diff --git a/research/fresh-stage-code-separation/.gitattributes b/research/fresh-stage-code-separation/.gitattributes
new file mode 100644
index 0000000000..5c3ebb21a9
--- /dev/null
+++ b/research/fresh-stage-code-separation/.gitattributes
@@ -0,0 +1,2 @@
+inputs/* -text
+inputs/CODE.json whitespace=cr-at-eol
diff --git a/research/fresh-stage-code-separation/MARKERS.json b/research/fresh-stage-code-separation/MARKERS.json
new file mode 100644
index 0000000000..da17f5279a
--- /dev/null
+++ b/research/fresh-stage-code-separation/MARKERS.json
@@ -0,0 +1,117 @@
+{
+  "candidates": [
+    {
+      "count": 1,
+      "markers": [
+        309
+      ],
+      "peak": 1,
+      "stages": 1
+    },
+    {
+      "count": 1,
+      "markers": [
+        126614
+      ],
+      "peak": 1,
+      "stages": 2
+    },
+    {
+      "count": 1,
+      "markers": [
+        3899261
+      ],
+      "peak": 26,
+      "stages": 3
+    },
+    {
+      "count": 1,
+      "markers": [
+        506572403
+      ],
+      "peak": 23,
+      "stages": 4
+    },
+    {
+      "count": 1,
+      "markers": [
+        833124451870,
+        1265346890653
+      ],
+      "peak": 4,
+      "stages": 5
+    },
+    {
+      "count": 1,
+      "markers": [
+        408929468020584
+      ],
+      "peak": 1,
+      "stages": 6
+    },
+    {
+      "count": 1,
+      "markers": [
+        49963241663044660,
+        139458250462523461
+      ],
+      "peak": 1,
+      "stages": 7
+    },
+    {
+      "count": 1,
+      "markers": [
+        22574143951628378081
+      ],
+      "peak": 25,
+      "stages": 8
+    },
+    {
+      "count": 1,
+      "markers": [
+        3269233485147391114919,
+        4403999331618672021121
+      ],
+      "peak": 9,
+      "stages": 9
+    },
+    {
+      "count": 1,
+      "markers": [
+        1910808833422019235783220062917221040555207,
+        31138120231488384951815458939426290644375402
+      ],
+      "peak": 2,
+      "stages": 18
+    },
+    {
+      "count": 1,
+      "markers": [
+        70541796919628375671566128214651723834380243,
+        7254591141270298746910948977345352434546466706
+      ],
+      "peak": 9,
+      "stages": 19
+    },
+    {
+      "count": 1,
+      "markers": [
+        90820347916622095582518564211431716385362683871828793962635448903515985308854,
+        10473238722956155051163163647634649414165919268007979792005949676167568968016,
+        138933692058999963102023854015813076970582531981952560053409013640878614458377
+      ],
+      "peak": 6,
+      "stages": 32
+    },
+    {
+      "count": 1,
+      "markers": [
+        3343955490819597787952613139068032833544208852026367057145856864438779104667712000068790382824883088091813720035528484315720325081696655061336528118435375,
+        7805584683125670274885243387008365246617964388761818552047635448596094037468158648266415105160820519742545074469325854219248677138452069352146598005629804
+      ],
+      "peak": 41,
+      "stages": 64
+    }
+  ],
+  "seed": 5376
+}
diff --git a/research/fresh-stage-code-separation/PROOF.md b/research/fresh-stage-code-separation/PROOF.md
new file mode 100644
index 0000000000..0525058917
--- /dev/null
+++ b/research/fresh-stage-code-separation/PROOF.md
@@ -0,0 +1,235 @@
+# Fresh-stage code products retain a terminal obstruction
+
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
+The source code is from Dillon / PR4933 and Dugongue / PR4929.
+Cinna Davis / PR5065 supplied the previous two-stage support theorem.
+
+## 1. Statement and source contract
+
+Fix k >= 1, independent of f. The binary address space is the direct sum of a common line E,
+with basis vector e, and k private spaces V_s of dimension eight. Each stage
+uses E + V_s and acts as the identity on all other private spaces. Each stage
+occurs once. Its exponent a_s can be any nonzero integer. Stage order is free.
+
+The 112 signed orthogonal monomial maps K_i and the rational matrix A are
+exactly the source data in inputs/. Their binary parts G_i satisfy
+
+    G_i e = q_i,       q_i != q_j for i != j,
+    A^2 + 12 A = 13 I,       A_01 = A_10 = -1/2.
+
+All G_i are orthogonal over F2. Define, at positive tensor width f,
+
+    (C_s,f)_ij = A_ij (K_s,i^-1 K_s,j)^(tensor f),
+    Q = (1+i) I/2 + (1-i) T_e/2,
+    B_f = C_k,f^a_k ... C_1,f^a_1,
+    J_f = Q^(-tensor f) B_f Q^(tensor f).
+
+Each owner coefficient is applied once, outside the tensor power. Tensoring
+the whole owner matrix would define a different operator.
+
+**Theorem.** Any exact implementation of J_f by scalar ADD/SCALE, monomial
+address maps, COPY and CLEAR has an ADD count g with
+
+    g >= max(0, 2f - 24k).
+
+There can be arbitrary mixing between owners and arbitrary owned workspace.
+The instruction schedule is linear and does not depend on input values.
+The scalar coefficients and monomial maps can depend on f. The bound still
+excludes an ADD count that is constant in f. It also applies to B_f^-1,
+because inversion reverses the distinct stages and negates their exponents.
+It does not bound the minimum number of paid Gaussian calls.
+
+For all sixteen negative-output banks in the saved PR4933 caller, the finite
+marker certificates below give the stronger bound
+
+    g >= max(0, 2f - 6).
+
+Some banks have offset three. The previous two-stage offset two is stronger
+for its two named banks and remains valid. No new kappa follows from these
+bounds. A bound linear in f does not exclude a scalar algorithm with that
+cost, an already-paid decoder, or a different recursive target type.
+
+## 2. Ordered local binary maps have a unique factorization
+
+Let H_s be the subgroup of GL(E + direct-sum V_t, F2) obtained by extending
+GL(E + V_s, F2) by the identity. If F_s and F'_s belong to H_s and
+
+    F_k ... F_1 = F'_k ... F'_1,
+
+then F_s = F'_s for every s. To prove this, move the last factors to one side:
+
+    (F'_k)^-1 F_k = F'_(k-1) ... F'_1 F_1^-1 ... F_(k-1)^-1.
+
+The left side is supported on E + V_k. The right side is supported on E plus
+the earlier private spaces. Their intersection is GL(E,F2). This group is
+trivial because E is a binary line. The last factors are equal. Remove them
+and repeat. This argument does not assume that the stages commute.
+
+Fix an input owner j_0 and an output owner j_k. A path j_0,...,j_k has binary
+map
+
+    G_path = product_(s=k,...,1) (G_s,j_s^-1 G_s,j_(s-1)).
+
+If two paths have the same map, the local factors are equal by the lemma.
+At the last stage the output owner is fixed, so equality forces the two
+previous G matrices to be equal. Their central images q_i are distinct,
+so the previous owner is the same. Repeat backwards. Thus every owner path
+has a different complete binary map, including paths with zero coefficients.
+Signed monomial terms therefore cannot cancel after collection.
+
+This is a statement about this ordered fresh-stage domain. It is not a
+unique-factorization claim for arbitrary words in the generated groups.
+
+## 3. A nonzero path survives every integer power
+
+The polynomial for A gives, for every integer a,
+
+    A^a = alpha_a A + (1-alpha_a) I,
+    alpha_a = (1-(-13)^a)/14.
+
+This follows by evaluating at the two distinct eigenvalues 1 and -13. It is
+valid for negative a because both eigenvalues are nonzero. Alpha_a is nonzero
+when a is nonzero. The same formula holds for C_s,f, since it is a block
+monomial conjugate of A tensored with the identity on the address space.
+
+Take the path j_s = s mod 2, starting at owner zero. Its coefficient is
+
+    c = (-1/2)^k product_s alpha_a_s != 0.
+
+At its first stage the map G_1,1^-1 G_1,0 sends e to a vector different from
+e. The vector is nonzero. It therefore has a nonzero component in V_1.
+Later stages cannot change that component. The complete G_path e differs
+from e. This path has a unique binary map by Section 2.
+
+The argument works for either parity of k. For even k the witness is in
+owner block (0,0); for odd k it is in block (1,0). It need not use the same
+owner block as the two-stage predecessor.
+
+## 4. Four nonzero entries after central conjugation
+
+Let M|x> = s(x)|Gx>, where s(x) is +1 or -1, and let G e != e. Direct expansion
+gives
+
+    2 Q^-1 M Q |x>
+      = s(x)|Gx> - i s(x+e)|Gx+Ge>
+        + i s(x)|Gx+e> + s(x+e)|Gx+Ge+e>.
+
+The four destinations are distinct because e and Ge are independent.
+Every coefficient has absolute value 1/2. The inverse map also moves e,
+so application of this argument to the adjoint proves that each row has
+four nonzero entries. This is the source's one-stage support argument.
+
+Write N_path = Q^-1 M_path Q. In one fixed owner block,
+
+    J_f = sum_path c_path N_path^(tensor f).
+
+This is a finite sum for fixed k. There can be exponentially many paths.
+The next step isolates one path without assuming that this sum is a tensor
+power of its width-one value.
+
+## 5. A coordinate contraction isolates a path
+
+All binary maps G_path are orthogonal. Two such maps that agree on the
+n-1 private basis vectors also agree on e, where n=8k+1. Indeed, the image
+of e is the unique nonzero vector in the orthogonal complement of the
+other n-1 orthonormal columns.
+
+Let G_* be the selected path in Section 3. For each private basis vector
+x_l, put y_l=G_* x_l and define a linear functional on base matrices by
+
+    ell_l(N) = (Q N Q^-1)[y_l,x_l].
+
+There are m=8k functionals. For each path, ell_l(N_path) is its signed
+monomial entry M_path[y_l,x_l]. The selected path has value +1 or -1 at
+every marker. Every other path has a zero marker. Contract the first m
+tensor factors of J_f with these functionals. For f>=m the result is
+
+    c_* eta N_*^(tensor (f-m)),       eta in {+1,-1}.
+
+This is a proof operation. It is not a free physical projector or an
+instruction that the caller can execute without charge.
+
+Each ell_l is a sum of four entries of N, using at most two output indices
+and two input indices. Fix any output row in the remaining factors. The
+contraction uses at most 2^m actual rows of J_f. If each actual row has at
+most S nonzero input coordinates, the contracted row has at most 2^m S
+nonzero remaining input coordinates. Summing over marker input indices
+cannot increase this union beyond S for each fixed actual row.
+
+The isolated row has exactly 4^(f-m) nonzero entries. Consequently
+
+    S >= 4^(f-m) / 2^m = 2^(2f-3m).
+
+Every initial role row depends on at most one independent input coordinate.
