174d0d 100644
--- a/docs/methodology/survey-theory.md
+++ b/docs/methodology/survey-theory.md
@@ -481,7 +481,7 @@ The total meat is sum_h V_h, computed by `_compute_stratified_psu_meat()` in
 ### IF-based TSL variance
 
 For scalar IF-based estimators (CallawaySantAnna, ImputationDiD, TwoStageDiD,
-TripleDifference, StaggeredTripleDifference, EfficientDiD, DMLDiD), the variance is
+TripleDifference, StaggeredTripleDifference, EfficientDiD, DMLDiD (bad-control lane: `cluster=` only; `survey_design` raises)), the variance is
 computed directly from per-unit influence function values without the bread
 matrix:
 
@@ -593,7 +593,7 @@ expensive.
 
 diff-diff avoids this for most IF-based estimators (CallawaySantAnna,
 EfficientDiD, ContinuousDiD, TripleDifference, StaggeredTripleDifference,
-DMLDiD) using weight-ratio rescaling: the replicate estimate is computed by
+DMLDiD (bad-control lane: `cluster=` only; `survey_design` raises)) using weight-ratio rescaling: the replicate estimate is computed by
 reweighting the per-unit IF values rather than re-running the estimator.
 The `SurveyDesign` parameter `combined_weights` controls the interpretation:
 
@@ -692,7 +692,7 @@ Each estimator uses one of three variance strategies under survey designs:
 | TwoWayFixedEffects | TSL sandwich | OLS-based, all weight types |
 | MultiPeriodDiD | TSL sandwich | OLS-based, all weight types |
 | CallawaySantAnna | TSL on IFs | pweight only |
-| DMLDiD | TSL on IFs | pweight only; cross-fitted augmented scores; replicate designs: IF-reweighting on augmented scores, per-cell + aggregate; library extension of Chang (2020) i.i.d. theory |
+| DMLDiD | TSL on IFs | pweight only; cross-fitted augmented scores; replicate designs: IF-reweighting on augmented scores, per-cell + aggregate; library extension of Chang (2020) i.i.d. theory (bad-control lane: `cluster=` only; `survey_design` raises) |
 | SunAbraham | TSL sandwich | OLS-based, all weight types |
 | TripleDifference | TSL on IFs | pweight only |
 | StaggeredTripleDifference | TSL on IFs | pweight only |
@@ -729,7 +729,7 @@ For IF-based estimators, the variance computation proceeds as:
 
 Two bootstrap strategies interact with survey designs:
 
-- **Multiplier bootstrap at PSU level** (CallawaySantAnna, DMLDiD,
+- **Multiplier bootstrap at PSU level** (CallawaySantAnna, DMLDiD (bad-control lane: `cluster=` only; `survey_design` raises),
   ImputationDiD, TwoStageDiD, ContinuousDiD, EfficientDiD,
   StaggeredTripleDifference):
   Generates multiplier weights at the PSU level within strata, with FPC
diff --git a/docs/methodology/variance-conventions.md b/docs/methodology/variance-conventions.md
index ee99a8c92..1e020181f 100644
--- a/docs/methodology/variance-conventions.md
+++ b/docs/methodology/variance-conventions.md
@@ -39,6 +39,7 @@ produced wrong figures three separate times while this inventory was drafted).
 | `two_stage_default` | — | None | **legitimate** | L3: Gardner two-stage variance, not the shared CR1 sandwich |
 | `callaway_santanna_default` | — | None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None | **legitimate** | L3: influence-function variance anchored to Stata csdid |
 | `dml_did` | — | None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None | **legitimate** | L3: Chang (2020) Thm 2 augmented-score plug-in variance (per-unit influence function; normal-theory safe_inference on no-design fits; survey_design=/cluster= fits use the design-based CR1/weighted-IF per-cell variance — replicate designs the IF-reweighting per-cell variance — with df=df_survey t-inference outside the shared CR1 sandwich) |
+| `dml_did_bad_control` | — | None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None | **legitimate** | L3: Caetano et al. (2026) Eq. 11 augmented-score plug-in variance (same psi_bar - D*theta/pi centering as Chang Thm 2; per-unit influence function; normal-theory safe_inference on no-design fits; cluster= fits use the CR1 per-cell variance with df=df_survey t-inference) and the per-cell ATT_X diagnostic tuple sharing the same branch and df (one extra safe_inference call per retained cell) |
 | `dml_did_rcs` | — | None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None | **legitimate** | L3: Chang (2020) Thm 2 lambda-corrected augmented-score plug-in variance (Case 2; per-observation influence function; normal-theory safe_inference on no-design fits; survey_design=/cluster= fits use the design-based CR1/weighted-IF per-cell variance — replicate designs the IF-reweighting per-cell variance — with df=df_survey t-inference outside the shared CR1 sandwich) |
 cr1_k is the sorted multiset of K_reference counts reaching the shared
 clustered CR1 denominator — visible columns + the signed cluster_k_adjustment
diff --git a/docs/practitioner_decision_tree.rst b/docs/practitioner_decision_tree.rst
index bec4b5159..871d5cc30 100644
--- a/docs/practitioner_decision_tree.rst
+++ b/docs/practitioner_decision_tree.rst
@@ -577,7 +577,10 @@ The six scenarios above cover the most common business use cases.
   λ-corrected variance). Survey/cluster support on both lanes:
   ``survey_design=`` (pweight full-design TSL or replicate weights via
   IF-reweighting — a documented library extension of Chang's i.i.d.
-  theory) and coarser-than-unit ``cluster=``.
+  theory) and coarser-than-unit ``cluster=``. A covariate that treatment
+  can affect (a "bad control") goes in ``fit(bad_control=...)`` for the
+  Caetano et al. (2026) orthogonal score and the ``ATT_X(g,t)`` pre-test
+  (panel only, ``cluster=`` only).
 
 For the full academic decision tree with all estimators, see :doc:`choosing_estimator`.
 
diff --git a/docs/references.rst b/docs/references.rst
index 5f7f7347d..13f0fcafa 100644
--- a/docs/references.rst
+++ b/docs/references.rst
@@ -301,6 +301,10 @@ Double/Debiased Machine Learning
 
   Neyman-orthogonal DiD scores with DML2 cross-fitting for ML first stages. The Case 1 (repeated outcomes) score pair ``chang_panel_score`` / ``chang_panel_score_augmented`` and the Case 2 (repeated cross sections) family ``chang_rcs_score`` / ``chang_rcs_lambda_slope`` / ``chang_rcs_score_augmented`` ship in ``diff_diff/_dr_scores.py`` (consumed by the shipped ``DMLDiD`` estimator, ``panel=True``/``False``); paper review on file at ``docs/methodology/papers/chang-2020-review.md``. The DoubleML parity anchors are committed at ``benchmarks/doubleml/chang_case1_parity.py`` (2-period) and ``benchmarks/doubleml/chang_staggered_parity.py`` (staggered per-cell); the Case 2 lane has no parity oracle — ``benchmarks/doubleml/chang_rcs_characterization.py`` documents the divergence from DoubleML's Sant'Anna-Zhao-style RCS score.
 
+- **Caetano, C., Callaway, B., Payne, S., & Sant'Anna, H. (2026).** "Difference-in-differences with 'bad controls'." arXiv:2608.03881 (v2, with Supplementary Appendix v1). https://arxiv.org/abs/2608.03881
+
+  Identification with covariates that treatment can affect. Approach 1 (parallel trends given the pre-treatment bad control, Theorem 1 / Proposition 3) is computable by passing the bad control in ``CallawaySantAnna`` / ``DMLDiD`` ``covariates`` on the panel lane; the covariate-unconfoundedness approach (Theorem 2) ships as the ``DMLDiD`` bad-control lane - ``fit(..., bad_control=, bad_control_covariates=)`` - with the Neyman-orthogonal doubly-robust score ``ccps_panel_score`` / ``ccps_panel_score_augmented`` (Equations 10-11, Algorithm 1) in ``diff_diff/_dr_scores.py`` and the per-cell ``ATT_X(g,t)`` pre-test (Remark 6). Paper review on file at ``docs/methodology/papers/caetano-2026-review.md`` (a deliberate exception to the published-source rule); black-box parity against the authors' GPL-3 R package ``badcontrols`` (executed only, never read) at ``benchmarks/R/generate_badcontrols_golden.R`` / ``tests/test_dml_did_bad_controls_parity.py``.
+
 - **Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., & Robins, J. (2018).** "Double/Debiased Machine Learning for Treatment and Structural Parameters." *The Econometrics Journal*, 21(1), C1-C68. https://doi.org/10.1111/ectj.12097
 
   The DML2 cross-fitting algorithm and Neyman-orthogonality framework that ``diff_diff/_crossfit.py`` implements at the fold level (unit/cluster-level replayable K-fold assignment, out-of-fold nuisance prediction).
diff --git a/docs/survey-roadmap.md b/docs/survey-roadmap.md
index ffdb16b8d..84607a4f0 100644
--- a/docs/survey-roadmap.md
+++ b/docs/survey-roadmap.md
@@ -278,6 +278,7 @@ the limitation and suggested alternative.
 | ImputationDiD | `pretrend_test()` + replicate weights | Use analytical survey design instead |
 | DiD, TWFE | `inference='wild_bootstrap'` + `survey_design` | Use analytical survey inference (default) |
 | EfficientDiD | `cluster` + `survey_design` | Use `survey_design` with PSU/strata |
+| DMLDiD | `fit(bad_control=...)` + `survey_design` | The Caetano et al. (2026) bad-control lane raises `NotImplementedError` under any `survey_design` (nested second-stage nuisances under design weights and replicate variances are unvalidated; DEFERRED.md). Use bare `cluster=` (PSU-cohesive folds, CR1 per-cell SE, t-inference) without a `survey_design`. |
 | WooldridgeDiD | Unsupported-period filtering + `survey_design` | Restrict the frame to the supported periods explicitly and re-fit. Deleting rows in-place is naive subsetting: it removes their PSUs and strata from the TSL meat and from `df_survey = n_PSU - n_strata`. Exact only if every PSU and stratum survives the restriction (true on a balanced panel; NOT in general — an unbalanced frame can hold a PSU observed only at unsupported periods). Verify before relying on it. |
 | WooldridgeDiD | Unidentified-cohort exclusion + `survey_design` | Same reason (ledger `M-123`). Drop the cohort from the frame yourself, or supply a panel where every cohort has a pre-treatment period. |
 | All bootstrap estimators | Bootstrap + replicate weights | These are alternative variance methods; pick one |
diff --git a/tests/test_crossfit.py b/tests/test_crossfit.py
index f593b7549..17daf8f34 100644
--- a/tests/test_crossfit.py
+++ b/tests/test_crossfit.py
@@ -602,3 +602,159 @@ def test_invalid_predict_method_raises(self):
         folds = assign_folds(10, 2, rng=_rng(8))
         with pytest.raises(ValueError, match="predict_method"):
             cross_fit_predict(LinearLearner(), X, y, folds, predict_method="proba")
+
+
+class TestIterFoldFits:
+    """The per-fold generator under ``cross_fit_predict`` (CCPS nested stages
+    consume it directly)."""
+
+    def test_yields_fitted_folds_with_contract(self):
+        from diff_diff._crossfit import FoldFit, _predict_subset, iter_fold_fits
+
+        X, y = _reg_setup(n=40)
+        folds = assign_folds(40, 4, rng=_rng(5))
+        fit_mask = np.arange(40) % 3 != 0
+        template = LinearLearner()
+        fits = list(iter_fold_fits(template, X, y, folds, fit_mask=fit_mask))
+        assert [ff.k for ff in fits] == [0, 1, 2, 3]
+        assert all(isinstance(ff, FoldFit) for ff in fits)
+        seen = np.concatenate([ff.test_idx for ff in fits])
+        assert np.array_equal(np.sort(seen), np.arange(40))  # disjoint, exhaustive
+        assert all(ff.learner is not template for ff in fits)  # per-fold deep copies
+        assert getattr(template, "coef_", None) is None  # template never fit
+        ref = cross_fit_predict(LinearLearner(), X, y, folds, fit_mask=fit_mask)
+        for ff in fits:
+            np.testing.assert_array_equal(ff.fit_idx, ff.train_idx[fit_mask[ff.train_idx]])
+            assert ff.n_fit == ff.fit_idx.size and ff.kind == "regressor"
+            pred = _predict_subset(
+                ff.learner,
+                ff.X[ff.test_idx],
+                kind="regressor",
+                k=ff.k,
+                label=ff.label,
+                n_fit=ff.n_fit,
+                w_fit=ff.w_fit,
+            )
+            np.testing.assert_allclose(pred, ref.oof_predictions[ff.test_idx], rtol=0, atol=1e-14)
+
+    def test_validation_is_eager(self):
+        from diff_diff._crossfit import iter_fold_fits
+
+        X, y = _reg_setup(n=20)
+        folds = assign_folds(20, 2, rng=_rng(1))
+        y_bad = y.copy()
+        y_bad[0] = np.nan
+        with pytest.raises(ValueError):
+            iter_fold_fits(LinearLearner(), X, y_bad, folds)  # no next() needed
+
+    def test_fit_subset_empty_message_interpolates_train_size(self):
+        from diff_diff._crossfit import _fit_subset
+
+        X, y = _reg_setup(n=20)
+        with pytest.raises(
+            DegenerateFoldError, match=r"fold 3: the fit subset is empty \(train size 17"
+        ):
+            _fit_subset(
+                LinearLearner(),
+                X,
+                y,
+                np.array([], dtype=np.int64),
+                n_train=17,
+                kind="regressor",
+                sample_weight=None,
+                k=3,
+                label="",
+                warn_stacklevel=2,
+            )
+
+    def test_predict_subset_chains_learner_error(self):
+        from diff_diff._crossfit import _predict_subset
+
+        class BadPredict:
+            def predict(self, X):
+                raise ValueError("boom")
+
+        with pytest.raises(
+            DegenerateFoldError,
+            match=r"fold 1: boom; the fold's fit subset has n=7, n_pos_weight=2",
+        ) as ei:
+            _predict_subset(
+                BadPredict(),
+                np.zeros((3, 2)),
+                kind="regressor",
+                k=1,
+                label="lbl ",
+                n_fit=7,
+                w_fit=np.array([1.0, 0.0, 2.0]),
+            )
+        assert isinstance(ei.value.__cause__, ValueError)
+
+    def test_learner_raised_degenerate_passes_through_unwrapped(self):
+        class SelfDegenerate:
+            def fit(self, X, y, sample_weight=None):
+                raise DegenerateFoldError("my own message")
+
+            def predict(self, X):  # pragma: no cover
+                return np.zeros(len(X))
+
+        X, y = _reg_setup(n=20)
+        folds = assign_folds(20, 2, rng=_rng(1))
+        with pytest.raises(DegenerateFoldError) as ei:
+            cross_fit_predict(SelfDegenerate(), X, y, folds)
+        assert str(ei.value) == "my own message"
+        assert ei.value.__cause__ is None
+
+    def test_deep_copy_warning_attribution(self):
+        import warnings as _w
+
+        import pandas as pd
+
+        from diff_diff import DMLDiD
+
+        class Undeepcopyable:
+            def __deepcopy__(self, memo):
+                raise TypeError("cannot deep-copy this learner")
+
+            def fit(self, X, y, sample_weight=None):
+                self.mean_ = float(np.mean(y))
+                return self
+
+            def predict(self, X):
+                return np.full(len(X), self.mean_)
+
+        X, y = _reg_setup()
+        folds = assign_folds(len(y), 2, rng=_rng(22))
+        with _w.catch_warnings(record=True) as rec:
+            _w.simplefilter("always")
+            cross_fit_predict(Undeepcopyable(), X, y, folds)
+        hits = [r for r in rec if "could not deep-copy" in str(r.message)]
+        assert hits and all(r.filename == __file__ for r in hits)
+        assert str(hits[0].message).startswith("_crossfit: could not deep-copy")
+
+        # Bad-control fit: a foreign learner takes the split-half branch, so
+        # both the iter_fold_fits route (default stacklevel) and the direct
+        # _fit_subset route attribute to dml_did.py.
+        rng = np.random.default_rng(3)
+        rows = []
+        for i in range(60):
+            g = 2 if i % 2 else 0
+            for t in (1, 2):
+                rows.append(
+                    (i, t, g, rng.normal() + (t == 2) * (g == 2), rng.normal(), rng.normal())
+                )
+        df = pd.DataFrame(rows, columns=["unit", "time", "first_treat", "y", "x", "z"])
+        import diff_diff.dml_did as dml_mod
+
+        with _w.catch_warnings(record=True) as rec:
+            _w.simplefilter("always")
+            DMLDiD(outcome_learner=Undeepcopyable(), seed=0).fit(
+                df,
+                outcome="y",
+                unit="unit",
+                time="time",
+                first_treat="first_treat",
+                covariates=["z"],
+                bad_control="x",
+            )
+        hits = [r for r in rec if "could not deep-copy" in str(r.message)]
+        assert hits and {r.filename for r in hits} == {dml_mod.__file__}
diff --git a/tests/test_dml_did.py b/tests/test_dml_did.py
index 6c54a63d3..e10bdf9af 100644
--- a/tests/test_dml_did.py
+++ b/tests/test_dml_did.py
@@ -2145,3 +2145,682 @@ def test_no_warning_on_clean_input(self, rcs_data):
             warnings.simplefilter("always")
             DMLDiD(panel=False, seed=0).fit(rcs_data, **FIT_KW, **COV)
         assert not any("were excluded" in str(w.message) for w in rec)
+
+
+# ===========================================================================
+# Bad-control lane (Caetano, Callaway, Payne & Sant'Anna 2026): API contract
+# ===========================================================================
+from diff_diff.dml_did import _is_parametric_learner_spec  # noqa: E402
+from diff_diff.dml_did_results import DMLDiDResults  # noqa: E402
+
+
+def add_bad_control(df, seed=7, jump=0.5):
+    """Append a time-varying ``xbad`` column (AR(1)-ish in x1 with noise) that
+    jumps by ``jump`` on treated post rows."""
+    rng = np.random.default_rng(seed)
+    df = df.sort_values(["unit", "time"]).reset_index(drop=True)
+    xbad = np.empty(len(df))
+    lag = {}
+    for i, (u, ft, t, x1) in enumerate(zip(df["unit"], df["first_treat"], df["time"], df["x1"])):
+        prev = lag.get(u, 0.5 * x1)
+        val = 0.7 * prev + 0.3 * x1 + 0.3 * rng.normal()
+        if ft > 0 and t >= ft:
+            val += jump
+        xbad[i] = val
+        lag[u] = val
+    return df.assign(xbad=xbad)
+
+
+BC_KW = dict(bad_control="xbad", bad_control_covariates=["y"])
+
+
+@pytest.fixture(scope="module")
+def bc_data(data):
+    return add_bad_control(data)
+
+
+@pytest.fixture(scope="module")
+def bc_fitted(bc_data):
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore")
+        return DMLDiD(seed=0).fit(bc_data, **FIT_KW, **COV, **BC_KW)
+
+
+class _MeanRegressor:
+    """Deterministic foreign regressor (fitted mean); takes the split-half branch."""
+
+    def fit(self, X, y, sample_weight=None):
+        self.m_ = float(np.mean(y))
+        return self
+
+    def predict(self, X):
+        return np.full(X.shape[0], self.m_)
+
+
+class _RecordingRegressor(_MeanRegressor):
+    seen = []
+
+    def fit(self, X, y, sample_weight=None):
+        type(self).seen.append((np.array(X, copy=True), np.array(y, copy=True)))
+        return super().fit(X, y)
+
+
+class TestBadControlAPI:
+    # ---- reduction: bad_control=None is the pre-existing code path ----------
+    def test_reduction_native_bit_identity(self, bc_data):
+        a = DMLDiD(seed=0).fit(bc_data, **FIT_KW, **COV)
+        b = DMLDiD(seed=0).fit(bc_data, **FIT_KW, **COV, bad_control=None)
+        assert a.att == b.att and a.se == b.se
+        assert a.group_time_effects == b.group_time_effects
+        ia, ib = a._aggregation_kit.influence, b._aggregation_kit.influence
+        assert set(ia) == set(ib)
+        for k in ia:
+            assert set(ia[k]) == set(ib[k])
+            for name, val in ia[k].items():
+                np.testing.assert_array_equal(np.asarray(val), np.asarray(ib[k][name]))
+        pd.testing.assert_frame_equal(a.to_dataframe(), b.to_dataframe())
+        assert set(a.to_dict()) == set(b.to_dict())
+        assert "bad_control" not in a.to_dict()
+        assert b.bad_control is None and b.bad_control_covariates is None
+        assert b.bad_control_diagnostics is None
+
+    def test_reduction_user_learners(self, bc_data):
+        kw = dict(outcome_learner=_MeanRegressor(), seed=0)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            a = DMLDiD(**kw).fit(bc_data, **FIT_KW, **COV)
+            b = DMLDiD(**kw).fit(bc_data, **FIT_KW, **COV, bad_control=None)
+        assert a.att == b.att and a.se == b.se
+        assert a.group_time_effects == b.group_time_effects
+
+    # ---- validation matrix ------------------------------------------------
+    def test_unsupported_combinations_fail_closed(self, bc_data):
+        with pytest.raises(NotImplementedError, match="panel=False"):
+            DMLDiD(panel=False).fit(bc_data, **FIT_KW, **COV, **BC_KW)
+        from diff_diff import SurveyDesign
+
+        df = bc_data.assign(w=1.0)
+        with pytest.raises(NotImplementedError, match="survey_design"):
+            DMLDiD().fit(df, **FIT_KW, **COV, **BC_KW, survey_design=SurveyDesign(weights="w"))
+        with pytest.raises(NotImplementedError, match="anticipation=0"):
+            DMLDiD(anticipation=1).fit(bc_data, **FIT_KW, **COV, **BC_KW)
+        with pytest.raises(NotImplementedError, match="base_period='varying'"):
+            DMLDiD(base_period="universal").fit(bc_data, **FIT_KW, **COV, **BC_KW)
+
+    @pytest.mark.parametrize(
+        "kwargs,match",
+        [
+            (dict(bad_control_covariates=["y"]), "requires bad_control"),
+            (dict(bad_control="xbad", bad_control_covariates="y"), "bare"),
+            (dict(bad_control=3), "single column name"),
+            (dict(bad_control=["xbad"]), "single column name"),
+            (dict(bad_control="y"), "collides with outcome"),
+            (dict(bad_control="unit"), "collides with unit"),
+            (dict(bad_control="time"), "collides with time"),
+            (dict(bad_control="first_treat"), "collides with first_treat"),
+            (dict(bad_control="xbad", bad_control_covariates=[1]), "must be column names"),
+            (dict(bad_control="xbad", bad_control_covariates=["y", "y"]), "duplicate"),
+            (dict(bad_control="xbad", bad_control_covariates=["unit"]), "role column"),
+            (dict(bad_control="xbad", bad_control_covariates=["time"]), "role column"),
+            (dict(bad_control="xbad", bad_control_covariates=["first_treat"]), "role column"),
+            (dict(bad_control="x1"), "also appears in covariates"),
+            (dict(bad_control="xbad", bad_control_covariates=["xbad"]), "bad control itself"),
+            (dict(bad_control="xbad", bad_control_covariates=["x2"]), "also appears in covariates"),
+            (dict(bad_control="nope"), "Missing"),
+            (dict(bad_control="xbad", bad_control_covariates=["nope"]), "Missing"),
+        ],
+    )
+    def test_name_level_errors(self, bc_data, kwargs, match):
+        with pytest.raises(ValueError, match=match):
+            DMLDiD().fit(bc_data, **FIT_KW, **COV, **kwargs)
+
+    def test_non_numeric_bad_control_rejected(self, bc_data):
+        df = bc_data.assign(xbad=bc_data["xbad"].astype(str) + "a")
+        with pytest.raises(ValueError, match="numeric-castable"):
+            DMLDiD().fit(df, **FIT_KW, **COV, bad_control="xbad")
+        df = bc_data.assign(wtxt="a")
+        with pytest.raises(ValueError, match="numeric-castable"):
+            DMLDiD().fit(df, **FIT_KW, **COV, bad_control="xbad", bad_control_covariates=["wtxt"])
+
+    def test_outcome_in_w_accepted_and_none_means_no_w(self, bc_data, bc_fitted):
+        assert bc_fitted.bad_control == "xbad"
+        assert bc_fitted.bad_control_covariates == ("y",)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            res = DMLDiD(seed=0).fit(bc_data, **FIT_KW, **COV, bad_control="xbad")
+        assert res.bad_control_covariates == ()
+        assert np.isfinite(res.att)
+        assert res.att != bc_fitted.att  # W changes S, hence the fit
+
+    def test_generator_w_equals_list(self, bc_data):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            a = DMLDiD(seed=0).fit(
+                bc_data, **FIT_KW, **COV, bad_control="xbad", bad_control_covariates=["y"]
+            )
+            b = DMLDiD(seed=0).fit(
+                bc_data,
+                **FIT_KW,
+                **COV,
+                bad_control="xbad",
+                bad_control_covariates=(c for c in ["y"]),
+            )
+        assert a.att == b.att and a.se == b.se
+        assert a.bad_control_covariates == b.bad_control_covariates == ("y",)
+
+    def test_is_parametric_learner_spec(self):
+        from diff_diff._learners import LinearLearner, LogitLearner, RidgeLearner
+
+        assert _is_parametric_learner_spec("linear") and _is_parametric_learner_spec("logit")
+        assert not _is_parametric_learner_spec("ridge")
+        assert not _is_parametric_learner_spec("sieve")
+        assert _is_parametric_learner_spec(LinearLearner())
+        assert _is_parametric_learner_spec(LogitLearner())
+        assert not _is_parametric_learner_spec(RidgeLearner())
+
+        class Sub(LinearLearner):
+            pass
+
+        assert not _is_parametric_learner_spec(Sub())
+
+        class Raising:
+            def __eq__(self, other):  # pragma: no cover - must never be called
+                raise RuntimeError("__eq__ called")
+
+        assert not _is_parametric_learner_spec(Raising())
+
+    # ---- complete-case policy ---------------------------------------------
+    def test_complete_case_drops_unit_with_nan_bad_control_or_w(self, bc_data, bc_fitted):
+        cell = (2001, 2001)
+        base_entry = bc_fitted.group_time_effects[cell]
+        treated_units = bc_data.loc[bc_data["first_treat"] == 2001, "unit"].unique()
+        control_units = bc_data.loc[bc_data["first_treat"] == 0, "unit"].unique()
+
+        def fit_with_nan(col, unit, period):
+            df = bc_data.copy()
+            df.loc[(df["unit"] == unit) & (df["time"] == period), col] = np.nan
+            with pytest.warns(UserWarning, match="non-finite bad control|bad-control covariate"):
+                return DMLDiD(seed=0).fit(df, **FIT_KW, **COV, **BC_KW)
+
+        # NaN xt on a treated unit -> that unit leaves the cell (treated side).