+A monomial map, SCALE, COPY or CLEAR cannot increase the maximum support.
+Each binary scalar ADD increases it by at most a factor two. Thus S<=2^g,
+and g>=2f-3m=2f-24k. For f<m the stated nonnegative bound is automatic.
+This proves the theorem. It permits arbitrary cross-owner scalar work;
+no source-preserving or two-read restriction was imposed.
+
+## 6. Short certificates for the actual caller
+
+A marker need not be a basis vector. Any inputs x_1,...,x_m that isolate the
+selected path give the same bound g>=max(0,2f-3m). MARKERS.json records such
+addresses. They were found by a deterministic bounded search; their validity
+does not depend on the search or its seed.
+
+The checker counts every surviving owner path by dynamic programming. At a
+stage boundary its state is the current owner and the m central bits. Each
+private input block is already fixed by the marker input. The stage must
+produce the prescribed private output block. Those bits never change again.
+The state then records the new owner and central bits. There are at most
+112*2^m states per layer. Counts are exact nonnegative integers.
+
+The transition domain includes every nonzero A edge and every diagonal edge.
+It therefore contains the nonzero paths of every nonzero integer power,
+regardless of signs. A final count of one proves that only the selected path
+survives. A second computation runs backwards, using separately composed
+inverse matrices instead of the forward literal K lookup tables. The small
+complete path censuses check the coordinate contraction directly.
+
+Every bank length in the source endpoint has a certificate with m<=2.
+The longest negative bank has eighteen distinct stages. The source specifies
+its endpoint as E_i=Q^-1 B_i D_i and its required Gaussian job as Q^-1 D_i.
+Its unique postdecoder is Q^-1 B_i^-1 Q, which is covered by the theorem.
+The saved endpoint and its source lineage remain premises: this package does
+not replay or admit the full producer, compiler, or outer construction.
+
+The theorem concerns decoding from the emitted bank and independent extra
+inputs. Additional retained histories correlated with the original main
+inputs can change that interface. Their complete charged consumer is outside
+this theorem and remains an active research route.
+
+## 7. Two explicit boundaries of the result
+
+Repeated stages can cancel: C_s C_s^-1=I. Their factors do not have distinct
+private supports, so Section 2 does not apply. This is an exact positive
+control, not a claim that a profitable repeated-stage caller exists.
+
+Two common axes also change the lemma. On four coordinates, let the common
+space have axes 0,1, and let the two private spaces have axes 2 and 3. Put
+
+    H=(0 1),       L=(0 3),       R=(0 2).
+
+Here permutations denote binary permutation matrices. Both factorizations
+
+    L R = (L H)(H R)
+
+use the correct two local supports, but their local factors differ. More
+concretely, choose K_t,0=K_s,1=I, K_t,2=L, K_s,2=R, and
+K_t,98=L H, K_s,98=R H. The two intermediate-owner paths 2 and 98 have the
+same signed monomial L R. Their port images are distinct within each named
+stage. In the actual scalar code,
+
+    A_02 A_21 = 1/4,       A_0,98 A_98,1 = -1/4.
+
+These two terms cancel exactly, at every tensor width, even after conjugation
+by Q. Each term alone is nonmonomial after that conjugation. The control uses
+permutation lifts with sign +1, so it also checks absolute phase.
+
+This is a concrete two-path cancellation under a changed interface. It is
+not a completed 112-owner provider, a replacement for all the source port
+normalizers, or a favorable paid invoice. The additional shared axis and its
+producer, targets, restoration, and routing must all be charged. It identifies
+an algebraic mechanism that the one-line theorem excludes, rather than a
+new kappa improvement.
diff --git a/research/fresh-stage-code-separation/README.md b/research/fresh-stage-code-separation/README.md
new file mode 100644
index 0000000000..48ff1cede8
--- /dev/null
+++ b/research/fresh-stage-code-separation/README.md
@@ -0,0 +1,115 @@
+# Fresh-stage terminal codes: an all-length obstruction and a changed interface
+
+For the actual PR4933 code, a product of any fixed number of distinct fresh
+stages cannot acquire a constant-size scalar/monomial terminal decoder. This
+holds for every order, every nonzero integer stage power, arbitrary scalar
+owner mixing, and owned workspace. The proof gives
+`ADDs >= max(0, 2f - 24k)` for k stages and tensor width f.
+
+Exact short certificates cover **all sixteen negative-output banks** in the
+saved caller, including its eighteen-stage bank. They give the stronger bound
+`ADDs >= max(0, 2f - 6)` for each bank. These bounds cannot be added across
+banks. The earlier two-stage result has a better constant for its two banks.
+
+The [proof](PROOF.md) separates every owner path through the private stage
+coordinates. It then contracts a few coordinate columns to retain one
+nonmonomial term. The [receipt](RESULT.json) and [marker certificates](MARKERS.json)
+contain the finite source and caller checks. The all-length statement rests
+on the written induction, not a stage-count census.
+
+**No new kappa is claimed.** The selected conditional value at the pinned base
+is 0.0030217758. This result rejects free terminal cancellation by adding more
+distinct fresh stages. It does not reject paid decoders, a number of scalar
+operations that grows with f, correlated retained histories, repeated stages,
+changed whole-controller boundaries, or a new recursive job family.
+
+There is a constructive boundary example. With **two shared central axes**,
+two different owner paths have the same complete operator. Actual source
+coefficients +1/4 and -1/4 then cancel at every tensor width. Section 7 gives
+all maps and checks their phases. This supplies a concrete cancellation
+mechanism outside the theorem. It is only a two-path construction, not a
+complete 112-owner provider or a favorable recursive invoice.
+
+## Reproduce
+
+Use Python 3.12 and its standard library, from the repository root:
+
+```sh
+python3 -B scripts/research_package.py --package research/fresh-stage-code-separation
+```
+
+The standalone, read-only checks are:
+
+```sh
+python3 -I -B research/fresh-stage-code-separation/verify.py
+python3 -I -O -B research/fresh-stage-code-separation/verify.py
+```
+
+Expected final marker:
+
+```text
+PASS_ALL_LENGTH_FRESH_STAGE_SEPARATION_NO_NEW_KAPPA
+```
+
+A direct normal replay took 7.91 seconds on the author's CPython 3.12.13
+macOS host. This is a local measurement, not a portable performance bound.
+The checks include 57,344 signed normalizer entries, 12,544 code-polynomial
+entries, all 12,656 two/three-stage paths, 12,654 explicit killing markers,
+and forward/reverse dynamic programs for the short certificates. The larger
+path controls reach 64 stages. Exact repeated-stage cancellation and a
+two-shared-axis collision check the excluded premises.
+
+The marker proposer is separate from the verifier. To reproduce its bounded
+search, use a new output file:
+
+```sh
+python3 -B research/fresh-stage-code-separation/select_markers.py --output /tmp/fresh-markers.json
+```
+
+The verifier imports no source evaluator or proposer. Its two path evaluators
+use composed signed maps and literal lookup tables. Its two dynamic programs
+run in opposite directions with different local calculations. They share the
+source data and elementary matrix code; this is not independent human or
+proof-kernel review. No complete supplier, compiler, outer, selected cold,
+Lean or Docker replay is claimed.
+
+## Open next questions
+
+1. Complete a two-shared-axis native provider that uses the displayed
+   cancellation. Start with one two-stage pair, complete every owner map and
+   every original-input output, then price the extra central axis and lost
+   targets. The current two-path witness supplies neither that provider nor
+   a favorable cost allowance. A full optimistic bill must pass before a
+   larger search is justified.
+2. Bind one original negative bank to an available paid IDLE or to a charged
+   scalar program whose length depends on f. Check every input, return,
+   precision and movement charge. The ADD lower bound alone cannot compare
+   that complete cost with the center saving. Existing paid-history and
+   coupled-helper caller claims remain separate.
+
+## Source, credit and status
+
+The base is canonical main `1ec1119972c9aefe42525172d07b332fcff81cb4`,
+priority revision 7. [SOURCES.json](SOURCES.json) binds all copied bytes and
+retains source notices and license. The
+[canonical claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19156145)
+records the scope and overlap. [RESEARCH-NOTES.md](RESEARCH-NOTES.md) records
+the route decision and the failed preliminary screen.
+
+Dillon's [PR #4933](https://github.com/CrocSwap/integer-mult-bounds/pull/4933)
+supplies the physical normalizers, one-stage support argument and complete
+coded caller. Cinna Davis's
+[PR #5065](https://github.com/CrocSwap/integer-mult-bounds/pull/5065) supplies
+the two-stage marker proof and the longer-product question. Dugongue's
+[PR #4929](https://github.com/CrocSwap/integer-mult-bounds/pull/4929) supplies
+the center-free code. Cao Yifan / intqwq, Cinna Davis / 1337isnot1337, zxv,
+Jacob Alan Sussman, Ryanson Jonathan and the native/controller lineage retain
+their source credit. The inherited code, its spectrum and the one-stage
+four-point expansion are not new results here.
+
+The new contribution is ordered fresh-stage path separation, the all-length
+support bound, short exact certificates for the other caller banks, and the
+explicit two-center path cancellation. These are author-checked mathematical
+results, without a literature-priority claim. Prepared by Ali Romman with
+substantial OpenAI Codex assistance; Apache-2.0. No selected frontier change,
+merge, or change to another contributor's work is requested.
diff --git a/research/fresh-stage-code-separation/RESEARCH-NOTES.md b/research/fresh-stage-code-separation/RESEARCH-NOTES.md
new file mode 100644
index 0000000000..495d924391
--- /dev/null
+++ b/research/fresh-stage-code-separation/RESEARCH-NOTES.md
@@ -0,0 +1,67 @@
+# Research decisions and checks
+
+The user asked for more progress after PR5376 applied the new Clifford
+verifier to the complete selected local provider. That earlier package
+excludes fixed early/late pair fusions. It stays unchanged.
+
+The new round started from canonical main
+`1ec1119972c9aefe42525172d07b332fcff81cb4`. Current priorities retain broad
+mechanism work. The selected value is 0.0030217758. The complete direct-caller
+comparison is PR5398 / PR5400 at 0.00302728823. No claim in this package raises
+those values.
+
+A preliminary frame-contact probe rebuilt the selected word as 1,068 contact
+components and 3,298 paid edges. With original endpoints, warps and centers
+fixed, 718 components were free. Replacing one component by a neighboring
+existing frame gave no lower approximate moment at exponent 0.997. This is
+only a small discovery screen. It is not an optimum or a new contribution.
+The live overlap check found broader active frame searches, so this lane was
+left to their owners. The probe scripts and receipts are saved in the task's
+project research record.
+
+The coded-reverse proposal has separate physical and compiler gaps. The
+existing one/two-stage terminal results explicitly leave longer distinct-stage
+products open. The new question takes that released mathematical gap. It does
+not take the active native paid-history or coupled-helper caller work.
+The overlap snapshot at 23:17/23:18 UTC on 2026-10-23 covered all 354 open PR
+bodies and 4,690 Discussion records with complete remote pagination. Local
+notes were sparse. It is not an exhaustive code or literature novelty search.
+
+The first proof used 8k private basis columns as markers. This gives an
+all-length theorem without expanding the owner paths. A bounded marker search
+then found one or two columns for every bank length in the actual caller.
+Exact forward/reverse dynamic counts, rather than a random sample, check each
+saved marker set against all paths. The count domain also includes diagonal
+edges, so the certificates cover every nonzero integer stage power.
+
+The scalar code relation extends the sign cases to arbitrary nonzero integer
+powers. No source coefficient is tensor powered. This distinction is retained
+in the proof and checks.
+
+The unique factorization uses GL(1,F2)={I}. A second common binary coordinate
+removes that premise. Two actual opposite scalar coefficients then admit an
+exact path cancellation with changed permutation normalizers. This is a useful
+new algebraic direction, but no complete changed native provider was built.
+The additional central axis, all remaining owners, targets and cleanup are
+unpriced. The family expansion decision is therefore: publish the theorem and
+small exact escape mechanism; require a complete two-stage budget before a
+larger synthesis campaign.
+
+A further local screen shared each of the eight possible old private axes
+between two actual source stages. In owner block (0,1), sharing old axis one
+merged 26 paths into 21 signed maps; all 21 coefficients stayed nonzero.
+The other seven choices retained 26 nonzero maps. Thus simple coordinate
+sharing did not supply a complete decoder. This bounded discovery screen is
+saved with the project record and is not used as a theorem premise. The
+positive two-path example instead changes the corresponding normalizers.
+
+The first commit normalized the CRLF end of the frozen CODE.json input.
+The committed-byte check caught the difference. Package attributes now keep
+all copied inputs byte-exact. The scientific data and proof are unchanged.
+
+Normal/optimized registered replays, committed bytes, export checks and
+publication evidence are reported in the final public handoff. This file does
+not treat a pending hosted check as a pass. The mathematical proof and finite
+checks are distinct. Independent human and formal-kernel review remain open.
+
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
diff --git a/research/fresh-stage-code-separation/RESULT.json b/research/fresh-stage-code-separation/RESULT.json
new file mode 100644
index 0000000000..11420b222f
--- /dev/null
+++ b/research/fresh-stage-code-separation/RESULT.json
@@ -0,0 +1,868 @@
+{
+  "code_polynomial_entries": 12544,
+  "complete_path_censuses": [
+    {
+      "active_paths": [
+        53,
+        52,
+        52,
+        52
+      ],
+      "all_paths": 112,
+      "marker_columns": 16,
+      "signs": [
+        [
+          -1,
+          -1
+        ],
+        [
+          -1,
+          1
+        ],
+        [
+          1,
+          -1
+        ],
+        [
+          1,
+          1
+        ]
+      ],
+      "stages": 2
+    },
+    {
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+}
diff --git a/research/fresh-stage-code-separation/SOURCES.json b/research/fresh-stage-code-separation/SOURCES.json
new file mode 100644
index 0000000000..289aea3b2e
--- /dev/null
+++ b/research/fresh-stage-code-separation/SOURCES.json
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+      "path": "research/coded-native-caller/LICENSE",
+      "usage": "provenance",
+      "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64",
+      "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4"
+    },
+    {
+      "path": "research/coded-native-caller/ORIGINS.json",
+      "usage": "provenance",
+      "git_blob": "e18a033d4de1d997f55e84d1535fc6cde20424c4",
+      "sha256": "10cf47173ca238c32adb923daae7c1137c2e9c86c7066301d68fc74442b3f4d7"
+    },
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b288ae44032fd84dd5564243422836cbcd29835e",
+      "sha256": "f9ed52bb642cd1e1486cf2743557ac5fa23cf1514a3277d786a644e39a565038"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "research/two-stage-coded-terminal/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "228baac8d81081e32995a3596e9a913924801d9a",
+      "sha256": "5a8d0b3f6179c6b5892d55638a6cb8d58ab0135224da07ac181b6edad4cf4e8e"
+    },
+    {
+      "path": "research/two-stage-coded-terminal/README.md",
+      "usage": "provenance",
+      "git_blob": "86e7af1c02878abd03e2287fa6c87f94d3371ef1",
+      "sha256": "1547a1b5fbb4b919fa90c6b2c3e476e51e52ca8f99c39a5f6a268757eced1365"
+    }
+  ]
+}
diff --git a/research/fresh-stage-code-separation/TASK.json b/research/fresh-stage-code-separation/TASK.json
new file mode 100644
index 0000000000..e72549b291
--- /dev/null
+++ b/research/fresh-stage-code-separation/TASK.json
@@ -0,0 +1,79 @@
+{
+  "schema_version": 1,
+  "task_id": "complex-rank-shape-decoder",
+  "priority_revision": 7,
+  "base_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+  "original_card": {
+    "id": "complex-rank-shape-decoder",
+    "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/complex-local-word-ceiling/README.md",
+      "research/complex-decoder-field-extension-seed44/README.md",
+      "research/complex-frame-pair-decoders/README.md",
+      "research/selected-k8-unrestricted-ends/README.md",
+      "research/eisenstein-reduction-copy-floor/README.md"
+    ],
+    "methods": [
+      "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.",
+      "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration."
+    ],
+    "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/complex-local-word-ceiling/verify.py"
+      ],
+      "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+      "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+      "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).",
+    "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.",
+    "allowed_variations": [
+      "One masked, overcomplete or block decoder family with exact labels and supports.",
+      "A scoped lower bound on effective rank for one alphabet.",
+      "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+    ],
+    "scope_change_triggers": [
+      "Repacking idle remainders of an unchanged word (covered by the packing ceiling).",
+      "Repeating the eight-term all-pairs search inside its proved scope.",
+      "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.",
+      "Searching below C=40 in the #2017 Eisenstein binary scalar-rectangle or fixed-support block-linear additive pairing model; specify a changed premise instead. This bound does not cover every complex decoder.",
+      "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+    ],
+    "overlap_terms": [
+      "rank shape",
+      "block climb",
+      "masked decoder",
+      "overcomplete",
+      "effective rank"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "All-length path separation and terminal support for distinct fresh code stages with one shared binary axis; short certificates for all sixteen source negative banks.",
+  "scope_change_reason": "The user requested a further structural result after the complete-provider fusion obstruction. The released two-stage handoff leaves arbitrary-length code products open.",
+  "bottleneck_link": "A center-free invoice cannot credit the old Gaussian targets until its coded output banks have a charged decoder. This result closes fixed scalar/monomial postdecoding at all distinct-stage lengths and exhibits a two-shared-axis path collision.",
+  "budget_minutes": 240,
+  "stop_rule": "Complete the all-length proof and source-bound checks. Do not take over the active paid-history, coupled-helper caller or contact-frame searches.",
+  "outcome": "negative-result",
+  "evidence": "PROOF.md, RESULT.json, MARKERS.json, verify.py",
+  "author": "Ali Romman with substantial OpenAI Codex assistance",
+  "ai_assistance": "Substantial OpenAI Codex assistance. No subagents, independent human review or proof-kernel acceptance.",
+  "open_questions": [
+    {
+      "question": "Can a two-shared-axis native provider use the exhibited path cancellation for a complete paid saving?",
+      "why_it_matters": "The one-axis separation theorem no longer applies, and two actual scalar code paths now cancel.",
+      "first_step": "Complete the remaining owner normalizers and required producer identities for one two-stage pair, then count every extra central Gaussian and lost target.",
+      "blocked_by": "Only the two-path algebraic cancellation is constructed; no complete provider or favorable cost bound is known."
+    },
+    {
+      "question": "Can an already-paid decoder or a charged width-dependent scalar program complete the original coded endpoint?",
+      "why_it_matters": "The theorem excludes fixed ADD count but does not charge or exclude these resources.",
+      "first_step": "Bind one full negative bank to its actual available paid IDLE and replay all inputs, including the bank return.",
+      "blocked_by": "A complete chronological decoder and its full paid, scalar, storage and precision bill are absent. The active coupled-helper caller claim remains separate."