+        r = fit_with_nan("xbad", treated_units[0], 2001)
+        e = r.group_time_effects[cell]
+        assert e["n_treated"] == base_entry["n_treated"] - 1
+        assert e["n_control"] == base_entry["n_control"]
+        # NaN xb on a control unit -> control side.
+        r = fit_with_nan("xbad", control_units[0], 2000)
+        e = r.group_time_effects[cell]
+        assert e["n_control"] == base_entry["n_control"] - 1
+        # NaN W (= Y_base) on a control unit -> the outcome NaN drops it too.
+        r = fit_with_nan("y", control_units[1], 2000)
+        e = r.group_time_effects[cell]
+        assert e["n_control"] == base_entry["n_control"] - 1
+
+    def test_complete_case_w_column_nan(self, bc_data, bc_fitted):
+        # A NON-outcome W column with a NaN at the base period drops the unit
+        # only on this lane (a plain fit never reads it).
+        cell = (2001, 2001)
+        control_units = bc_data.loc[bc_data["first_treat"] == 0, "unit"].unique()
+        df = bc_data.assign(w1=np.cos(bc_data["unit"] * 0.37 + bc_data["time"]))
+        df.loc[(df["unit"] == control_units[2]) & (df["time"] == 2000), "w1"] = np.nan
+        with pytest.warns(UserWarning, match="bad-control covariate"):
+            r = DMLDiD(seed=0).fit(
+                df, **FIT_KW, **COV, bad_control="xbad", bad_control_covariates=["w1", "y"]
+            )
+        assert (
+            r.group_time_effects[cell]["n_control"]
+            == bc_fitted.group_time_effects[cell]["n_control"] - 1
+        )
+
+    # ---- column-order contract --------------------------------------------
+    def test_design_matrix_column_order(self, bc_data):
+        df = bc_data.assign(
+            z1=lambda d: np.sin(d["unit"]) + 0.1 * d["time"],
+            w1=lambda d: np.cos(d["unit"] * d["time"]),
+            w2=lambda d: 0.3 * d["x1"] + 0.01 * d["time"],
+        )
+        _RecordingRegressor.seen = []
+        est = DMLDiD(outcome_learner=_RecordingRegressor(), seed=0, control_group="never_treated")
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            est.fit(
+                df,
+                **FIT_KW,
+                covariates=["z1"],
+                bad_control="xbad",
+                bad_control_covariates=["w1", "y", "w2"],
+            )
+        # Hand-build S and R for the first estimated cell (g=2001, t=2001;
+        # base 2000): the recorder's very first fit is the fold-0 outcome
+        # regression on R over training controls; its S-shaped fits carry
+        # five columns.
+        wide = {
+            c: df.pivot(index="unit", columns="time", values=c)
+            for c in ("xbad", "w1", "y", "w2", "z1")
+        }
+        units = wide["xbad"].index
+        ft = df.groupby("unit")["first_treat"].first().reindex(units)
+        cell_units = units[(ft == 2001) | (ft == 0)]
+        S_hand = np.column_stack(
+            [
+                wide["xbad"].loc[cell_units, 2000],
+                wide["w1"].loc[cell_units, 2000],
+                wide["y"].loc[cell_units, 2000],
+                wide["w2"].loc[cell_units, 2000],
+                wide["z1"].loc[cell_units, 2000],
+            ]
+        )
+        R_hand = np.column_stack(
+            [
+                wide["xbad"].loc[cell_units, 2001],
+                wide["xbad"].loc[cell_units, 2000],
+                wide["z1"].loc[cell_units, 2000],
+            ]
+        )
+
+        # Every recorded design row must be a row of the hand-built matrix of
+        # the same width (rows are subsets of the cell in unit order).
+        def rows_subset(X, H):
+            return all(any(np.allclose(x, h) for h in H) for x in X)
+
+        first_cell_fits = [(X, y) for X, y in _RecordingRegressor.seen[:20]]
+        assert any(X.shape[1] == 5 for X, _ in first_cell_fits)
+        assert any(X.shape[1] == 3 for X, _ in first_cell_fits)
+        for X, _ in first_cell_fits:
+            if X.shape[1] == 5:
+                assert rows_subset(X, S_hand)
+            elif X.shape[1] == 3:
+                assert rows_subset(X, R_hand)
+
+    # ---- results surface ----------------------------------------------------
+    def test_results_surface(self, bc_fitted):
+        assert isinstance(bc_fitted, DMLDiDResults)
+        assert bc_fitted.bad_control_diagnostics
+        s = bc_fitted.summary()
+        assert "CCPS 2026 bad-control score" in s
+        assert "Bad control:" in s and "xbad" in s
+        assert "ATT_X cells (post / pre):" in s
+        assert "CS simple" in s
+        assert "bad_control_summary()" in s
+        assert "ATT_X SE: analytical" not in s  # analytical fit
+        tab = bc_fitted.bad_control_summary()
+        assert list(tab.columns) == [
+            "group",
+            "time",
+            "post",
+            "att_x",
+            "se_x",
+            "t_stat",
+            "p_value",
+            "conf_int_lower",
+            "conf_int_upper",
+        ]
+        keys = set(zip(tab["group"], tab["time"]))
+        assert keys == set(bc_fitted.bad_control_diagnostics)
+        assert (tab["post"] == (tab["time"] >= tab["group"])).all()
+        for (g, t), entry in bc_fitted.bad_control_diagnostics.items():
+            assert set(entry) == {
+                "effect",
+                "se",
+                "t_stat",
+                "p_value",
+                "conf_int",
+                "n_treated",
+                "n_control",
+            }
+            row = tab[(tab["group"] == g) & (tab["time"] == t)].iloc[0]
+            assert row["att_x"] == entry["effect"] and row["se_x"] == entry["se"]
+        # skipped cells carry no ATT_X row
+        for (g, t), e in bc_fitted.group_time_effects.items():
+            if e.get("skip_reason") is not None:
+                assert (g, t) not in bc_fitted.bad_control_diagnostics
+        df_gt = bc_fitted.to_dataframe()
+        assert "att_x" in df_gt.columns and "se_x" in df_gt.columns
+        d = bc_fitted.to_dict()
+        json.dumps(d)
+        assert d["bad_control"] == "xbad" and d["bad_control_covariates"] == ["y"]
+        assert all(k.startswith("g=") for k in d["bad_control_diagnostics"])
+        import pickle
+
+        rt = pickle.loads(pickle.dumps(bc_fitted))
+        assert rt.bad_control_diagnostics == bc_fitted.bad_control_diagnostics
+
+    def test_pre_upgrade_pickle_behaves_as_plain(self, fitted):
+        import copy
+
+        res = copy.copy(fitted)
+        for name in ("bad_control", "bad_control_covariates", "bad_control_diagnostics"):
+            res.__dict__.pop(name, None)
+        assert "Bad control:" not in res.summary()
+        assert res.bad_control_summary().empty
+        assert "att_x" not in res.to_dataframe().columns
+        assert "bad_control" not in res.to_dict()
+
+    def test_plain_results_have_typed_empty_bad_control_summary(self, fitted):
+        tab = fitted.bad_control_summary()
+        assert tab.empty and "att_x" in tab.columns
+
+    def test_diagnostics_schema(self, bc_fitted, bc_data):
+        for (g, t), d in bc_fitted.cross_fit_diagnostics.items():
+            if d.get("skip_reason") is not None:
+                continue
+            for key in ("propensity", "outcome", "nu", "omega"):
+                assert set(d[key]) == {"fold_losses", "n_fit_per_fold"}
+                assert len(d[key]["n_fit_per_fold"]) == 5
+            assert all(np.isnan(v) for v in d["nu"]["fold_losses"])
+            assert d["nested_stage"] == "in_sample"
+            assert isinstance(d["n_clipped_omega"], int)
+            assert set(d["bad_control_outcome"]) == {"fold_losses", "n_fit_per_fold"}
+            assert "att_x" not in d  # moved to bad_control_diagnostics
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            ridge = DMLDiD(outcome_learner="ridge", seed=0).fit(bc_data, **FIT_KW, **COV, **BC_KW)
+            user = DMLDiD(outcome_learner=_MeanRegressor(), seed=0).fit(
+                bc_data, **FIT_KW, **COV, **BC_KW
+            )
+        for res in (ridge, user):
+            stages = {
+                d.get("nested_stage")
+                for d in res.cross_fit_diagnostics.values()
+                if d.get("skip_reason") is None
+            }
+            assert stages == {"split_half"}
+        json.dumps(ridge.to_dict())
+
+    # ---- omega clipping -------------------------------------------------------
+    def test_omega_clip_warning(self, bc_data):
+        # A wildly extrapolating omega projection: pscore_trim close to 0.5
+        # makes the cap (1-trim)/trim tiny so the odds regression's
+        # predictions overshoot it on a real cell.