+    }
+  ],
+  "canonical_claim": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19156145"
+}
diff --git a/research/fresh-stage-code-separation/VERIFY.json b/research/fresh-stage-code-separation/VERIFY.json
new file mode 100644
index 0000000000..4edbdc9eec
--- /dev/null
+++ b/research/fresh-stage-code-separation/VERIFY.json
@@ -0,0 +1,30 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 300,
+      "checks": "Source polynomial and signed maps; all two/three-stage paths; forward/reverse marker counts; sixteen actual banks; exact scope controls"
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 300,
+      "checks": "The same exact evidence with Python assertions disabled"
+    }
+  ]
+}
diff --git a/research/fresh-stage-code-separation/inputs/CODE.json b/research/fresh-stage-code-separation/inputs/CODE.json
new file mode 100644
index 0000000000..03170f4a31
--- /dev/null
+++ b/research/fresh-stage-code-separation/inputs/CODE.json
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diff --git a/research/fresh-stage-code-separation/inputs/GAUGE.json b/research/fresh-stage-code-separation/inputs/GAUGE.json
new file mode 100644
index 0000000000..69877f1514
--- /dev/null
+++ b/research/fresh-stage-code-separation/inputs/GAUGE.json
@@ -0,0 +1,4741 @@
+{
+  "chronology": {
+    "first_unmatched_bridge": {
+      "event_index": 51,
+      "from_pair": 7,
+      "left_word": [
+        [
+          15,
+          -1
+        ],
+        [
+          13,
+          -1
+        ],
+        [
+          11,
+          -1
+        ],
+        [
+          9,
+          -1
+        ],
+        [
+          7,
+          -1
+        ],
+        [
+          5,
+          -1
+        ],
+        [
+          3,
+          -1
+        ],
+        [
+          1,
+          -1
+        ],
+        [
+          0,
+          1
+        ]
+      ],
+      "right_word": [],
+      "to_pair": 8
+    },
+    "full_calls": 18,
+    "matched_prefix_bridges": [
+      0,
+      1,
+      2,
+      3,
+      4,
+      5,
+      6
+    ],
+    "paid_idles": 15,
+    "scope": "This records the candidate per-pair gauge policy; it does not prove that every whole-word policy fails.",
+    "source_sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f"
+  },
+  "complete_gaussian_supplier": false,
+  "complete_typed_rational_caller": true,
+  "idle": {
+    "missing_stage_rejected": true,
+    "mixed_orientations": true,
+    "stages": 4
+  },
+  "local": {
+    "backward": true,
+    "forward": true,
+    "noncommuting_controls": 3,
+    "wrong_word_controls": 2
+  },
+  "noncommutative_core": {
+    "both_scalar_boundaries": true,
+    "diagonal_words": [
+      [
+        18,
+        17
+      ],
+      [
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+        17,
+        16
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+      [
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+      [
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+      [
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+      [
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+      [
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+      [
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+        "code_word_left_to_right": [
+          [
+            5,
+            -1
+          ],
+          [
+            3,
+            -1
+          ],
+          [
+            1,
+            -1
+          ],
+          [
+            0,
+            1
+          ]
+        ],
+        "gaussian_stages": [
+          5,
+          3,
+          1,
+          0
+        ],
+        "operator": "B D Q",
+        "plain_gaussian_after_free_postdecode": true,
+        "role": 26
+      },
+      {
+        "central_exponent": 1,
+        "code_word_left_to_right": [
+          [
+            7,
+            -1
+          ],
+          [
+            5,
+            -1
+          ],
+          [
+            3,
+            -1
+          ],
+          [
+            1,
+            -1
+          ],
+          [
+            0,
+            1
+          ]
+        ],
+        "gaussian_stages": [
+          7,
+          5,
+          3,
+          1,
+          0
+        ],
+        "operator": "B D Q",
+        "plain_gaussian_after_free_postdecode": true,
+        "role": 27
+      },
+      {
+        "central_exponent": 1,
+        "code_word_left_to_right": [
+          [
+            9,
+            -1
+          ],
+          [
+            7,
+            -1
+          ],
+          [
+            5,
+            -1
+          ],
+          [
+            3,
+            -1
+          ],
+          [
+            1,
+            -1
+          ],
+          [
+            0,
+            1
+          ]
+        ],
+        "gaussian_stages": [
+          9,
+          7,
+          5,
+          3,
+          1,
+          0
+        ],
+        "operator": "B D Q",
+        "plain_gaussian_after_free_postdecode": true,
+        "role": 28
+      },
+      {
+        "central_exponent": 1,
+        "code_word_left_to_right": [
+          [
+            11,
+            -1
+          ],
+          [
+            9,
+            -1
+          ],
+          [
+            7,
+            -1
+          ],
+          [
+            5,
+            -1
+          ],
+          [
+            3,
+            -1
+          ],
+          [
+            1,
+            -1
+          ],
+          [
+            0,
+            1
+          ]
+        ],
+        "gaussian_stages": [
+          11,
+          9,
+          7,
+          5,
+          3,
+          1,
+          0
+        ],
+        "operator": "B D Q",
+        "plain_gaussian_after_free_postdecode": true,
+        "role": 29
+      },
+      {
+        "central_exponent": 1,
+        "code_word_left_to_right": [
+          [
+            13,
+            -1
+          ],
+          [
+            11,
+            -1
+          ],
+          [
+            9,
+            -1
+          ],
+          [
+            7,
+            -1
+          ],
+          [
+            5,
+            -1
+          ],
+          [
+            3,
+            -1
+          ],
+          [
+            1,
+            -1
+          ],
+          [
+            0,
+            1
+          ]
+        ],
+        "gaussian_stages": [
+          13,
+          11,
+          9,
+          7,
+          5,
+          3,
+          1,
+          0
+        ],
+        "operator": "B D Q",
+        "plain_gaussian_after_free_postdecode": true,
+        "role": 30
+      },
+      {
+        "central_exponent": 1,
+        "code_word_left_to_right": [
+          [
+            32,
+            1
+          ],
+          [
+            31,
+            -1
+          ],
+          [
+            29,
+            -1
+          ],
+          [
+            27,
+            -1
+          ],
+          [
+            25,
+            -1
+          ],
+          [
+            23,
+            -1
+          ],
+          [
+            21,
+            -1
+          ],
+          [
+            19,
+            -1
+          ],
+          [
+            17,
+            -1
+          ],
+          [
+            15,
+            -1
+          ],
+          [
+            13,
+            -1
+          ],
+          [
+            11,
+            -1
+          ],
+          [
+            9,
+            -1
+          ],
+          [
+            7,
+            -1
+          ],
+          [
+            5,
+            -1
+          ],
+          [
+            3,
+            -1
+          ],
+          [
+            1,
+            -1
+          ],
+          [
+            0,
+            1
+          ]
+        ],
+        "gaussian_stages": [
+          32,
+          31,
+          29,
+          27,
+          25,
+          23,
+          21,
+          19,
+          17,
+          15,
+          13,
+          11,
+          9,
+          7,
+          5,
+          3,
+          1,
+          0
+        ],
+        "operator": "B D Q",
+        "plain_gaussian_after_free_postdecode": true,
+        "role": 31
+      }
+    ],
+    "factored_code_adds_each": 896,
+    "factored_code_adds_total": 173824,
+    "factored_code_clears_total": 3104,
+    "factored_code_owned_temporaries": 8,
+    "helper_reward_multiplicity": 18,
+    "independent_helper_inputs": 7344,
+    "independent_main_inputs": 3584,
+    "left_boundary_row_parities": [
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1
+    ],
+    "positive_half_postdecode": [
+      {
+        "execution_order": [
+          [
+            32,
+            -1
+          ],
+          [
+            31,
+            1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 16
+      },
+      {
+        "execution_order": [
+          [
+            32,
+            -1
+          ],
+          [
+            31,
+            1
+          ],
+          [
+            29,
+            1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 17
+      },
+      {
+        "execution_order": [
+          [
+            32,
+            -1
+          ],
+          [
+            31,
+            1
+          ],
+          [
+            29,
+            1
+          ],
+          [
+            27,
+            1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 18
+      },
+      {
+        "execution_order": [
+          [
+            32,
+            -1
+          ],
+          [
+            31,
+            1
+          ],
+          [
+            29,
+            1
+          ],
+          [
+            27,
+            1
+          ],
+          [
+            25,
+            1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 19
+      },
+      {
+        "execution_order": [
+          [
+            32,
+            -1
+          ],
+          [
+            31,
+            1
+          ],
+          [
+            29,
+            1
+          ],
+          [
+            27,
+            1
+          ],
+          [
+            25,
+            1
+          ],
+          [
+            23,
+            1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 20
+      },
+      {
+        "execution_order": [
+          [
+            32,
+            -1
+          ],
+          [
+            31,
+            1
+          ],
+          [
+            29,
+            1
+          ],
+          [
+            27,
+            1
+          ],
+          [
+            25,
+            1
+          ],
+          [
+            23,
+            1
+          ],
+          [
+            21,
+            1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 21
+      },
+      {
+        "execution_order": [
+          [
+            32,
+            -1
+          ],
+          [
+            31,
+            1
+          ],
+          [
+            29,
+            1
+          ],
+          [
+            27,
+            1
+          ],
+          [
+            25,
+            1
+          ],
+          [
+            23,
+            1
+          ],
+          [
+            21,
+            1
+          ],
+          [
+            19,
+            1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 22
+      },
+      {
+        "execution_order": [
+          [
+            32,
+            -1
+          ],
+          [
+            31,
+            1
+          ],
+          [
+            29,
+            1
+          ],
+          [
+            27,
+            1
+          ],
+          [
+            25,
+            1
+          ],
+          [
+            23,
+            1
+          ],
+          [
+            21,
+            1
+          ],
+          [
+            19,
+            1
+          ],
+          [
+            17,
+            1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 23
+      },
+      {
+        "execution_order": [
+          [
+            1,
+            1
+          ],
+          [
+            0,
+            -1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 24
+      },
+      {
+        "execution_order": [
+          [
+            3,
+            1
+          ],
+          [
+            1,
+            1
+          ],
+          [
+            0,
+            -1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 25
+      },
+      {
+        "execution_order": [
+          [
+            5,
+            1
+          ],
+          [
+            3,
+            1
+          ],
+          [
+            1,
+            1
+          ],
+          [
+            0,
+            -1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 26
+      },
+      {
+        "execution_order": [
+          [
+            7,
+            1
+          ],
+          [
+            5,
+            1
+          ],
+          [
+            3,
+            1
+          ],
+          [
+            1,
+            1
+          ],
+          [
+            0,
+            -1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 27
+      },
+      {
+        "execution_order": [
+          [
+            9,
+            1
+          ],
+          [
+            7,
+            1
+          ],
+          [
+            5,
+            1
+          ],
+          [
+            3,
+            1
+          ],
+          [
+            1,
+            1
+          ],
+          [
+            0,
+            -1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 28
+      },
+      {
+        "execution_order": [
+          [
+            11,
+            1
+          ],
+          [
+            9,
+            1
+          ],
+          [
+            7,
+            1
+          ],
+          [
+            5,
+            1
+          ],
+          [
+            3,
+            1
+          ],
+          [
+            1,
+            1
+          ],
+          [
+            0,
+            -1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 29
+      },
+      {
+        "execution_order": [
+          [
+            13,
+            1
+          ],
+          [
+            11,
+            1
+          ],
+          [
+            9,
+            1
+          ],
+          [
+            7,
+            1
+          ],
+          [
+            5,
+            1
+          ],
+          [
+            3,
+            1
+          ],
+          [
+            1,
+            1
+          ],
+          [
+            0,
+            -1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 30
+      },
+      {
+        "execution_order": [
+          [
+            32,
+            -1
+          ],
+          [
+            31,
+            1
+          ],
+          [
+            29,
+            1
+          ],
+          [
+            27,
+            1
+          ],
+          [
+            25,
+            1
+          ],
+          [
+            23,
+            1
+          ],
+          [
+            21,
+            1
+          ],
+          [
+            19,
+            1
+          ],
+          [
+            17,
+            1
+          ],
+          [
+            15,
+            1
+          ],
+          [
+            13,
+            1
+          ],
+          [
+            11,
+            1
+          ],
+          [
+            9,
+            1
+          ],
+          [
+            7,
+            1
+          ],
+          [
+            5,
+            1
+          ],
+          [
+            3,
+            1
+          ],
+          [
+            1,
+            1
+          ],
+          [
+            0,
+            -1
+          ]
+        ],
+        "op": "OUTPUT_CODE_INVERSE",
+        "role": 31
+      }
+    ],
+    "positive_half_postdecode_adds": 86912,
+    "positive_half_postdecode_clears": 1552,
+    "positive_half_postdecode_evaluations": 97,
+    "positive_half_postdecode_monomial_passes": 21728,
+    "recursive_delta_vs_retained_caller": {
+      "rank_8": -144
+    },
+    "right_boundary_column_parities": [
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      0,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1,
+      1
+    ],
+    "shared_owned_code_temporaries": 112,
+    "status": "EXACT_TYPED_CODED_ENDPOINT_RECIPE_NOT_GAUSSIAN_SUPPLIER_ADMISSION"
+  }
+}
diff --git a/research/fresh-stage-code-separation/inputs/GAUGE.md b/research/fresh-stage-code-separation/inputs/GAUGE.md
new file mode 100644
index 0000000000..13269f7b1f
--- /dev/null
+++ b/research/fresh-stage-code-separation/inputs/GAUGE.md
@@ -0,0 +1,77 @@
+# Deferred native code: exact local transport and the actual caller junction
+
+Apache-2.0. Substantial OpenAI Codex assistance. Credit PR4929's center-free code, Cao Yifan's native/controller sources, and the retained compiler and helper lineage.
+
+The physical wrapper construction in this package supplies a real monomial-conjugate code C_s of A=I-14 P at each FULL stage s, in the common central-line convention. Write Q for the central Gaussian, D_s for that stage's fresh rank-eight Gaussian, and R_s=D_s Q. The physical gate is
+
+    [C_s,R_s]=0.
+
+Different C_s need not commute each other or Q. Each C_s is supported on the central coordinate and its own fresh block; thus it commutes D_t when t differs from s. Phase-correct native normalizers, rather than the mere binary orthogonality of a route, are needed for these exact operator statements. The raw-dual backward convention uses the stated monomial Q^2 conjugation on X.
+
+Set H(B)=diag(B,Q^-1 B Q). If B involves only earlier code stages, then [B,D_s]=0. With F_s(C)=diag(D_s,D_s)L(CQ^-1) and B_s(C)=diag(D_s,D_s)U(-QC), direct block multiplication gives
+
+    diag(C_s,I) F_s(C_s) diag(I,C_s) H(B)
+      = H(C_s B) F_s(I),
+    diag(C_s^-1,I) B_s(C_s) diag(I,C_s^-1) H(B)
+      = H(C_s^-1 B) B_s(I).
+
+All newly exposed pre-Y and post-X codes are fixed nonrecursive owner/address circuits, with the explicit local bill in PHYSICAL.md. The inverse code has the explicit coefficient 13 denominator inherited from A^-1; that coefficient's allowed implementation and precision remain part of physical closure. There is no assumption that C_s commutes Q or B.
+
+For a chronological product B_S of codes whose distinct stages comprise an already-paid IDLE D_S, the same relations give
+
+    Q^-1 B_S Q = D_S B_S D_S^-1.
+
+Pre-Y B_S and post-X B_S therefore install H(B_S) around that paid IDLE. This reuses its actual Gaussian work; it does not add an unpriced IDLE.
+
+## Exact algebraic replay
+
+`gauge.py` implements the group algebra of a semidirect product. Q, every C_s and an independent previous-code B freely generate a free group. The commuting D_s act by the automorphisms C_s -> Q^-1 C_s Q while fixing Q, other C_t and B. A canonical reduced free word and an integer D-vector represent each monomial. Thus the replay is symbolic noncommutative algebra, not a numerical matrix sample or an assumption that tensor powers preserve sums.
+
+The checker compares every block of both displayed identities, a four-stage mixed-orientation IDLE, and controls that retain [C,Q], [B,Q] and [B,C] as nonzero. Reversed update order, the wrong backward exponent and an omitted IDLE stage are rejected. The written block argument establishes applicability to every operator representation satisfying the stated relations; the symbolic checker corroborates its transcription. This is not proof-kernel acceptance.
+
+## Initial per-pair proof attempt (superseded below)
+
+The retained main `research/joint-helper-lattice/CONTROLLER.json` has 18 FULL calls at stages 0,1,3,...,31,32 and 15 paidIDLEs. Its seven initial IDLEs are on pairs 1 through 7. Under the declared per-pair gauge policy, after the backward FULL at stage 2 j+1, pairj carries
+
+    W_j=C_(2 j+1)^-1 ... C_3^-1 C_1^-1 C_0.
+
+For j=0,...,6, the already-paid initial IDLE puts pair(j+1) in the same gauge, so the next bridge has matching gauges. At j=7, pair 7 carries W_7 while pair 8 still carries I: the source has deliberately omitted that initial IDLE. The exact chronology control records that first mismatch and its two symbolic words. Tail IDLEs and the full scalar boundary remain available resources, but the local identities do not establish their complete coded endpoint.
+
+The recorded mismatch is a stopping control for this particular forward per-pair policy. It is not a lower bound for all caller designs. In particular, a bidirectional gauge, a whole-word factorization or a separately paid junction could change the conclusion. Likewise, a terminal Q^-1 B Q gauge cannot simply be declared a free output code or an independent Gaussian target. A complete favorable caller must bind the actual terminal outputs and its whole invoice before using the supplier compiler or claiming a new kappa.
+
+## Open next questions
+
+Can the 16 explicit negative-Q coded output types be admitted with their 15 matched paid IDLE types, or converted to ordinary Gaussian targets for a favorable full bill? The complete coded word below makes that question concrete. The first step is a typed completion identity on one paid-IDLE/negative-output pair; a Gaussian supplier admission and new recursive saving remain unproved.
+
+## Independent binding of the predecessor noncommuting-stage identity
+
+Dugongue's existing `research/frame-aware-native/noncommuting-controller/PROOF.md` already proves the universal p16 identity for freely noncommuting stages and a central Q, crediting Cinna Davis / 1337 isnot 1337 #4470 and Ryanson Jonathan #4516. The present Q=I calculation is an independent binding/control for that predecessor theorem, not a new noncommuting-controller theorem. Its README and proof were read during this investigation.
+
+The retained controller has the following already established algebraic property. Set Q=I, replace every one of its 18 FULL-stage diagonals by a distinct freely noncommuting letter Z_s, and implement each already-paid IDLE as its chronological ordered product. Keep all 154 physical events and both actual 32-by-32 scalar boundary matrices. The resulting 32-by-32 operator matrix is exactly diagonal. Its i-th diagonal is the chronological ordered product of precisely the stages selected by the source's i-th target word.
+
+The checker proves this finite word identity by expanding all 1,024 entries over the free associative group algebra with rational coefficients. No commutative collection of stage letters is performed. Reversing the first two-stage IDLE is a semantic mutation that fails, although a commuting specialization could miss it. A separate exact 2-by-2 matrix experiment with noncommuting integer stages was used as a discovery check; the registered result is the stronger symbolic identity.
+
+This is directly useful for the coded caller constructed below. Under H=diag(I,Q), the modified local gauge identities turn the core into scalar L/U steps with decorated stage diagonals Z_s=C_s^epsilon D_s. The core identity therefore accommodates their noncommutativity. It removes one possible obstruction to the proposed construction. It does not remove H from the two physical scalar boundaries, implement those Q-dependent boundaries for free, or establish independent Gaussian terminal jobs. The positive complete-core identity and the unresolved physical entrance/exit interface are separate statements.
+
+## Complete typed coded caller, superseding the local junction concern
+
+The direct global proof avoids requiring a separate matching gauge on each pair. Define H=diag(I,Q) on every pair. For each FULL stage s, emit the nonrecursive pre-Y code C_s^epsilon, the center-free native FULL in its actual orientation, and the nonrecursive post-X code C_s^epsilon, with epsilon=+1 for forward and -1 for backward. The resulting block is
+
+    H^-1 diag(Z_s,Z_s) L(I) H       (forward),
+    H^-1 diag(Z_s,Z_s) U(-I) H      (backward),
+    Z_s=C_s^epsilon D_s.
+
+For each of the 15 actual paid IDLEs, emit its chronological code product on Y, its unchanged paid Gaussian IDLE, and the same chronological code product on X. Since each code commutes the other stages' Gaussian factors, the result is H^-1 diag(Z_word,Z_word) H. Each retained thin query similarly conjugates to its original scalar shear. Every internal ADD bridge preserves X/Y parity, so adjacent H factors cancel. No extra initial IDLE is inserted. The earlier pair 7/pair 8 mismatch therefore identifies only a limitation of the per-pair proof strategy; it does not obstruct this global construction.
+
+The global final signed swaps are retained. The actual left boundary has pure parity rows (first 16 even, last 16 odd); the right boundary has pure parity columns (first 16 even, last 16 odd). The checker binds all 64 of these facts. Moving H through those scalar boundaries and signed swaps gives the exact 32 main operator blocks
+
+    Q^-1 B_i D_i              for i=0,...,15,
+    B_i D_i Q                for i=16,...,31.
+
+Here D_i is the chronological product of the Gaussian stages selected by the authenticated original target, and B_i is the corresponding chronological product of C_s^epsilon. The ordered words are emitted explicitly in GAUGE.json. This proves a complete *typed coupled/coded endpoint* for 3584 independent main inputs, with all 7344 independent source helpers retained once. It is not the old Gaussian endpoint. The positive-Q half can be postdecoded by B_i^-1; the negative-Q half retains its specified code between the central operation and the remaining Gaussian product.
+
+GAUGE.json emits every retained event and every inserted code block. There are 66 inserted code blocks, comprising 194 individual code evaluations: 34 A and 160 A^-1. Each code is conjugated by 112 known monomial field maps in each direction, giving 43,456 field-monomial passes before any positive-output decoding. One conservative implementation of a dense code computes (A-I)x, or (A-I)x/13, in 112 owned temporary fields and then adds the result to x. The exact A-I support has 5,936 entries, so this uses at most 6,048 scalar ADDs per code, or 1,173,312 ADDs for the 194 evaluations. The 112 owned temporaries can be reused chronologically; each evaluation initializes and clears them. These counts exclude the separately retained native scalar work, monomial primitive lowering, optional positive-output decoding, routing/storage accounting and fixed-precision realization of denominator 13. They are explicit additional finite costs, not an outer-admission certificate.
+
+The recursive paid profile differs from the retained caller by precisely 144 rank-eight calls removed. Every original IDLE and thin query remains paid. The source helpers remain independent and productive once per FULL. A new numerical moment cannot count the 16 negative-Q coded outputs as the original Gaussian jobs. Their new job family, a changed compiler/completion theorem, or an actually paid endpoint adapter is the remaining integration question.