+        with pytest.warns(UserWarning, match="omega_hat"):
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", message=".*could not be estimated.*")
+                warnings.filterwarnings("ignore", message=".*empirical.*")
+                warnings.filterwarnings("ignore", message=".*propensity.*")
+                res = DMLDiD(seed=0, pscore_trim=0.45).fit(bc_data, **FIT_KW, **COV, **BC_KW)
+        assert any((d.get("n_clipped_omega") or 0) > 0 for d in res.cross_fit_diagnostics.values())
+
+    # ---- ATT_X NaN contract -------------------------------------------------
+    def test_att_x_nan_when_only_mu_x_degenerate(self, bc_data):
+        import diff_diff.dml_did as mod
+        from diff_diff._crossfit import DegenerateFoldError
+        from tests.conftest import assert_nan_inference
+
+        orig_cf = mod.cross_fit_predict
+
+        def cf(learner, X, y, folds, **kw):
+            if "bad-control outcome" in kw.get("context_label", ""):
+                raise DegenerateFoldError("mu_x degenerate")
+            return orig_cf(learner, X, y, folds, **kw)
+
+        mod.cross_fit_predict = cf
+        try:
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore")
+                res = DMLDiD(seed=0).fit(bc_data, **FIT_KW, **COV, **BC_KW)
+        finally:
+            mod.cross_fit_predict = orig_cf
+        assert np.isfinite(res.att)
+        assert res.bad_control_diagnostics
+        for (g, t), entry in res.bad_control_diagnostics.items():
+            assert res.group_time_effects[(g, t)]["skip_reason"] is None
+            assert np.isnan(entry["effect"])
+            assert_nan_inference(entry)
+            assert "error" in res.cross_fit_diagnostics[(g, t)]["bad_control_outcome"]
+        assert not res.bad_control_summary()["att_x"].notna().any()
+
+    # ---- split-half branch ----------------------------------------------------
+    def test_split_half_hand_replication_with_mean_learners(self, bc_data):
+        """With fitted-mean regressors every nested model is a constant, so the
+        split-half average is reproducible by hand from the same RNG stream."""
+        from diff_diff._crossfit import assign_folds
+        from diff_diff._learners import LogitLearner
+
+        est = DMLDiD(outcome_learner=_MeanRegressor(), seed=0, control_group="never_treated")
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            res = est.fit(bc_data, **FIT_KW, **COV, **BC_KW)
+        g, t = 2001, 2001
+        d = res.cross_fit_diagnostics[(g, t)]
+        assert d["nested_stage"] == "split_half"
+        # Rebuild the cell exactly as the estimator does.
+        df = bc_data
+        units = np.sort(df["unit"].unique())
+        ft = df.groupby("unit")["first_treat"].first().reindex(units).to_numpy()
+        keep = (ft == g) | (ft == 0)
+        D = (ft[keep] == g).astype(float)
+
+        def wide(c):
+            return df.pivot(index="unit", columns="time", values=c).reindex(units)
+
+        dY = (wide("y")[2001] - wide("y")[2000]).to_numpy()[keep]
+        xt = wide("xbad")[2001].to_numpy()[keep]
+        xb = wide("xbad")[2000].to_numpy()[keep]
+        Z = np.column_stack([wide("x1")[2000].to_numpy()[keep], wide("x2")[2000].to_numpy()[keep]])
+        R = np.column_stack([xt, xb, Z])
+        S = np.column_stack([xb, wide("y")[2000].to_numpy()[keep], Z])
+        n = D.shape[0]
+        seed_seq = np.random.SeedSequence(
+            entropy=d["fold_seed"]["entropy"], spawn_key=tuple(d["fold_seed"]["spawn_key"])
+        )
+        rng = np.random.default_rng(seed_seq)
+        folds = assign_folds(n, 5, rng=rng, stratify=D)
+        ctrl = D == 0.0
+        trim = est.pscore_trim
+        nu_hand = np.empty(n)
+        om_hand = np.empty(n)
+        for k, train, test in folds.iter_folds():
+            halves = assign_folds(int(train.shape[0]), 2, rng=rng, stratify=D[train])
+            nu_k = 0.0
+            om_k = 0.0
+            for h in (0, 1):
+                a = train[halves.fold_ids == h]
+                b = train[halves.fold_ids != h]
+                a_c = a[ctrl[a]]
+                b_c = b[ctrl[b]]
+                m_b = np.full(b_c.size, dY[a_c].mean())
+                p_b = np.clip(
+                    LogitLearner().fit(S[a], D[a]).predict_proba(S[b_c])[:, 1], trim, 1 - trim
+                )
+                nu_k += 0.5 * m_b.mean()
+                om_k += 0.5 * (p_b / (1 - p_b)).mean()
+            nu_hand[test] = nu_k
+            om_hand[test] = om_k
+        # Replay the estimator's own stream (fold draw first, then one half
+        # draw per outer fold) through _ccps_nuisances directly.
+        # The generator above consumed the fold draw first, then K half draws:
+        # replay identically.
+        rng2 = np.random.default_rng(seed_seq)
+        folds2 = assign_folds(n, 5, rng=rng2, stratify=D)
+        m_hat, ps_raw, nu_hat, om_raw, stage = est._ccps_nuisances(
+            R, S, dY, D, folds2, rng2, None, False, "x"
+        )
+        assert stage["nested_stage"] == "split_half"
+        np.testing.assert_allclose(nu_hat, nu_hand, rtol=0, atol=1e-12)
+        np.testing.assert_allclose(om_raw, om_hand, rtol=0, atol=1e-12)
+        assert stage["nu"]["n_fit_per_fold"] == [
+            int(ctrl[tr].sum()) for _, tr, _ in folds2.iter_folds()
+        ]
+
+    def test_split_half_degenerate_cell_skips(self, bc_data):
+        # Tiny never-treated pool: the 2-way stratified half split of a
+        # training complement with < 2 controls per half fails -> the cell is
+        # skipped as cross_fit_degenerate (user learner -> split-half branch).
+        from diff_diff._crossfit import DegenerateFoldError, assign_folds
+
+        # Two never-treated controls: the outer 5-fold split places them in
+        # different folds (a fitted-mean learner fits on ONE control), but the
+        # training complement then holds a single control and the stratified
+        # half split has a singleton stratum -> DegenerateFoldError labelled
+        # split-half -> the cell is skipped as cross_fit_degenerate; with
+        # every cell sharing those controls the fit raises the all-degenerate
+        # ValueError.
+        keep_ctrl = bc_data.loc[bc_data["first_treat"] == 0, "unit"].unique()[:2]
+        df = bc_data[(bc_data["first_treat"] != 0) | bc_data["unit"].isin(keep_ctrl)]
+        est = DMLDiD(outcome_learner=_MeanRegressor(), seed=0, control_group="never_treated")
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            with pytest.raises(ValueError, match="Could not estimate"):
+                est.fit(df, **FIT_KW, **COV, **BC_KW)
+        rng = np.random.default_rng(0)
+        n = 12
+        D = np.array([0.0, 0.0] + [1.0] * (n - 2))
+        R = rng.normal(size=(n, 3))
+        S = rng.normal(size=(n, 3))
+        dY = rng.normal(size=n)
+        folds = assign_folds(n, 5, rng=rng, stratify=D)
+        with pytest.raises(DegenerateFoldError, match="split-half"):
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore")
+                est._ccps_nuisances(R, S, dY, D, folds, rng, None, False, "cell")
+
+    def test_split_half_psu_cohesive_under_cluster(self, bc_data):
+        from diff_diff._crossfit import assign_folds
+
+        df = bc_data.assign(grp=lambda d: d["unit"] % 12)
+        est = DMLDiD(
+            outcome_learner=_MeanRegressor(), seed=0, cluster="grp", control_group="never_treated"
+        )
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            res = est.fit(df, **FIT_KW, **COV, **BC_KW)
+        g, t = 2001, 2001
+        d = res.cross_fit_diagnostics[(g, t)]
+        assert d["psu_folds"] is True and d["nested_stage"] == "split_half"
+        units = np.sort(df["unit"].unique())
+        ft = df.groupby("unit")["first_treat"].first().reindex(units).to_numpy()
+        keep = (ft == g) | (ft == 0)
+        D = (ft[keep] == g).astype(float)
+        psu = (units % 12)[keep]
+        rng = np.random.default_rng(
+            np.random.SeedSequence(
+                entropy=d["fold_seed"]["entropy"], spawn_key=tuple(d["fold_seed"]["spawn_key"])
+            )
+        )
+        folds = assign_folds(int(D.shape[0]), 5, rng=rng, cluster_ids=psu)
+        for k, train, test in folds.iter_folds():
+            halves = assign_folds(int(train.shape[0]), 2, rng=rng, cluster_ids=psu[train])
+            for h in (0, 1):
+                psus_h = set(psu[train][halves.fold_ids == h])
+                psus_o = set(psu[train][halves.fold_ids != h])
+                assert not (psus_h & psus_o)
+        assert np.isfinite(res.att)
+
+    # ---- cluster / inference ------------------------------------------------
+    def test_cluster_unit_and_coarser_finite(self, bc_data):
+        df = bc_data.assign(grp=lambda d: d["unit"] % 10)
+        for col in ("unit", "grp"):
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore")
+                res = DMLDiD(seed=0, cluster=col).fit(df, **FIT_KW, **COV, **BC_KW)
+            assert np.isfinite(res.att) and np.isfinite(res.se)
+            for (g, t), e in res.bad_control_diagnostics.items():
+                assert np.isfinite(e["se"])
+                # same df_inference as the ATT: t-quantile CI half-width ratio
+                # matches for both tuples
+                gt = res.group_time_effects[(g, t)]
+                hw_att = (gt["conf_int"][1] - gt["conf_int"][0]) / (2 * gt["se"])
+                hw_x = (e["conf_int"][1] - e["conf_int"][0]) / (2 * e["se"])
+                np.testing.assert_allclose(hw_att, hw_x, rtol=1e-10)
+
+    def test_single_psu_cluster_nan_inference_incl_att_x(self, bc_data):
+        from tests.conftest import assert_nan_inference
+
+        df = bc_data.assign(one=0)
+        with pytest.warns(UserWarning, match="PSU"):
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", message=".*excluded.*")
+                res = DMLDiD(seed=0, cluster="one").fit(df, **FIT_KW, **COV, **BC_KW)
+        found = False
+        for (g, t), e in res.group_time_effects.items():
+            if e.get("skip_reason") is not None:
+                continue
+            assert np.isfinite(e["effect"])
+            assert_nan_inference(e)
+            x = res.bad_control_diagnostics[(g, t)]
+            assert np.isfinite(x["effect"])
+            assert_nan_inference(x)
+            found = True
+        assert found
+
+    # ---- bootstrap + aggregation ----------------------------------------------
+    def test_bootstrap_lane_and_aggregations(self, bc_data):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            boot = DMLDiD(seed=0, n_bootstrap=49).fit(bc_data, **FIT_KW, **COV, **BC_KW)
+            plain = DMLDiD(seed=0).fit(bc_data, **FIT_KW, **COV, **BC_KW)
+        assert "ATT_X SE: analytical (not bootstrapped)" in boot.summary()
+        moved = False
+        for k, e in boot.group_time_effects.items():
+            if e.get("skip_reason") is not None:
+                continue
+            p = plain.group_time_effects[k]
+            assert e["effect"] == p["effect"]
+            moved |= e["se"] != p["se"]
+            assert boot.bad_control_diagnostics[k]["se"] == plain.bad_control_diagnostics[k]["se"]
+        assert moved
+        df_gt = boot.to_dataframe()
+        assert {"se", "se_x"} <= set(df_gt.columns)
+        for level in ("event_study", "group", "total"):
+            df_a = boot.aggregate(level).to_dataframe()
+            assert np.isfinite(df_a["att"]).any()
+
+    def test_total_raises_on_incomplete_treated_support_under_cluster(self, bc_data):
+        df = bc_data.copy()
+        treated_unit = df.loc[df["first_treat"] == 2001, "unit"].unique()[0]
+        df.loc[(df["unit"] == treated_unit) & (df["time"] == 2002), "xbad"] = np.nan
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            res = DMLDiD(seed=0, cluster="unit").fit(df, **FIT_KW, **COV, **BC_KW)
+        with pytest.raises(NotImplementedError, match="incomplete treated support"):
+            res.aggregate("total")
+
+    # ---- time-invariant bad control -------------------------------------------
+    def test_time_invariant_bad_control(self, bc_data):
+        # Time-invariant AND not collinear with Z (S stays full rank; only
+        # R = [xt, xb, Z] loses rank because xt == xb).