+
+The primary finite scalar realization is the already checked eight-mode program in NORMALIZERS: 896 ADDs, 224 field-monomial passes and 16 owned-CLEAR operations per C evaluation, with 8 reusable owned temporary fields. For the complete typed caller this gives 173,824 ADDs, 43,456 field-monomial passes and 3,104 CLEARs. The dense 112-temporary implementation above is an alternative upper bound, not the primary invoice. If the positive-Q half is explicitly postdecoded to ordinary Gaussian jobs, its 16 inverse code words contain 97 additional C evaluations: 86,912 ADDs, 21,728 monomial passes and 1,552 CLEARs. GAUGE.json emits those optional output decoding words and prices them separately. The typed caller alone has 3584 coded main outputs; after that priced postdecoding 1792 of them are autonomous Gaussian jobs, while 1792 retain the exact negative-Q code. The denominator 13 fixed-precision arithmetic realization remains an explicit assumption/obligation for both recipes.
diff --git a/research/fresh-stage-code-separation/inputs/LICENSE b/research/fresh-stage-code-separation/inputs/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/fresh-stage-code-separation/inputs/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/fresh-stage-code-separation/inputs/NORMALIZERS.json b/research/fresh-stage-code-separation/inputs/NORMALIZERS.json
new file mode 100644
index 0000000000..bca92c222c
--- /dev/null
+++ b/research/fresh-stage-code-separation/inputs/NORMALIZERS.json
@@ -0,0 +1,126 @@
+{
+  "clifford_sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+  "code_sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0",
+  "finite_checks": {"absolute_phase_mutations_rejected":112,"exact_endpoint_factor_identities":896,"gaussian_free_compiled_wrappers":896,"monomial_wrappers":896,"omitted_phase_rejections":112,"ports":112,"scalar_basis_recodings":224,"weight_congruence_addresses":57344},
+  "local_gauge_bill": {"added_recursive_calls":0,"backward_extra_monomial_field_maps_upper":448,"main_wrapper_field_maps":448,"owned_fields_reused":8,"recoding_monomial_field_maps":448,"recoding_owned_clears":32,"recoding_scalar_adds":1792,"recodings":2},
+  "mode_columns": [[1,1,1,1,1,1,1,-1,1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,-1,1,-1,1,1,1,0,1,1,1,1,1,1,-1,1,-1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,-1,0,0,0,0,1,1,1,1,1,-1,-1,-1,0,0,0,0,0,0,0,-1,-1,-1,-1,1,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,-1,1,0,0,-1,1,1,1,0,-1,-1,0,0,0,0,1,-1,0,0,0,0,0,1,1,1,1,-1,1,1,1,0,0,0,0,0],[1,0,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0],[1,0,0,1,1,1,0,1,-1,0,0,0,0,1,1,1,-1,0,0,0,0,0,-1,-1,-1,0,-1,-1,0,0,0,0,1,1,1,-1,0,0,0,0,0,-1,-1,-1,-1,-1,0,0,1,1,1,1,1,1,0,0,0,-1,0,0,0,0,0,0,-1,-1,-1,1,1,1,0,0,0,0,0,0,-1,0,1,0,1,-1,0,0,0,1,0,1,1,0,0,0,1,0,0,-1,-1,-1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0],[0,1,1,0,1,1,-1,0,0,1,0,0,0,-1,0,0,1,0,-1,-1,1,1,0,0,-1,-1,0,0,-1,0,0,0,-1,0,0,1,-1,-1,0,1,1,0,0,-1,-1,-1,-1,-1,1,0,0,1,0,0,1,1,0,0,1,0,0,-1,0,0,1,1,0,0,-1,-1,0,0,-1,0,0,-1,0,0,1,-1,0,0,1,0,0,1,1,0,0,1,0,0,0,-1,1,0,-1,-1,-1,-1,0,-1,-1,0,1,0,0,1,0,0,1,1],[0,1,0,1,0,0,-1,0,-1,0,1,1,-1,0,-1,-1,0,-1,0,0,-1,-1,0,0,1,0,1,0,1,0,0,1,1,0,0,1,-1,-1,1,0,0,-1,-1,0,0,-1,-1,-1,-1,0,0,0,1,1,0,0,1,0,-1,0,0,0,-1,-1,0,0,1,-1,0,0,-1,-1,0,0,0,1,0,1,0,0,-1,0,-1,0,0,1,1,0,1,0,1,1,0,-1,0,-1,0,0,-1,0,-1,0,0,-1,0,1,1,-1,0,0,-1,-1],[0,0,1,1,0,0,0,0,1,-1,0,0,1,1,0,0,1,-1,0,0,1,1,-1,-1,0,-1,-1,0,0,-1,-1,-1,0,-1,-1,0,1,1,1,0,0,0,0,1,-1,0,-1,-1,0,1,1,-1,0,0,0,0,1,0,0,1,1,1,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,0,0,-1,1,-1,1,0,0,1,1,0,0,0,-1,-1,0,0,0,0,1,-1,0,0,0,-1,-1,0,0,1,-1,0,0,0,1,1,-1,-1],[0,0,0,0,1,-1,0,0,0,0,-1,1,0,0,1,-1,0,0,-1,1,1,-1,-1,1,0,0,0,0,0,1,-1,0,0,1,-1,0,-1,1,0,1,-1,-1,1,0,0,0,1,-1,0,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,1,-1,-1,1,0,0,-1,1,-1,1,0,-1,1,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,-1,1,0,0,0,0,-1,1,0,0,0,-1,1,0,0,-1,1,0,-1,1,1,-1]],
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+  ],
+  "recoding_bill": {"forward_prefix_component_l1_upper":57,"forward_update_coefficient":"-1/4","inverse_output_prefix_component_l1_upper":"69/13","inverse_prefix_component_l1_upper":56,"inverse_update_coefficient":"-1/52","monomial_field_maps":224,"output_scaled_adds":448,"owned_fields":8,"owned_initial_clears":8,"owned_terminal_clears":8,"signed_mode_adds":448},
+  "schema": "coded-native-real-normalizers/1",
+  "scope": "Exact physical central ABI and local gauges; not full-controller or multiplication admission.",
+  "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd",
+  "status": "PASS_CODED_NATIVE_REAL_NORMALIZERS"
+}
diff --git a/research/fresh-stage-code-separation/inputs/NOTICE b/research/fresh-stage-code-separation/inputs/NOTICE
new file mode 100644
index 0000000000..985b6b1bc7
--- /dev/null
+++ b/research/fresh-stage-code-separation/inputs/NOTICE
@@ -0,0 +1,6 @@
+Coded native caller research
+Apache-2.0. Prepared for Dillon with substantial OpenAI Codex assistance.
+
+Retained sources: Cao Yifan / intqwq, joint-helper/native-map round-three word and PR4610; Dugongue / mdumitrean, PR4929 center-free coded producer; Cinna Davis / 1337isnot1337, PR4694 center-free cache, PR4698 helper basis, PR4470 controller and cumulative construction; zxv, retained exact Clifford implementation and native/compiler lineage; Jacob Alan Sussman, mixed-target recursion. Preserve all original source-specific headers. See ORIGINS.json for exact byte origins and README.md for the new result and limits.
+
+The new contribution is the phase-correct commuting physical port normalization, its corrected coded raw-dual convention, and scoped caller analysis. Center deletion, code A, its spectrum and helper compensation are predecessor work.
diff --git a/research/fresh-stage-code-separation/inputs/ORIGINS.json b/research/fresh-stage-code-separation/inputs/ORIGINS.json
new file mode 100644
index 0000000000..e18a033d4d
--- /dev/null
+++ b/research/fresh-stage-code-separation/inputs/ORIGINS.json
@@ -0,0 +1,30 @@
+[
+  {
+    "path": "native-source.json.gz",
+    "source_path": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
+    "commit": "624de9dc66858af0945e5f8a0942488d62280d43",
+    "source_blob": "46d929df83817b85a5387bcdb9745e0627d6366e",
+    "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05"
+  },
+  {
+    "path": "CODE.json",
+    "source_path": "research/native-center-free-code/CODE.json",
+    "commit": "361f5d4100640177d6a983dd2f336021c75bfd5e",
+    "source_blob": "03170f4a31f7a8a3db7228f1cd5a6fdcb32720ae",
+    "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0"
+  },
+  {
+    "path": "clifford_exact.py",
+    "source_path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py",
+    "commit": "624de9dc66858af0945e5f8a0942488d62280d43",
+    "source_blob": "166841a037f069249f6f7f6dedb89248812f59e2",
+    "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+  },
+  {
+    "path": "CONTROLLER.json",
+    "source_path": "research/joint-helper-lattice/CONTROLLER.json",
+    "commit": "624de9dc66858af0945e5f8a0942488d62280d43",
+    "source_blob": "49a2f0675819f9deeea27ed77be2c2b6ff2e87e5",
+    "sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f"
+  }
+]
diff --git a/research/fresh-stage-code-separation/inputs/TERMINAL.md b/research/fresh-stage-code-separation/inputs/TERMINAL.md
new file mode 100644
index 0000000000..213a172676
--- /dev/null
+++ b/research/fresh-stage-code-separation/inputs/TERMINAL.md
@@ -0,0 +1,74 @@
+# The one-stage terminal gauge has a real cost
+
+The physical normalizers make the coded supplier and its local gauge identities
+constructive. They do not make the Y terminal gauge free. This note proves that
+distinction for one actual source code, at every positive fiber width. It does
+not prove the same statement for a product of different stage codes.
+
+Let `Q` be the Gaussian on the common central line, let `K_i` be the signed
+orthogonal permutation taking that line to source port `q_i`, and put
+
+`C_ij = A_ij K_i^{-1} K_j`.
+
+The source code has exactly 5,824 nonzero entries, all off diagonal and equal to
+`+1/2` or `-1/2`. Its 112 port vectors are distinct. Write a nonzero block's
+monomial as `M = K_i^{-1} K_j`, with binary linear part `G`. Then
+
+`G e = G_i^{-1} q_j != e`,
+
+because `G_i e = q_i` and `q_i != q_j`. Also `G e != 0`. Thus `e` and `G e`
+are independent binary vectors. This statement uses the actual source ports,
+not just the polynomial satisfied by `A`.
+
+For one digit column, write the central Gaussian as
+`Q = (1+i)/2 (I-i T_e)`, where `T_e` translates the address by `e`. If
+`M |x> = s(x) |Gx>`, with `s(x)` in `{+1,-1}`, direct expansion gives
+
+`2 Q^{-1} M Q |x>`
+
+`= s(x)|Gx> - i s(x+e)|Gx+Ge> + i s(x)|Gx+e> + s(x+e)|Gx+Ge+e>`.
+
+The four destinations are distinct and every coefficient is nonzero. Every
+column, and every row, therefore has exactly four nonzero entries. Equivalently
+the Gaussian support rank is two. At fiber width `f`, the same native monomial
+and Gaussian act as tensor powers on the digit columns. Each nonzero owner
+block consequently has exactly `4^f` nonzero entries per row. The coefficient
+`A_ij` is applied once to this block; this argument does not tensor the owner
+code or replace a sum by a tensor product.
+
+The different input owners `j` are arbitrary and independent. Entries belonging
+to different owners cannot cancel each other in the full operator. Hence the
+single-code terminal operator `Q^{-1} C Q` has at least `4^f` input-coordinate
+dependencies in each row that meets a nonzero block.
+
+The inverse code has the same obstruction: `C^{-1}=(C+12I)/13`, so every
+off-diagonal block of `Q^{-1} C^{-1} Q` is precisely `1/13` times the block
+just analyzed. The added diagonal identity cannot cancel an independent input
+owner's off-diagonal block.
+
+A fixed finite word made from scalar ADD/SCALE, monomial address maps, and
+owned COPY/CLEAR has uniformly bounded row support. Initially the support is
+at most one. Monomial operations, scaling, copying and clearing do not increase
+the maximum support; an ADD increases it by at most a factor two. A word with
+`g` ADDs therefore has support at most `2^g`, even when clean scratch is allowed.
+Realizing this terminal operator needs `g >= 2f`. In particular a fixed number
+of those physical primitives cannot implement the one-stage decoder uniformly
+in the fiber width.
+
+This is a statement about the repository's fixed native scalar/monomial word
+model. It is not a general arithmetic-circuit lower bound, a lower bound for
+paid Gaussian decoders, or an impossibility theorem for coded callers. It also
+does not exclude cancellation in a product `B` of different stage codes. The
+terminal gauge `Q^{-1} B Q` of a complete controller needs its own proof.
+
+The independent verifier reconstructs every binary normalizer from the frozen
+ports without importing the primary normalizer implementation. It checks the
+rank-two support argument for all 5,824 blocks, enumerates every one-column
+row and column for three actual blocks, and rejects a diagonal-code mutation.
+The identity-conjugation control has support one, so the support test does not
+mistake the cancelling case for a rank-two case.
+
+Predecessor credit remains with Dugongue's PR #4929 coded producer, Cinna
+Davis's center-free construction, Cao Yifan's native word, and the retained
+native and controller contributors. The new result here is the exact terminal
+support gate for the actual common-line normalizers.
diff --git a/research/fresh-stage-code-separation/select_markers.py b/research/fresh-stage-code-separation/select_markers.py
new file mode 100644
index 0000000000..35e5c3cfc8
--- /dev/null
+++ b/research/fresh-stage-code-separation/select_markers.py
@@ -0,0 +1,35 @@
+"""Find small marker sets. This search is not an acceptance check.
+
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
+"""
+import argparse
+import json
+from pathlib import Path
+import random
+import verify
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--output', type=Path, required=True)
+    args = parser.parse_args()
+    verify.need(not args.output.exists(), 'Refuse to overwrite an existing file')
+    a, operators, literal = verify.source_checks(verify.load())
+    path, _ = verify.path_functions(operators, literal)
+    rng = random.Random(5376)
+    rows = []
+    for count in (1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 32, 64):
+        inputs = []
+        for _ in range(16):
+            inputs.append(rng.getrandbits(8*count+1))
+            survivors, peak = verify.marker_path_count(a, operators, literal, path, count, inputs)
+            if survivors == 1:
+                break
+        verify.need(survivors == 1, 'No marker certificate in the declared search budget')
+        rows.append(dict(stages=count, markers=inputs, count=survivors, peak=peak))
+    args.output.write_text(json.dumps(dict(seed=5376, candidates=rows), indent=2, sort_keys=True)+'\n')
+    print('WROTE_MARKER_CANDIDATES')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/fresh-stage-code-separation/verify.py b/research/fresh-stage-code-separation/verify.py
new file mode 100644
index 0000000000..cabc1789f7
--- /dev/null
+++ b/research/fresh-stage-code-separation/verify.py
@@ -0,0 +1,434 @@
+"""Check the source data and finite controls for fresh-stage path separation.
+
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
+"""
+from collections import defaultdict
+from fractions import Fraction as F
+from functools import lru_cache
+import hashlib
+import itertools
+import json
+from pathlib import Path
+import sys
+
+HERE = Path(__file__).resolve().parent
+
+
+def need(value, message):
+    if not value:
+        raise ValueError(message)
+
+
+def act(columns, x):
+    y = 0
+    while x:
+        bit = x & -x
+        y ^= columns[bit.bit_length() - 1]
+        x ^= bit
+    return y
+
+
+def transpose(columns):
+    return tuple(sum(((c >> j) & 1) << i for i, c in enumerate(columns))
+                 for j in range(len(columns)))
+
+
+def compose(left, right):
+    a, b = left
+    c, d = right
+    return tuple(act(a, x) for x in c), d ^ act(transpose(c), b)
+
+
+def inverse_orthogonal(operator):
+    a, b = operator
+    inverse = transpose(a)
+    return inverse, act(transpose(inverse), b)
+
+
+def embed(operator, stage, count):
+    columns, beta = operator
+    positions = [0] + list(range(1 + 8*stage, 9 + 8*stage))
+    def lift(x):
+        return sum(((x >> j) & 1) << p for j, p in enumerate(positions))
+    out = [1 << j for j in range(1 + 8*count)]
+    for p, col in zip(positions, columns):
+        out[p] = lift(col)
+    return tuple(out), lift(beta)
+
+
+def signed_apply(operator, x):
+    columns, beta = operator
+    return act(columns, x), -1 if (beta & x).bit_count() % 2 else 1
+
+
+# Exact Gaussian numbers are pairs of rational numbers.
+def plus(a, b):
+    return a[0] + b[0], a[1] + b[1]
+
+
+def times(a, b):
+    return a[0]*b[0] - a[1]*b[1], a[0]*b[1] + a[1]*b[0]
+
+
+def q_entries(sign):
+    return ((0, (F(1, 2), F(sign, 2))),
+            (1, (F(1, 2), F(-sign, 2))))
+
+
+def n_column(operator, x):
+    """Apply Q inverse, M, Q in matrix order Q^-1 M Q."""
+    out = defaultdict(lambda: (F(0), F(0)))
+    for shift, q in q_entries(1):
+        y, s = signed_apply(operator, x ^ shift)
+        for back, z in q_entries(-1):
+            out[y ^ back] = plus(out[y ^ back], times((s*q[0], s*q[1]), z))
+    return {y: z for y, z in out.items() if z != (0, 0)}
+
+
+def n_entry(operator, y, x):
+    return n_column(operator, x).get(y, (F(0), F(0)))
+
+
+def marker(operator, y, x):
+    """Contract an N entry with the literal left Q and right Q inverse."""
+    out = (F(0), F(0))
+    for a, u in q_entries(1):
+        for b, v in q_entries(-1):
+            out = plus(out, times(times(u, n_entry(operator, y ^ a, x ^ b)), v))
+    return out
+
+
+def alpha(exponent):
+    return (1 - F(-13)**exponent) / 14
+
+
+def code_power_entry(a, exponent, i, j):
+    return alpha(exponent)*a[i][j] + (1-alpha(exponent))*(i == j)
+
+
+def validate_stages(stages, shared_axes=1):
+    need(shared_axes == 1, "The common coordinate space has dimension one")
+    need(stages and len(set(stages)) == len(stages), "Each stage has a distinct private block")
+
+
+def reject(function):
+    try:
+        function()
+    except ValueError:
+        return 1
+    raise ValueError("A negative control was accepted")
+
+
+def load():
+    manifest = json.loads((HERE / 'SOURCES.json').read_bytes())
+    objects = {}
+    for item in manifest['inputs']:
+        raw = (HERE / item['path']).read_bytes()
+        need(hashlib.sha256(raw).hexdigest() == item['sha256'], 'Pinned source: ' + item['path'])
+        if item['path'].endswith('.json'):
+            objects[Path(item['path']).name] = json.loads(raw)
+    return objects
+
+
+def source_checks(objects):
+    a = [[F(x) for x in row] for row in objects['CODE.json']['A']]
+    ports = objects['NORMALIZERS.json']['ports']
+    need(len(a) == len(ports) == 112 and all(len(row) == 112 for row in a), '112-owner code')
+    need(all(a[i][i] == 0 for i in range(112)), 'Zero code diagonal')
+    need(a[0][1] == a[1][0] == F(-1, 2), 'Nonzero alternating witness edge')
+    need(len({p['q'] for p in ports}) == 112, 'Distinct port images')
+    for i in range(112):
+        for j in range(112):
+            need(sum(a[i][t]*a[t][j] for t in range(112)) + 12*a[i][j] == 13*(i == j),
+                 'Exact code polynomial')
+    operators = []
+    literal = []
+    for index, p in enumerate(ports):
+        rows = p['G_rows']
+        columns = transpose(rows)
+        need(len(columns) == 9 and all(0 <= x < 512 for x in columns), 'Nine-axis map')
+        need(all(((x & y).bit_count() % 2) == (i == j)
+                 for i, x in enumerate(columns) for j, y in enumerate(columns)), 'Orthogonal map')
+        need(p['port'] == index and columns[0] == p['q'], 'Central port image')
+        need(p['K_word'] == [['P', rows], ['D', [0]*9,
+             [2*((p['Z_mask'] >> j) & 1) for j in range(9)]]], 'Literal signed K word')
+        beta = act(transpose(columns), p['Z_mask'])
+        operator = columns, beta
+        # This second evaluator uses row dot products and the literal output sign.
+        table = []
+        for x in range(512):
+            y = sum(((row & x).bit_count() % 2) << j for j, row in enumerate(rows))
+            s = (-1)**((p['Z_mask'] & y).bit_count() % 2)
+            need(signed_apply(operator, x) == (y, s), 'Independent signed K action')
+            table.append((y, s))
+        operators.append(operator)
+        literal.append(table)
+    for exponent in range(-5, 6):
+        if exponent:
+            need(alpha(exponent) != 0, 'Nonzero power coefficient')
+        # Check the two exact eigenvalues, including negative powers.
+        for eigenvalue in (1, -13):
+            need(alpha(exponent)*eigenvalue + 1-alpha(exponent) == F(eigenvalue)**exponent,
+                 'Power interpolation')
+    return a, operators, literal
+
+
+def path_functions(operators, literal):
+    @lru_cache(None)
+    def transition(i, j):
+        return compose(inverse_orthogonal(operators[i]), operators[j])
+
+    @lru_cache(None)
+    def path(owners):
+        count = len(owners)-1
+        out = tuple(1 << j for j in range(1 + 8*count)), 0
+        for stage, (j, i) in enumerate(zip(owners, owners[1:])):
+            out = compose(embed(transition(i, j), stage, count), out)
+        return out
+
+    inverse_tables = []
+    for table in literal:
+        inv = [None]*512
+        for x, (y, sign) in enumerate(table):
+            inv[y] = x, sign
+        inverse_tables.append(inv)
+
+    def direct(owners, x):
+        sign = 1
+        for stage, (j, i) in enumerate(zip(owners, owners[1:])):
+            shift = 1 + 8*stage
+            local = (x & 1) | (((x >> shift) & 255) << 1)
+            y, s = literal[j][local]
+            y, t = inverse_tables[i][y]
+            x = (x & ~(1 | (255 << shift))) | (y & 1) | ((y >> 1) << shift)
+            sign *= s*t
+        return x, sign
+    return path, direct
+
+
+def finite_paths(a, path, direct):
+    results = []
+    total_markers = 0
+    for count in (2, 3):
+        last = count % 2
+        chosen = tuple(j % 2 for j in range(count+1))
+        selected = path(chosen)
+        maps = set()
+        selected_markers = []
+        for j in range(1, 1+8*count):
+            x, y = 1 << j, selected[0][j]
+            selected_markers.append(marker(selected, y, x))
+        need(all(z in ((1, 0), (-1, 0)) for z in selected_markers), 'Selected marker coefficient')
+        sign_patterns = list(itertools.product((-1, 1), repeat=count))
+        active = [0]*len(sign_patterns)
+        for middle in itertools.product(range(112), repeat=count-1):
+            owners = (0,) + middle + (last,)
+            op = path(owners)
+            need(op[0] not in maps, 'Distinct complete binary path maps')
+            maps.add(op[0])
+            # All private columns determine an orthogonal address map.