+        df = bc_data.assign(xbad=lambda d: np.sin(0.7 * d["unit"]))
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            with pytest.raises(ValueError, match="Could not estimate"):
+                DMLDiD(seed=0).fit(df, **FIT_KW, **COV, bad_control="xbad")
+            res = DMLDiD(seed=0, outcome_learner="ridge").fit(
+                df, **FIT_KW, **COV, bad_control="xbad"
+            )
+        assert np.isfinite(res.att)
+
+    # ---- reporting surfaces ------------------------------------------------------
+    def test_reporting_surfaces(self, bc_fitted, fitted):
+        from diff_diff._reporting_helpers import describe_target_parameter
+        from diff_diff.business_report import BusinessReport
+        from diff_diff.practitioner import practitioner_next_steps
+
+        tp = describe_target_parameter(bc_fitted)
+        assert "Caetano" in tp["reference"] and "Caetano" in tp["definition"]
+        assert "W" in tp["definition"]  # W non-empty on this fit
+        assert "Caetano" not in describe_target_parameter(fitted)["reference"]
+
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            br = BusinessReport(bc_fitted, auto_diagnostics=False).to_dict()
+            br_plain = BusinessReport(fitted, auto_diagnostics=False).to_dict()
+        blob = json.dumps(br)
+        assert "covariate unconfoundedness" in blob
+        cites = [r["citation"] for r in br["references"]]
+        assert any(c.startswith("Caetano, C., Callaway, B.") for c in cites)
+        assert not any(
+            c.startswith("Caetano") for r in br_plain["references"] for c in [r["citation"]]
+        )
+
+        out = practitioner_next_steps(bc_fitted, verbose=False)
+        step = next(s for s in out["next_steps"] if "alt = DMLDiD(" in (s.get("code") or ""))
+        code = step["code"]
+        fit_part = code.split(".fit(", 1)[1]
+        assert "bad_control='xbad'" in fit_part
+        assert "bad_control_covariates=['y']" in fit_part
+        assert "control_group='never_treated'" in code.split(".fit(", 1)[0]
+        plain_out = practitioner_next_steps(fitted, verbose=False)
+        plain_code = next(
+            s for s in plain_out["next_steps"] if "alt = DMLDiD(" in (s.get("code") or "")
+        )["code"]
+        assert "bad_control" not in plain_code and "control_group" not in plain_code
diff --git a/tests/test_dml_did_bad_controls_parity.py b/tests/test_dml_did_bad_controls_parity.py
new file mode 100644
index 000000000..ce0eae269
--- /dev/null
+++ b/tests/test_dml_did_bad_controls_parity.py
@@ -0,0 +1,214 @@
+"""Black-box parity of the DMLDiD bad-control lane against R ``badcontrols``.
+
+Caetano, Callaway, Payne & Sant'Anna (2026) ship their estimator as the
+GPL-3 R package ``badcontrols`` (1.0.0, GitHub commit ``651ccc92``; no
+tags or releases exist). The Python lane is derived from the paper alone
+(``docs/methodology/papers/caetano-2026-review.md``); the R package is only
+EXECUTED as an oracle by ``benchmarks/R/generate_badcontrols_golden.R`` -
+its source is never read (license posture; a direct port was rejected).
+
+Why tolerance-based, not bit-exact: ``didbc()`` cross-fits with its own fold
+draw (``nfolds = 1`` errors), so no shared fold assignment exists. The
+2026-09-05 spike measured single-seed fold noise of ~0.1-0.25 analytical SE
+on most cells and up to ~0.5 SE on the smallest cells (n = 500, W = lagged
+outcome); ``att_seed_sd`` in the fixture records it per cell. Each R run is
+therefore recorded as the per-cell mean over ``n_seeds`` seeds (per-seed
+rows kept) and the Python side averages the same number of its own seeds,
+which shrinks the fold noise of the DIFFERENCE of means to ~0.1-0.2 SE.
+
+Assertion rules (fixed up front; a failing cell is a defect to investigate,
+never a tolerance to loosen):
+
+- Runs 1-2 (W = [W]; not-yet-treated / never-treated) on every cell, and run
+  3 (W = [Y], Remark 5) on POST cells: per cell
+  ``|mean_att_py - mean_att_R| < 0.5 * SE_R`` with ``SE_R = sqrt(V_R / n_R)``,
+  ``|mean_se_py / SE_R - 1| < 0.3``, and the run's mean absolute gap
+  ``< 2 * mean(SE_R) / sqrt(n_cells)``.
+- Run 3 PRE cells: only ``|mean_att_py - mean_att_R| < 1.0 * SE_R`` (the
+  period at which R evaluates the lagged-outcome W on pre-period cells is
+  not established by the black-box spike; the library reads ``Y_{t-1}``).
+- Run 4 (no bad control): a CHARACTERIZATION, not a same-estimator
+  comparison - R's ``dr_ml`` path still regresses the propensity odds on Z
+  for ``omega_0`` whereas DMLDiD uses ``ps/(1-ps)`` pointwise - asserted at
+  ``|mean_att_py - mean_att_R| < 1.0 * SE_R`` per cell only.
+
+Fixture: ``benchmarks/data/badcontrols_golden.json`` (+ the shared panel
+``benchmarks/data/badcontrols_panel.csv``). Per ``feedback_golden_file_pytest_skip``
+a missing fixture skips (CI isolated-install jobs copy ``tests/`` only).
+"""
+
+from __future__ import annotations
+
+import json
+import warnings
+from pathlib import Path
+
+import numpy as np
+import pandas as pd
+import pytest
+
+from diff_diff import DMLDiD
+
+DATA_DIR = Path(__file__).parent.parent / "benchmarks" / "data"
+FIXTURE_PATH = DATA_DIR / "badcontrols_golden.json"
+PANEL_PATH = DATA_DIR / "badcontrols_panel.csv"
+
+BADCONTROLS_VERSION = "1.0.0"
+BADCONTROLS_SHA = "651ccc925776125bb9233d76867c862107ea0ba5"
+PTETOOLS_VERSION = "1.0.0"
+
+POINT_TOL_SE = 0.5
+POINT_TOL_SE_CHARACTERIZATION = 1.0
+SE_RATIO_TOL = 0.3
+
+RUN_SPECS = {
+    "w_nyt": dict(control_group="not_yet_treated", bad_control="X", bad_control_covariates=["W"]),
+    "w_nt": dict(control_group="never_treated", bad_control="X", bad_control_covariates=["W"]),
+    "ylag_nyt": dict(
+        control_group="not_yet_treated", bad_control="X", bad_control_covariates=["Y"]
+    ),
+    "plain_nyt": dict(control_group="not_yet_treated"),
+}
+
+
+def _load_fixture():
+    if not FIXTURE_PATH.exists() or not PANEL_PATH.exists():
+        pytest.skip(
+            f"Golden fixture {FIXTURE_PATH} / {PANEL_PATH} missing - regenerate via "
+            "`Rscript benchmarks/R/generate_badcontrols_golden.R`."
+        )
+    with open(FIXTURE_PATH) as f:
+        return json.load(f)
+
+
+@pytest.fixture(scope="module")
+def fixture():
+    return _load_fixture()
+
+
+@pytest.fixture(scope="module")
+def panel(fixture):
+    return pd.read_csv(PANEL_PATH)
+
+
+def _python_seed_mean(panel, spec, n_seeds):
+    """Per-cell seed-mean of (att, se) over ``n_seeds`` Python fold draws."""
+    cg = spec["control_group"]
+    kw = {k: v for k, v in spec.items() if k != "control_group"}
+    acc: dict = {}
+    for seed in range(n_seeds):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            res = DMLDiD(control_group=cg, base_period="varying", pscore_trim=1e-6, seed=seed).fit(
+                panel,
+                outcome="Y",
+                unit="id",
+                time="period",
+                first_treat="G",
+                covariates=["Z"],
+                **kw,
+            )
+        for (g, t), e in res.group_time_effects.items():
+            assert e.get("skip_reason") is None, (g, t, e)
+            acc.setdefault((g, t), []).append((e["effect"], e["se"]))
+    return {
+        k: (float(np.mean([a for a, _ in v])), float(np.mean([s for _, s in v])))
+        for k, v in acc.items()
+    }
+
+
+def _r_rows(fixture, key):
+    rows = fixture["runs"][key]["att_gt_mean"]
+    return {(int(r["group"]), int(r["t"])): r for r in rows}
+
+
+def _compare(py, r_rows, *, cells, point_tol_se, se_ratio_tol=None, mean_gap=False):
+    gaps = []
+    se_rs = []
+    for cell in cells:
+        r = r_rows[cell]
+        att_r = r["att"]
+        se_r = float(np.sqrt(r["V_analytical"] / r["n"]))
+        att_py, se_py = py[cell]
+        assert abs(att_py - att_r) < point_tol_se * se_r, (
+            f"cell {cell}: |{att_py:.5f} - {att_r:.5f}| = {abs(att_py - att_r):.5f} "
+            f">= {point_tol_se} * SE_R ({se_r:.5f}); R seed sd {r['att_seed_sd']:.5f}"
+        )
+        if se_ratio_tol is not None:
+            assert (
+                abs(se_py / se_r - 1.0) < se_ratio_tol
+            ), f"cell {cell}: se_py/SE_R = {se_py / se_r:.4f}"
+        gaps.append(abs(att_py - att_r))
+        se_rs.append(se_r)
+    if mean_gap:
+        bound = 2.0 * float(np.mean(se_rs)) / np.sqrt(len(cells))
+        assert float(np.mean(gaps)) < bound, (float(np.mean(gaps)), bound)
+
+
+class TestBadControlsParity:
+    def test_metadata_versions_match(self, fixture):
+        meta = fixture["meta"]
+        assert meta["badcontrols_version"] == BADCONTROLS_VERSION
+        assert meta["badcontrols_remote_sha"] == BADCONTROLS_SHA
+        assert meta["ptetools_version"] == PTETOOLS_VERSION
+        assert meta["common_args"]["overlap_threshold"] == 1
+        assert meta["common_args"]["nuisance_method"] == "parametric"
+        assert int(meta["n_seeds"]) >= 5
+        for key in RUN_SPECS:
+            assert len(fixture["runs"][key]["seeds"]) == int(meta["n_seeds"])
+
+    def test_panel_matches_metadata(self, fixture, panel):
+        meta = fixture["meta"]
+        assert panel["id"].nunique() == meta["n"]
+        assert sorted(panel["period"].unique()) == list(range(1, meta["T_max"] + 1))
+        assert set(panel.columns) >= {"id", "period", "G", "Y", "X", "Z", "W"}
+
+    @pytest.mark.parametrize("key", ["w_nyt", "w_nt"])
+    def test_bad_control_runs_all_cells(self, fixture, panel, key):
+        r_rows = _r_rows(fixture, key)
+        py = _python_seed_mean(panel, RUN_SPECS[key], int(fixture["meta"]["n_seeds"]))
+        assert set(py) == set(r_rows)
+        _compare(
+            py,
+            r_rows,
+            cells=sorted(r_rows),
+            point_tol_se=POINT_TOL_SE,
+            se_ratio_tol=SE_RATIO_TOL,
+            mean_gap=True,
+        )
+
+    def test_lagged_outcome_w_post_cells(self, fixture, panel):
+        r_rows = _r_rows(fixture, "ylag_nyt")
+        py = _python_seed_mean(panel, RUN_SPECS["ylag_nyt"], int(fixture["meta"]["n_seeds"]))
+        post = sorted(c for c in r_rows if c[1] >= c[0])
+        assert post
+        _compare(
+            py,
+            r_rows,
+            cells=post,
+            point_tol_se=POINT_TOL_SE,
+            se_ratio_tol=SE_RATIO_TOL,
+            mean_gap=True,
+        )
+
+    def test_lagged_outcome_w_pre_cells_characterization(self, fixture, panel):
+        r_rows = _r_rows(fixture, "ylag_nyt")
+        py = _python_seed_mean(panel, RUN_SPECS["ylag_nyt"], int(fixture["meta"]["n_seeds"]))
+        pre = sorted(c for c in r_rows if c[1] < c[0])
+        assert pre
+        _compare(py, r_rows, cells=pre, point_tol_se=POINT_TOL_SE_CHARACTERIZATION)
+
+    def test_no_bad_control_characterization(self, fixture, panel):
+        # NOT a same-estimator comparison (see module docstring).
+        r_rows = _r_rows(fixture, "plain_nyt")
+        py = _python_seed_mean(panel, RUN_SPECS["plain_nyt"], int(fixture["meta"]["n_seeds"]))
+        _compare(py, r_rows, cells=sorted(r_rows), point_tol_se=POINT_TOL_SE_CHARACTERIZATION)
+
+    def test_true_att_recovered_by_post_cells(self, fixture, panel):
+        # The simulated truth is the paper's own DGP target; a coarse sanity
+        # anchor independent of R (3 SE on the seed-mean).
+        truth = {(int(r["g"]), int(r["t"])): r["att"] for r in fixture["true_att_gt"]}
+        py = _python_seed_mean(panel, RUN_SPECS["w_nyt"], 3)
+        for cell, att_true in truth.items():
+            att_py, se_py = py[cell]
+            assert abs(att_py - att_true) < 3.0 * se_py, (cell, att_py, att_true, se_py)
diff --git a/tests/test_guides.py b/tests/test_guides.py
index ef39c2920..822209749 100644
--- a/tests/test_guides.py
+++ b/tests/test_guides.py
@@ -814,6 +814,10 @@ def test_llms_full_dml_fit_documents_covariates_required(self):
         # The new public fit parameter must be documented in the guide's
         # .fit( block too (constructor parity is pinned separately).
         assert "survey_design" in fit_block
+        assert "bad_control" in inspect.signature(DMLDiD.fit).parameters
+        assert "bad_control_covariates" in inspect.signature(DMLDiD.fit).parameters
+        assert "bad_control=" in fit_block
+        assert "bad_control_covariates=" in fit_block
         assert "REQUIRED" in section  # the covariates-required contract
 
     def test_llms_full_dml_documents_post_fit_aggregation_and_seed(self):
diff --git a/tests/test_methodology_dml_did.py b/tests/test_methodology_dml_did.py
index 848cbe112..4f10d4468 100644
--- a/tests/test_methodology_dml_did.py
+++ b/tests/test_methodology_dml_did.py
@@ -887,3 +887,362 @@ def test_coverage_sanity(self, ci_params):
         coverage = hits / n_reps
         lo_band, hi_band = (0.90, 0.99) if n_reps >= 100 else (0.80, 1.00)
         assert lo_band <= coverage <= hi_band, coverage
+
+
+# ===========================================================================
+# CCPS (2026) bad-control lane: Supplementary Appendix SD DGPs, numpy oracle
+# of Equation 11 / Algorithm 1, the Assumption-8 plug-in identity, and the
+# split-half branch via oracle user learners (docs/methodology/papers/
+# caetano-2026-review.md, "Monte Carlo evidence" + Section 6.2)
+# ===========================================================================
+#
+# Common SA DGP (review lines 854-880), two periods t = 1, 2 (t* = 2):
+#   Z ~ N(0,1), eta ~ N(0,1), all noise N(0,1) mutually independent
+#   W       = 0.8 eta + 0.3 Z + 0.2 e_W
+#   D       = 1{0.2 Z + 0.4 W + 0.3 eta + e_D > 0}
+#   X_1     = 0.5 eta + 0.4 Z + 0.3 e_X1
+#   X_2(0)  = per DGP (below);  X_2(1) = X_2(0) + lambda, lambda = 0.5
+#   Y_t(0)  = theta_t + 0.5 eta + 0.3 Z + X_t(0) + 0.3 e_Yt, theta_1 = 0.3, theta_2 = 0.6
+#   Y_2(1)  = Y_2(0) + (X_2(1) - X_2(0)) + delta, delta = 0.5
+#   True ATT = delta + lambda = 1.00; true ATT_X = lambda = 0.50.
+# DGP 1: X_2(0) = 0.7 X_1 + 0.3 Z + 0.2 W + 0.15 + 0.3 e   (linear W)
+# DGP 4: X_2(0) =     X_1 + 0.3 Z + 0.2 W + 0.15 + 0.3 e   (PT for the bad control)
+# Table S1 marks the parametric DR estimator consistent on DGPs 1 and 4 only;
+# DGPs 2/3/5 (nonlinear W / X) need a flexible-learner fixture (TODO.md).
+from diff_diff._dr_scores import ccps_panel_score, ccps_panel_score_augmented  # noqa: E402
+
+CCPS_TRUE_ATT = 1.0
+CCPS_TRUE_ATT_X = 0.5
+CCPS_FIT_KW = dict(outcome="y", unit="unit", time="time", first_treat="first_treat")
+
+
+def ccps_two_period_frame(n=1000, dgp=1, seed=0):
+    """SA common DGP in long panel form; cohort 2 treated at period 2."""
+    rng = np.random.default_rng(seed)
+    Z = rng.standard_normal(n)
+    eta = rng.standard_normal(n)
+    W = 0.8 * eta + 0.3 * Z + 0.2 * rng.standard_normal(n)
+    D = ((0.2 * Z + 0.4 * W + 0.3 * eta + rng.standard_normal(n)) > 0).astype(float)
+    X1 = 0.5 * eta + 0.4 * Z + 0.3 * rng.standard_normal(n)
+    e2 = rng.standard_normal(n)
+    if dgp == 1:
+        X2_0 = 0.7 * X1 + 0.3 * Z + 0.2 * W + 0.15 + 0.3 * e2
+    elif dgp == 2:
+        X2_0 = 0.7 * X1 + 0.3 * Z + 0.2 * W + 0.03 * W**2 + 0.15 + 0.3 * e2
+    elif dgp == 3:
+        X2_0 = 0.7 * X1 + 0.3 * Z + 0.4 * X1 * Z + 0.2 * X1**2 + 0.15 + 0.3 * e2
+    elif dgp == 4:
+        X2_0 = X1 + 0.3 * Z + 0.2 * W + 0.15 + 0.3 * e2
+    elif dgp == 5:
+        X2_0 = 0.7 * X1 + 0.3 * Z + 0.2 * W + 0.03 * W**2 + 0.05 * X1 * W + 0.15 + 0.3 * e2
+    else:
+        raise ValueError(dgp)
+    X2_1 = X2_0 + 0.5
+    Y1 = 0.3 + 0.5 * eta + 0.3 * Z + X1 + 0.3 * rng.standard_normal(n)
+    Y2_0 = 0.6 + 0.5 * eta + 0.3 * Z + X2_0 + 0.3 * rng.standard_normal(n)
+    Y2_1 = Y2_0 + (X2_1 - X2_0) + 0.5
+    X2 = np.where(D == 1, X2_1, X2_0)
+    Y2 = np.where(D == 1, Y2_1, Y2_0)
+    rows = []
+    for i in range(n):
+        g = 2 if D[i] == 1 else 0
+        rows.append((i, 1, g, Y1[i], X1[i], Z[i], W[i]))
+        rows.append((i, 2, g, Y2[i], X2[i], Z[i], W[i]))
+    return pd.DataFrame(rows, columns=["unit", "time", "first_treat", "y", "x", "z", "w"])
+
+
+def _ccps_cell_arrays(df, w_cols=("w", "y")):
+    """Hand-built cell arrays in DMLDiD's canonical unit order: R = [xt, xb, Z],
+    S = [xb, W (listed order; 'y' = Y at the base period), Z]."""
+    unit_info = df.groupby("unit")["first_treat"].first()
+    order = unit_info.index
+    D = (unit_info.to_numpy() > 0).astype(float)
+    wide = {
+        c: df.pivot(index="unit", columns="time", values=c).reindex(order)
+        for c in ("y", "x", "z", "w")
+    }
+    dY = wide["y"][2].to_numpy() - wide["y"][1].to_numpy()
+    xt = wide["x"][2].to_numpy()
+    xb = wide["x"][1].to_numpy()
+    Z = wide["z"][1].to_numpy()[:, None]
+    W = (
+        np.column_stack([wide[c][1].to_numpy() for c in w_cols])
+        if w_cols
+        else np.empty((len(D), 0))
+    )
+    R = np.column_stack([xt, xb, Z])
+    S = np.column_stack([xb, W, Z])
+    return D, dY, xt, xb, R, S
+
+
+def _naive_include_xt_contrast(df):
+    """The paper's Section 3.1 'use the bad control' estimand: regression
+    adjustment of dY on (X_t, Z) among controls, evaluated at treated units."""
+    D, dY, xt, xb, R, S = _ccps_cell_arrays(df, w_cols=())
+    Xn = np.column_stack([np.ones(len(D)), xt, S[:, -1]])
+    ctrl = D == 0.0
+    beta, *_ = np.linalg.lstsq(Xn[ctrl], dY[ctrl], rcond=None)
+    return float(np.mean(dY[D == 1.0] - Xn[D == 1.0] @ beta))
+
+
+class TestCCPSFrameShape:
+    """Pin the DGP's defining moments BEFORE any estimator runs (recovery
+    alone passes under plausible mis-codings)."""
+
+    def test_dgp1_moments(self):
+        df = ccps_two_period_frame(n=200_000, dgp=1, seed=1)
+        base = df[df["time"] == 1].set_index("unit")
+        post = df[df["time"] == 2].set_index("unit")
+        w = base["w"].to_numpy()
+        np.testing.assert_allclose(w.mean(), 0.0, atol=0.02)
+        np.testing.assert_allclose(w.var(), 0.64 + 0.09 + 0.04, rtol=0.03)
+        np.testing.assert_allclose((base["first_treat"] > 0).mean(), 0.5, atol=0.01)
+        # X_2(0) coefficients on (X_1, Z, W) among CONTROLS = (0.7, 0.3, 0.2).
+        ctrl = base["first_treat"] == 0
+        Xr = np.column_stack(
+            [np.ones(ctrl.sum()), base.loc[ctrl, "x"], base.loc[ctrl, "z"], base.loc[ctrl, "w"]]
+        )
+        beta, *_ = np.linalg.lstsq(Xr, post.loc[ctrl, "x"].to_numpy(), rcond=None)
+        np.testing.assert_allclose(beta, [0.15, 0.7, 0.3, 0.2], atol=0.02)
+        # Treated units' bad control jumps by lambda = 0.5 relative to controls
+        # with the same (X_1, Z, W).
+        Xt = np.column_stack(
+            [
+                np.ones((~ctrl).sum()),
+                base.loc[~ctrl, "x"],
+                base.loc[~ctrl, "z"],
+                base.loc[~ctrl, "w"],
+            ]
+        )
+        gap = float(np.mean(post.loc[~ctrl, "x"].to_numpy() - Xt @ beta))
+        np.testing.assert_allclose(gap, CCPS_TRUE_ATT_X, atol=0.03)
+
+    def test_dgp4_moments(self):
+        df = ccps_two_period_frame(n=200_000, dgp=4, seed=2)
+        base = df[df["time"] == 1].set_index("unit")
+        post = df[df["time"] == 2].set_index("unit")
+        ctrl = base["first_treat"] == 0
+        Xr = np.column_stack(
+            [np.ones(ctrl.sum()), base.loc[ctrl, "x"], base.loc[ctrl, "z"], base.loc[ctrl, "w"]]
+        )
+        beta, *_ = np.linalg.lstsq(Xr, post.loc[ctrl, "x"].to_numpy(), rcond=None)
+        np.testing.assert_allclose(beta, [0.15, 1.0, 0.3, 0.2], atol=0.02)
+
+
+class TestCCPSNumpyOracle:
+    def test_parametric_lane_matches_hand_algorithm_1(self):
+        """Equation 11 / Algorithm 1 with the parametric (in-sample nested
+        target) convention, folds re-derived from the same spawned seed."""
+        df = ccps_two_period_frame(n=600, dgp=1, seed=3)
+        seed, trim = 9, 0.01
+        res = DMLDiD(seed=seed, pscore_trim=trim).fit(
+            df, **CCPS_FIT_KW, covariates=["z"], bad_control="x", bad_control_covariates=["w", "y"]
+        )
+        D, dY, xt, xb, R, S = _ccps_cell_arrays(df, w_cols=("w", "y"))
+        n = len(D)
+        rng = np.random.default_rng(np.random.SeedSequence(entropy=seed, spawn_key=(0, 1)))
+        folds = assign_folds(n, 5, rng=rng, stratify=D)
+        ctrl = D == 0.0
+        m_hat = np.empty(n)
+        ps_raw = np.empty(n)
+        nu_hat = np.empty(n)
+        om_raw = np.empty(n)
+        for k, train, test in folds.iter_folds():
+            fit_idx = train[ctrl[train]]
+            m_k = LinearLearner().fit(R[fit_idx], dY[fit_idx])
+            p_k = LogitLearner().fit(S[train], D[train])
+            m_hat[test] = m_k.predict(R[test])
+            ps_raw[test] = p_k.predict_proba(S[test])[:, 1]
+            m_tr = m_k.predict(R[fit_idx])
+            p_tr = np.clip(p_k.predict_proba(S[fit_idx])[:, 1], trim, 1 - trim)
+            nu_hat[test] = LinearLearner().fit(S[fit_idx], m_tr).predict(S[test])
+            om_raw[test] = LinearLearner().fit(R[fit_idx], p_tr / (1 - p_tr)).predict(R[test])
+        ps = np.clip(ps_raw, trim, 1 - trim)
+        omega = np.clip(om_raw, 0.0, (1 - trim) / trim)
+        p_hat = float(D.mean())
+        summand = ccps_panel_score(dY, D, m_hat, nu_hat, ps, omega, p_hat)
+        theta = float(np.mean(summand))
+        psi_bar = ccps_panel_score_augmented(summand, D, theta, p_hat)
+        se = float(np.sqrt(np.mean(psi_bar**2) / n))
+        np.testing.assert_allclose(res.att, theta, rtol=1e-12, atol=0)
+        np.testing.assert_allclose(res.se, se, rtol=1e-12, atol=0)
+        # ATT_X: AIPW with mu_X = cross-fitted control regression of xt on S.