+            if owners != chosen:
+                different = next((j for j in range(1, len(op[0])) if op[0][j] != selected[0][j]), None)
+                need(different is not None, 'Private-column separation')
+                need(marker(op, selected[0][different], 1 << different) == (0, 0),
+                     'A literal four-term marker kills this path')
+                total_markers += 1
+            # Every basis column has a separately evaluated literal source action.
+            for j, y in enumerate(op[0]):
+                need(direct(owners, 1 << j) == (y, (-1)**((op[1] >> j) & 1)),
+                     'Literal path and composed map agree')
+            for position, signs in enumerate(sign_patterns):
+                if all(code_power_entry(a, s, i, j) for s, j, i in zip(signs, owners, owners[1:])):
+                    active[position] += 1
+        need(selected[0][0] != 1, 'Selected path moves the central vector')
+        for x in (0, 1, 3, (1 << (8*count+1))-1):
+            need(len(n_column(selected, x)) == 4, 'Four nonzero conjugated entries')
+        results.append(dict(stages=count, all_paths=len(maps), signs=[list(s) for s in sign_patterns],
+                            active_paths=active, marker_columns=8*count))
+    return results, total_markers
+
+
+def marker_path_count(a, operators, literal, path, count, inputs, reverse=False):
+    """Count every path that survives the marker columns, without path expansion."""
+    owners = tuple(j % 2 for j in range(count+1))
+    selected = path(owners)
+    outputs = [act(selected[0], x) for x in inputs]
+    to_mask = lambda xs: sum((x & 1) << j for j, x in enumerate(xs))
+    initial = (count % 2, to_mask(outputs)) if reverse else (0, to_mask(inputs))
+    final = (0, to_mask(inputs)) if reverse else (count % 2, to_mask(outputs))
+    state, peak = {initial: 1}, 1
+    tables = [[y for y, sign in table] for table in literal]
+    inverses = [[0]*512 for _ in range(112)]
+    for i, table in enumerate(tables):
+        for x, y in enumerate(table):
+            inverses[i][y] = x
+    stages = range(count-1, -1, -1) if reverse else range(count)
+    for stage in stages:
+        shift = 8*stage+1
+        incoming = [(x >> shift) & 255 for x in (outputs if reverse else inputs)]
+        outgoing = [(x >> shift) & 255 for x in (inputs if reverse else outputs)]
+        next_state = defaultdict(int)
+        for (owner, central), multiplicity in state.items():
+            local = [(v << 1) | ((central >> j) & 1) for j, v in enumerate(incoming)]
+            for other in range(112):
+                coefficient = a[owner][other] if reverse else a[other][owner]
+                if other != owner and not coefficient:
+                    continue
+                if reverse:
+                    # Separate matrix composition, in the reverse direction.
+                    op = compose(inverse_orthogonal(operators[other]), operators[owner])
+                    images = [act(op[0], x) for x in local]
+                else:
+                    images = [inverses[other][tables[owner][x]] for x in local]
+                if all(y >> 1 == target for y, target in zip(images, outgoing)):
+                    next_state[other, to_mask(images)] += multiplicity
+        state = next_state
+        peak = max(peak, len(state))
+    return state.get(final, 0), peak
+
+
+def short_markers(a, operators, literal, path):
+    saved = json.loads((HERE/'MARKERS.json').read_bytes())
+    result = []
+    for row in saved['candidates']:
+        count, inputs = row['stages'], row['markers']
+        need(all(type(x) is int and 0 <= x < 1 << (8*count+1) for x in inputs),
+             'Marker address domain')
+        forward, peak = marker_path_count(a, operators, literal, path, count, inputs)
+        backward, _ = marker_path_count(a, operators, literal, path, count, inputs, True)
+        need(forward == backward == row['count'] == 1 and peak == row['peak'],
+             'Exactly one path survives in both dynamic programs')
+        selected = path(tuple(j % 2 for j in range(count+1)))
+        for x in inputs:
+            need(marker(selected, act(selected[0], x), x) in ((1, 0), (-1, 0)),
+                 'Every selected short marker is nonzero')
+        result.append(dict(stages=count, markers=len(inputs), paths=forward,
+                           maximum_states=peak, add_offset=3*len(inputs)))
+    need(marker_path_count(a, operators, literal, path, 2, [])[0] > 1,
+         'An empty marker set does not isolate a path')
+    return result
+
+
+def bank_checks(objects, a, path, direct, short):
+    banks = []
+    for bank in objects['GAUGE.json']['typed_caller']['endpoint']:
+        if bank['central_exponent'] != -1:
+            continue
+        word = bank['code_word_left_to_right']
+        stages = [s for s, e in word]
+        validate_stages(stages)
+        need(bank['operator'] == 'Q^-1 B D' and stages == bank['gaussian_stages'], 'Actual terminal type')
+        count = len(word)
+        owners = tuple(j % 2 for j in range(count+1))
+        op = path(owners)
+        need(op[0][0] != 1, 'Actual-bank witness has four-point support')
+        for j, y in enumerate(op[0]):
+            need(direct(owners, 1 << j) == (y, (-1)**((op[1] >> j) & 1)), 'Actual-bank literal path')
+        powers = [-e for s, e in word]
+        coefficient = F(1)
+        for exponent in powers:
+            coefficient *= alpha(exponent)*a[0][1]
+        need(coefficient != 0, 'Inverse decoder retains the selected path')
+        banks.append(dict(role=bank['role'], stages=count, source_word=word,
+                          decoder_execution_powers=powers, marker_columns=next(r['markers'] for r in short if r['stages'] == count),
+                          add_lower_bound=f"max(0, 2*f - {next(r['add_offset'] for r in short if r['stages'] == count)})",
+                          selected_path_coefficient=str(coefficient)))
+    need([b['role'] for b in banks] == list(range(16)), 'All sixteen negative banks')
+    return banks
+
+
+def boundary_checks(a, path):
+    controls = 0
+    controls += reject(lambda: validate_stages([0, 0]))
+    controls += reject(lambda: validate_stages([0, 1], 2))
+    controls += reject(lambda: validate_stages([]))
+    # Reusing one block gives C*C^-1=I. These scalar identities bind the full
+    # monomial blocks because K_i^-1 K_t K_t^-1 K_j = K_i^-1 K_j.
+    for i in range(112):
+        for j in range(112):
+            value = sum(a[i][t]*(a[t][j]+12*(t == j))/13 for t in range(112))
+            need(value == (i == j), 'Repeated-stage inverse cancellation')
+    # With two common axes, nonidentity gauges can pass between fresh blocks.
+    def permutation(images):
+        return tuple(1 << j for j in images), 0
+    h = permutation([1, 0, 2, 3])
+    left = permutation([3, 1, 2, 0])
+    right = permutation([2, 1, 0, 3])
+    left2, right2 = compose(left, h), compose(h, right)
+    need(left != left2 and right != right2, 'Different local factors')
+    need(compose(left, right) == compose(left2, right2), 'Two-center factor collision')
+    # The actual owner coefficients 2 and 98 have opposite signs. With
+    # two shared axes, this change makes their complete monomials equal.
+    need(a[0][2]*a[2][1] == -a[0][98]*a[98][1] == F(1, 4),
+         'Actual owner coefficients cancel on the changed two-center paths')
+    need(compose(left, right)[0][0] != 1, 'Each cancelling term is nonmonomial after Q')
+    need(len({1, left[0][0], left2[0][0]}) == 3
+         and len({1, right[0][0], inverse_orthogonal(right2)[0][0]}) == 3,
+         'The specified port images remain distinct in each changed stage')
+    common = compose(left, right)
+    other = compose(left2, right2)
+    for x in range(16):
+        need(n_column(common, x) == n_column(other, x) and len(n_column(common, x)) == 4,
+             'The two cancelling terms agree with exact phases at every base input')
+    # A wrong Q orientation fails the literal contraction even on a diagonal term.
+    op = path((0, 1))
+    x, y = 0, 0
+    correct = marker(op, y, x)
+    wrong = (F(0), F(0))
+    for u, cu in q_entries(-1):
+        for v, cv in q_entries(-1):
+            wrong = plus(wrong, times(times(cu, n_entry(op, y ^ u, x ^ v)), cv))
+    need(correct != wrong, 'Wrong marker orientation changes an actual entry')
+    controls += 1
+    need(alpha(-1) == F(1, 13) and alpha(2) == -12, 'Inverse and square coefficients')
+    need(F(1, 4) != F(1, 4)**2, 'Owner coefficients are not tensor powered')
+    controls += 1
+    return dict(rejection_controls=controls, repeated_stage_inverse=True,
+                two_common_axes_collision=True)
+
+
+def run():
+    objects = load()
+    a, operators, literal = source_checks(objects)
+    path, direct = path_functions(operators, literal)
+    census, markers = finite_paths(a, path, direct)
+    short = short_markers(a, operators, literal, path)
+    banks = bank_checks(objects, a, path, direct, short)
+    boundary = boundary_checks(a, path)
+    # The written induction has no stage-count bound. These longer paths are controls.
+    longer = []
+    for count in (1, 4, 8, 16, 19, 32, 64):
+        owners = tuple(j % 2 for j in range(count+1))
+        op = path(owners)
+        need(op[0][0] != 1, 'Long path preserves an earlier private component')
+        for x in (0, 1, 3, 1 << (8*count)):
+            need(signed_apply(op, x) == direct(owners, x), 'Long literal path check')
+            need(len(n_column(op, x)) == 4, 'Long path four-point support')
+        longer.append(count)
+    return dict(status='PASS_ALL_LENGTH_FRESH_STAGE_SEPARATION_NO_NEW_KAPPA',
+                scope='Every nonempty product of distinct fresh stages with nonzero integer powers',
+                owner_count=112, normalizer_entries=112*512, code_polynomial_entries=112*112,
+                complete_path_censuses=census, literal_killing_markers=markers,
+                negative_banks=banks, short_marker_certificates=short,
+                long_path_stage_counts=longer, controls=boundary,
+                theorem_add_lower_bound='g >= max(0, 2*f - 24*k)',
+                selected_kappa_unchanged='0.0030217758')
+
+
+def main():
+    need(sys.argv[1:] in ([], ['--write']), 'Use no arguments or --write')
+    result = run()
+    encoded = json.dumps(result, indent=2, sort_keys=True)+'\n'
+    destination = HERE/'RESULT.json'
+    if sys.argv[1:]:
+        need(not destination.exists(), 'Refuse to overwrite the result')
+        destination.write_text(encoded)
+    else:
+        need(destination.read_text() == encoded, 'Exact recorded result')
+    print(result['status'])
+    print(json.dumps(dict(paths=sum(c['all_paths'] for c in result['complete_path_censuses']),
+                          markers=result['literal_killing_markers'], banks=len(result['negative_banks']))))
+
+
+if __name__ == '__main__':
+    main()