+        mu = cross_fit_predict(
+            LinearLearner(), S, xt, folds, predict_method="predict", fit_mask=ctrl
+        )
+        sx = chang_panel_score(xt, D, mu.oof_predictions, ps, p_hat)
+        att_x = float(np.mean(sx))
+        se_x = float(np.sqrt(np.mean(chang_panel_score_augmented(sx, D, att_x, p_hat) ** 2) / n))
+        entry = res.bad_control_diagnostics[(2, 2)]
+        np.testing.assert_allclose(entry["effect"], att_x, rtol=1e-12, atol=0)
+        np.testing.assert_allclose(entry["se"], se_x, rtol=1e-12, atol=0)
+        assert res.cross_fit_diagnostics[(2, 2)]["nested_stage"] == "in_sample"
+
+    def test_gapped_time_grid_uses_preceding_observed_period(self):
+        """Periods relabelled to a gapped grid: the bad control, W and dY are
+        read at the preceding OBSERVED period (positional base), so the fit
+        equals the fit on the unit-spaced labels."""
+        df = ccps_two_period_frame(n=400, dgp=1, seed=8)
+        a = DMLDiD(seed=1).fit(
+            df, **CCPS_FIT_KW, covariates=["z"], bad_control="x", bad_control_covariates=["y"]
+        )
+        gapped = df.replace({"time": {1: 1997, 2: 2003}, "first_treat": {2: 2003}})
+        b = DMLDiD(seed=1).fit(
+            gapped, **CCPS_FIT_KW, covariates=["z"], bad_control="x", bad_control_covariates=["y"]
+        )
+        assert a.att == b.att and a.se == b.se
+        assert (
+            b.bad_control_diagnostics[(2003, 2003)]["effect"]
+            == a.bad_control_diagnostics[(2, 2)]["effect"]
+        )
+
+
+class TestCCPSPlugInIdentity:
+    def test_native_nested_stage_is_assumption_8_plug_in(self):
+        """Per fold, OLS of the in-sample fitted R'beta on S among training
+        controls equals beta_1 * OLS(xt ~ S) + beta_2 xb + beta_3 Z (Section 6.1
+        plug-in), because xb and Z are columns of S."""
+        df = ccps_two_period_frame(n=500, dgp=1, seed=5)
+        D, dY, xt, xb, R, S = _ccps_cell_arrays(df, w_cols=("w",))
+        n = len(D)
+        folds = assign_folds(n, 5, rng=np.random.default_rng(0), stratify=D)
+        est = DMLDiD(seed=0)
+        _, _, nu_hat, _, stage = est._ccps_nuisances(
+            R, S, dY, D, folds, np.random.default_rng(1), None, False, "identity"
+        )
+        assert stage["nested_stage"] == "in_sample"
+        ctrl = D == 0.0
+        nu_hand = np.empty(n)
+        for k, train, test in folds.iter_folds():
+            fit_idx = train[ctrl[train]]
+            Rc = np.column_stack([np.ones(fit_idx.size), R[fit_idx]])
+            beta, *_ = np.linalg.lstsq(Rc, dY[fit_idx], rcond=None)
+            Sc = np.column_stack([np.ones(fit_idx.size), S[fit_idx]])
+            gamma, *_ = np.linalg.lstsq(Sc, xt[fit_idx], rcond=None)
+            S_test = np.column_stack([np.ones(test.size), S[test]])
+            xt_proj = S_test @ gamma
+            # R = [xt, xb, Z]; S = [xb, w, Z] -> xb = S[:, 0], Z = S[:, -1]
+            nu_hand[test] = (
+                beta[0] + beta[1] * xt_proj + beta[2] * S[test, 0] + beta[3] * S[test, -1]
+            )
+        np.testing.assert_allclose(nu_hat, nu_hand, rtol=0, atol=1e-10)
+
+
+class TestCCPSOracleLearnersSplitHalf:
+    def test_oracle_user_learners_match_closed_form(self):
+        """Foreign (oracle) learners take the split-half branch; with exact
+        nuisances the two half-models coincide and the fit equals the
+        closed-form score mean. DGP: xt(0) = 0.7 xb + 0.3 Z + e, m0 = xt (so
+        nu0 = mu_X = 0.7 xb + 0.3 Z), p(S) = expit(0.5 xb + 0.3 Z) on S = (xb, Z)
+        (W empty), so omega0(R) = exp(0.5 xb + 0.3 Z) exactly."""
+        rng = np.random.default_rng(12)
+        n = 800
+        xb = rng.standard_normal(n)
+        Z = rng.standard_normal(n)
+        p = 1 / (1 + np.exp(-(0.5 * xb + 0.3 * Z)))
+        D = (rng.uniform(size=n) < p).astype(float)
+        xt0 = 0.7 * xb + 0.3 * Z + 0.3 * rng.standard_normal(n)
+        xt = xt0 + 0.5 * D
+        y0 = rng.standard_normal(n)
+        dY = xt0 + 1.0 * D + 0.4 * rng.standard_normal(n)
+        rows = []
+        for i in range(n):
+            g = 2 if D[i] else 0
+            rows.append((i, 1, g, y0[i], xb[i], Z[i]))
+            rows.append((i, 2, g, y0[i] + dY[i], xt[i], Z[i]))
+        df = pd.DataFrame(rows, columns=["unit", "time", "first_treat", "y", "x", "z"])
+
+        class OracleProp:
+            def fit(self, X, y, sample_weight=None):
+                return self
+
+            def predict_proba(self, X):  # S = [xb, Z]
+                q = 1 / (1 + np.exp(-(0.5 * X[:, 0] + 0.3 * X[:, 1])))
+                return np.column_stack([1 - q, q])
+
+        class OracleReg:
+            omega = False
+
+            def fit(self, X, y, sample_weight=None):
+                # omega targets (odds) are strictly positive; dY / xt are not.
+                self.omega = X.shape[1] == 3 and bool(np.all(y > 0))
+                return self
+
+            def predict(self, X):
+                if X.shape[1] == 2:  # nu0(S) == mu_X(S)
+                    return 0.7 * X[:, 0] + 0.3 * X[:, 1]
+                if self.omega:  # omega0(R) with R = [xt, xb, Z]
+                    return np.exp(0.5 * X[:, 1] + 0.3 * X[:, 2])
+                return X[:, 0]  # m0(R) = xt
+
+        trim = 0.01
+        res = DMLDiD(
+            propensity_learner=OracleProp(), outcome_learner=OracleReg(), seed=0, pscore_trim=trim
+        ).fit(df, **CCPS_FIT_KW, covariates=["z"], bad_control="x")
+        assert res.cross_fit_diagnostics[(2, 2)]["nested_stage"] == "split_half"
+        ps = np.clip(p, trim, 1 - trim)
+        omega = np.clip(np.exp(0.5 * xb + 0.3 * Z), 0.0, (1 - trim) / trim)
+        p_hat = float(D.mean())
+        summand = ccps_panel_score(dY, D, xt, 0.7 * xb + 0.3 * Z, ps, omega, p_hat)
+        theta = float(np.mean(summand))
+        se = float(np.sqrt(np.mean(ccps_panel_score_augmented(summand, D, theta, p_hat) ** 2) / n))
+        np.testing.assert_allclose(res.att, theta, rtol=0, atol=1e-12)
+        np.testing.assert_allclose(res.se, se, rtol=0, atol=1e-12)
+        sx = chang_panel_score(xt, D, 0.7 * xb + 0.3 * Z, ps, p_hat)
+        np.testing.assert_allclose(
+            res.bad_control_diagnostics[(2, 2)]["effect"], float(np.mean(sx)), rtol=0, atol=1e-12
+        )
+
+
+class TestCCPSRecovery:
+    """Seed-pinned recovery on SA DGPs 1 and 4 (parametric DR: Tables S2 / S5)."""
+
+    @pytest.mark.parametrize("dgp,seed", [(1, 101), (1, 102), (4, 103), (4, 104)])
+    def test_att_and_att_x_recovery(self, dgp, seed):
+        df = ccps_two_period_frame(n=2000, dgp=dgp, seed=seed)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            res = DMLDiD(seed=seed).fit(
+                df, **CCPS_FIT_KW, covariates=["z"], bad_control="x", bad_control_covariates=["w"]
+            )
+        err = abs(res.att - CCPS_TRUE_ATT)
+        assert err < 3 * res.se, (res.att, res.se)
+        assert err < 0.15, (res.att, res.se)
+        # Discriminating assertion: the naive 'include X_t' contrast is biased
+        # (Section 3.1; the paper's TWFE-with-bad-control column carries the
+        # full -lambda = -0.50 bias, the regression-adjusted contrast here a
+        # partial share of it because X_t enters through a fitted slope).
+        naive_err = abs(_naive_include_xt_contrast(df) - CCPS_TRUE_ATT)
+        assert err < naive_err and naive_err > 0.1, (err, naive_err)
+        entry = res.bad_control_diagnostics[(2, 2)]
+        assert abs(entry["effect"] - CCPS_TRUE_ATT_X) < 3 * entry["se"], entry
+        assert abs(entry["effect"] - CCPS_TRUE_ATT_X) < 0.1, entry
+
+
+@pytest.mark.slow
+class TestCCPSMonteCarloCoverage:
+    @pytest.mark.parametrize("dgp", [1, 4])
+    def test_coverage_sanity(self, ci_params, dgp):
+        # Sanity check, not a calibration claim; band conditional on the
+        # scaled rep count (Tables S2 / S5 report ~0.95 for the parametric DR).
+        n_reps = ci_params.bootstrap(200)
+        hits_att = 0
+        hits_x = 0
+        for rep in range(n_reps):
+            df = ccps_two_period_frame(n=500, dgp=dgp, seed=50_000 + rep)
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore")
+                res = DMLDiD(seed=rep).fit(
+                    df,
+                    **CCPS_FIT_KW,
+                    covariates=["z"],
+                    bad_control="x",
+                    bad_control_covariates=["w"],
+                )
+            lo, hi = res.conf_int
+            hits_att += int(lo <= CCPS_TRUE_ATT <= hi)
+            ci = res.bad_control_diagnostics[(2, 2)]["conf_int"]
+            hits_x += int(ci[0] <= CCPS_TRUE_ATT_X <= ci[1])
+        lo_band, hi_band = (0.90, 0.99) if n_reps >= 100 else (0.80, 1.00)
+        assert lo_band <= hits_att / n_reps <= hi_band, hits_att / n_reps
+        assert lo_band <= hits_x / n_reps <= hi_band, hits_x / n_reps
diff --git a/tests/test_methodology_dr_scores.py b/tests/test_methodology_dr_scores.py
index 23cc5b043..18a9b18ec 100644
--- a/tests/test_methodology_dr_scores.py
+++ b/tests/test_methodology_dr_scores.py
@@ -354,3 +354,177 @@ def test_lambda_correction_changes_the_variance(self):
         se_full = np.sqrt(np.mean(psi_bar**2) / len(D))
         se_no_lambda = np.sqrt(np.mean(psi_no_lambda**2) / len(D))
         assert abs(se_full - se_no_lambda) / se_full > 1e-4
+
+
+# ===========================================================================
+# CCPS (2026) bad-control score (Equation 10) - pure-function methodology
+# ===========================================================================
+from diff_diff._dr_scores import ccps_panel_score, ccps_panel_score_augmented  # noqa: E402
+
+CCPS_TAU = 1.0
+
+
+def _ccps_dgp(n=300_000, seed=17):
+    """Two-period bad-control DGP with CLOSED-FORM nuisances (W empty).
+
+    xb, Z ~ N(0, 1); p(S) = expit(0.5 xb + 0.3 Z) is a function of
+    S = (xb, Z) only, so omega0(R) = p/(1-p) EXACTLY (Equation 9 with the
+    odds already S-measurable); xt(0) = 0.7 xb + 0.3 Z + e (independent of D
+    given S: Assumption 4); xt = xt(0) + 0.5 D (a genuine bad control);
+    m0(xt, xb, Z) = xt + 0.5 xb + 0.3 Z at the UNTREATED bad control;
+    dY = m0 + tau D + noise. Hence nu0(S) = E[m0 | S, D=0] = 1.2 xb + 0.6 Z and
+    the ATT is tau. Returns arrays evaluated at the OBSERVED bad control (the
+    score only reads m_hat/omega_hat on controls, where xt == xt(0)).
+    """
+    rng = np.random.default_rng(seed)
+    xb = rng.standard_normal(n)
+    Z = rng.standard_normal(n)
+    p = 1.0 / (1.0 + np.exp(-(0.5 * xb + 0.3 * Z)))
+    D = (rng.uniform(size=n) < p).astype(float)
+    xt0 = 0.7 * xb + 0.3 * Z + 0.3 * rng.standard_normal(n)
+    xt = xt0 + 0.5 * D
+    m0_untreated = xt0 + 0.5 * xb + 0.3 * Z
+    dY = m0_untreated + CCPS_TAU * D + 0.5 * rng.standard_normal(n)
+    m_true = xt + 0.5 * xb + 0.3 * Z
+    nu_true = 1.2 * xb + 0.6 * Z
+    omega_true = p / (1.0 - p)
+    return dict(xt=xt, xb=xb, Z=Z, D=D, dY=dY, p=p, m=m_true, nu=nu_true, omega=omega_true)
+
+
+class TestCCPSScore:
+    def _score_mean(self, d, m=None, nu=None, ps=None, omega=None):
+        m = d["m"] if m is None else m
+        nu = d["nu"] if nu is None else nu
+        ps = d["p"] if ps is None else ps
+        omega = d["omega"] if omega is None else omega
+        ps = np.clip(ps, 1e-3, 1 - 1e-3)
+        return float(
+            ccps_panel_score(d["dY"], d["D"], m, nu, ps, omega, float(d["D"].mean())).mean()
+        )
+
+    def test_score_mean_recovers_att_with_oracle_nuisances(self):
+        d = _ccps_dgp()
+        assert abs(self._score_mean(d) - CCPS_TAU) < 0.02
+
+    def test_double_robustness_paired_outcome_side(self):
+        # Proposition 6 (i): correct (m0, nu0) with WRONG (p, omega0) (an
+        # internally consistent wrong pair: constant propensity, its odds).
+        d = _ccps_dgp()
+        ps_wrong = np.full_like(d["p"], 0.4)
+        omega_wrong = np.full_like(d["p"], 0.4 / 0.6)
+        assert abs(self._score_mean(d, ps=ps_wrong, omega=omega_wrong) - CCPS_TAU) < 0.02
+
+    def test_double_robustness_paired_weighting_side(self):
+        # Proposition 6 (ii): correct (p, omega0) with WRONG (m0, nu0), keeping
+        # nu_wrong = E[m_wrong | S, D=0] (the pair stays functionally linked).
+        d = _ccps_dgp()
+        h = 0.8 * d["xb"] ** 2
+        assert abs(self._score_mean(d, m=d["m"] + h, nu=d["nu"] + h) - CCPS_TAU) < 0.02
+
+    def test_single_swaps_break_double_robustness(self):
+        # The pairing is m0 <-> omega0 and nu0 <-> p (Lemma S2 / Lemma S3):
+        # breaking BOTH members of a cancellation pair leaves an O(1) bias.
+        d = _ccps_dgp()
+        h = 0.8 * d["xb"] ** 2
+        omega_const = np.full_like(d["p"], 0.2)
+        bias_m_omega = self._score_mean(d, m=d["m"] + h, omega=omega_const) - CCPS_TAU
+        assert abs(bias_m_omega) > 0.05, bias_m_omega
+        ps_wrong = np.full_like(d["p"], 0.4)
+        bias_nu_p = self._score_mean(d, nu=d["nu"] + h, ps=ps_wrong) - CCPS_TAU
+        assert abs(bias_nu_p) > 0.05, bias_nu_p
+
+    @pytest.mark.parametrize("direction", ["m", "nu", "p", "omega"])
+    def test_neyman_orthogonality_vs_nonorthogonal_comparator(self, direction):
+        """Gateaux derivative of E[score] is zero in each nuisance direction at
+        the truth (Lemma S3's cross-terms), so the finite-sample shift under an
+        eps-perturbation is Monte Carlo noise, while a purpose-built
+        NON-orthogonal comparator shifts by O(eps). Orthogonal shift must be at
+        least 20x smaller.
+        """
+        d = _ccps_dgp(n=400_000, seed=23)
+        dY, D, xt, xb, Z = d["dY"], d["D"], d["xt"], d["xb"], d["Z"]
+        m, nu, omega = d["m"], d["nu"], d["omega"]
+        ps = np.clip(d["p"], 1e-3, 1 - 1e-3)
+        p_hat = float(D.mean())
+        eps = 0.05
+
+        def score(m_=m, nu_=nu, ps_=ps, om_=omega):
+            return float(ccps_panel_score(dY, D, m_, nu_, ps_, om_, p_hat).mean())
+
+        base_orth = score()
+        if direction == "m":
+            # h is a function of R; its S-projection is E[h | S, D=0].
+            h = 0.5 * xt + 0.3
+            h_proj = 0.5 * (0.7 * xb + 0.3 * Z) + 0.3
+            pert_orth = score(m_=m + eps * h)
+            # Comparator: regression-adjustment plug-in mean_D(dY - nu) with nu
+            # re-projected from the perturbed m (no reweighting terms).
+            base_naive = float((D * (dY - nu) / p_hat).mean())
+            pert_naive = float((D * (dY - (nu + eps * h_proj)) / p_hat).mean())
+        elif direction == "nu":
+            h = 0.5 * xb + 0.3
+            pert_orth = score(nu_=nu + eps * h)
+            base_naive = float((D * (dY - nu) / p_hat).mean())
+            pert_naive = float((D * (dY - (nu + eps * h)) / p_hat).mean())
+        elif direction == "p":
+            h = 0.5 * xb + 0.3
+            ps_pert = np.clip(ps + eps * h * ps * (1 - ps), 1e-3, 1 - 1e-3)
+            pert_orth = score(ps_=ps_pert)
+
+            def ipw(p_):  # Abadie IPW plug-in (no outcome adjustment)
+                return float(((D - p_ * (1 - D) / (1 - p_)) * dY / p_hat).mean())
+
+            base_naive = ipw(ps)
+            pert_naive = ipw(ps_pert)
+        else:
+            h = 0.5 * xt + 0.3
+            d_omega = eps * h
+            pert_orth = score(om_=omega + d_omega)
+            # Comparator: the omega term multiplies a NON-mean-zero residual
+            # (a biased outcome regression m + c inside the omega term only),
+            # so its omega-derivative is +c E[(1-D) d_omega]/p_hat != 0.
+            c = 0.5
+
+            def biased(om_):
+                return score(om_=om_) + float(((1 - D) / p_hat * c * om_).mean())
+
+            base_naive = biased(omega)
+            pert_naive = biased(omega + d_omega)
+
+        shift_orth = abs(pert_orth - base_orth)
+        shift_naive = abs(pert_naive - base_naive)
+        assert shift_orth < shift_naive / 20.0, (direction, shift_orth, shift_naive)
+
+    def test_reduces_to_chang_score_without_bad_control(self):
+        # nu = m and omega = ps/(1-ps): Equation 10 IS Chang's Case 1 score.
+        d = _ccps_dgp(n=5000, seed=3)
+        ps = np.clip(d["p"], 1e-3, 1 - 1e-3)
+        p_hat = float(d["D"].mean())
+        a = ccps_panel_score(d["dY"], d["D"], d["m"], d["m"], ps, ps / (1 - ps), p_hat)
+        b = chang_panel_score(d["dY"], d["D"], d["m"], ps, p_hat)
+        np.testing.assert_allclose(a, b, rtol=1e-12, atol=1e-14)
+
+    def test_augmented_step_is_chang_augmented(self):
+        # phi_i = phi_1i - ATT - (ATT/pi)(D_i - pi) == summand - D theta / pi.
+        d = _ccps_dgp(n=5000, seed=4)
+        ps = np.clip(d["p"], 1e-3, 1 - 1e-3)
+        p_hat = float(d["D"].mean())
+        s = ccps_panel_score(d["dY"], d["D"], d["m"], d["nu"], ps, d["omega"], p_hat)
+        theta = float(s.mean())
+        aug = ccps_panel_score_augmented(s, d["D"], theta, p_hat)
+        hand = s - theta - (theta / p_hat) * (d["D"] - p_hat)
+        np.testing.assert_allclose(aug, hand, rtol=0, atol=1e-12)
+        np.testing.assert_array_equal(aug, chang_panel_score_augmented(s, d["D"], theta, p_hat))
+        assert abs(aug.mean()) < 1e-12
+
+    def test_input_validation(self):
+        d = _ccps_dgp(n=50, seed=5)
+        ps = np.clip(d["p"], 1e-3, 1 - 1e-3)
+        with pytest.raises(ValueError, match="omega_hat must be non-negative"):
+            ccps_panel_score(d["dY"], d["D"], d["m"], d["nu"], ps, -d["omega"], 0.5)
+        with pytest.raises(ValueError, match="ps must lie in"):
+            ccps_panel_score(d["dY"], d["D"], d["m"], d["nu"], np.ones(50), d["omega"], 0.5)
+        with pytest.raises(ValueError, match="has length"):
+            ccps_panel_score(d["dY"], d["D"], d["m"][:-1], d["nu"], ps, d["omega"], 0.5)
+        with pytest.raises(ValueError, match="p_hat must satisfy"):
+            ccps_panel_score(d["dY"], d["D"], d["m"], d["nu"], ps, d["omega"], 1.0)
diff --git a/tests/test_variance_conventions.py b/tests/test_variance_conventions.py
index bc70123ec..2f5e2a01e 100644
--- a/tests/test_variance_conventions.py
+++ b/tests/test_variance_conventions.py
@@ -457,6 +457,40 @@ def snapshot(self):
             "outside the shared CR1 sandwich)"
         ),
     ),
+    dict(
+        key="dml_did_bad_control",
+        # The dml_did row plus a bad control that is time-varying WITH a
+        # unit-by-time interaction (so xt - xb varies within a cell and
+        # [1, xt, xb, Z] has full rank) but carries no treatment information
+        # (so S = [xb, W, Z] cannot separate D); W = the base-period outcome
+        # (Remark 5). The callable form is required: assign() exposes the
+        # in-flight x0 column only through callables.
+        fit=lambda df: diff_diff.DMLDiD(seed=0).fit(
+            df.assign(
+                x0=(df["unit"] % 7) * 0.1 + df["time"] * 0.01,
+                xb0=lambda d: 0.5 * d["x0"] + 0.1 * np.sin(d["unit"] * d["time"]),
+            ),
+            outcome="y",
+            unit="unit",
+            time="time",
+            first_treat="first_treat",
+            covariates=["x0"],
+            bad_control="xb0",
+            bad_control_covariates=["y"],
+        ),
+        cr1_k=(),
+        tail_df=(None,) * 31,
+        status="legitimate",
+        reason=(
+            "L3: Caetano et al. (2026) Eq. 11 augmented-score plug-in "
+            "variance (same psi_bar - D*theta/pi centering as Chang Thm 2; "
+            "per-unit influence function; normal-theory safe_inference on "
+            "no-design fits; cluster= fits use the CR1 per-cell variance with "
+            "df=df_survey t-inference) and the per-cell ATT_X diagnostic "
+            "tuple sharing the same branch and df (one extra safe_inference "
+            "call per retained cell)"
+        ),
+    ),
     dict(
         key="dml_did_rcs",
         # Declared repeated cross sections: every ROW becomes its own