diff --git a/research/p104-free-endpoint-contract-audit/PROOF.md b/research/p104-free-endpoint-contract-audit/PROOF.md
new file mode 100644
index 0000000000..bee55f26aa
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+++ b/research/p104-free-endpoint-contract-audit/PROOF.md
@@ -0,0 +1,53 @@
+# Why free helper endpoints are the audited P104 contract
+
+## Setting
+A P104 local word has 735 public registers: 104 X sources r, 104 Y targets r+112, and 527 helpers.
+Frames are subspaces F of F_2^9 with native charts T_F. Each helper h has an initial frame A_h and a
+final frame B_h with A_h ⊂ B_h. A MOVE F → G applies T_G T_F⁻¹ and is paid at rank dim G − dim F. An
+ADD/COPY/SCALE requires its registers to sit in one common frame.
+
+## Lemma 1 (chart invariant)
+Let x_k be the independent inputs. If every register r starts with physical content T_{A_r}(x_r), then
+after every event its physical content is T_{cur(r)}(row_r · x). Here row_r is the exact rational row
+replayed by `local.replay`.
+
+*Proof.* MOVE: T_G T_F⁻¹ T_F(v) = T_G(v). Same-chart ADD: T_f(u) + q·T_f(v) = T_f(u + q v), by linearity of T_f.
+COPY and SCALE are the same. INIT/CLEAR of owned fields set the row and the content to zero. ∎
+
+## Lemma 2 (helper autonomy)
+`local.replay` requires every helper row to end as {h:1}, every main row to have the literal expected
+form, and every owned row to end at zero. By Lemma 1, the module therefore maps a helper input
+y = T_{A_h}(x_h) to T_{B_h}(x_h) = T_{B_h} T_{A_h}⁻¹ y. It does not contaminate any other output. ∎
+
+## Proposition (delivered target)
+`native()` lowers U_h = T_{B_h} T_{A_h}⁻¹ = M_left · G_r · M_right. Here M_left and M_right are Clifford
+monomials and G_r is the canonical rank-r native Gaussian with r = dim B_h − dim A_h. Exact signed-Pauli images and a dense
+phase anchor are checked; the independent #5550 checker repeats both checks. Feed the module M_right⁻¹ z for an
+arbitrary fresh z, and apply M_left⁻¹ to its helper output. The composite is then G_r z. So every helper
+delivers one productive rank-r Gaussian on an arbitrary fresh input. The two monomials are ordinary
+routes, priced in `local_routes` and bounded by #5550's ordinary census.
+
+The proposition does not depend on A_h being the zero frame. A higher start reduces the credited rank r
+by exactly the dimension of the removed climb. Nothing beyond the paid MOVEs and the two priced
+monomials enters the delivered target.
+
+## Consequence for #5561
+The #5561 words change only helper initial/final frames, frame labels and MOVE stops. Their legality
+against the #5551 word is #5561's own `retime.py`. The unmodified `local.py` replay and native maps
+accept them, and #5561's verifier passes. The #5550 checker, with only its input lines swapped, binds all 527
+helper endpoints by exact native checks. It reproduces the invoice from MOVEs and native ranks, and fits the
+ordinary census inside the retained allowance (`verify.py`). Hence hypothesis (c) adds nothing to the
+contract under which #5545 was audited.
+
+## Precedent
+- #5545 (audited by #5550): 192 nonzero helper starts and 65 below-FULL finals.
+- T74 entering helpers: S_E = T_FULL T_E⁻¹ = L_E (C_[w] ⊗ I) R_E, with paid wrappers (#458, Lemma A).
+- Hyperplane-ended helpers: residual T_U T_E⁻¹ with pair wrappers R_(E,U), L_(E,U) (#591 review).
+- The one recorded failure of an entering helper (PR2478 audit of T74) came from that emitter's separate
+  zero-frame precondition phase, which ran before the entry adapters. A P104 word is a single chronology
+  checked by Lemma 1, and it has no such phase.
+
+## Not covered
+Retime legality, pricing, strictification and outer funding of #5561. Validity of the #5551 parent.
+Inherited local all-input native semantics and the five framework assumptions. Human or proof-kernel
+acceptance.
diff --git a/research/p104-free-endpoint-contract-audit/README.md b/research/p104-free-endpoint-contract-audit/README.md
new file mode 100644
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+# Free helper endpoints of #5561 under the audited P104 endpoint contract
+
+**Result (scoped audit, no new κ).** The "free helper start and final frames" hypothesis (c) of
+[#5561](https://github.com/CrocSwap/integer-mult-bounds/pull/5561) is the general helper-endpoint
+contract that the unmodified P104 `local.py` already implements. Chris R's independent caller audit
+[#5550](https://github.com/CrocSwap/integer-mult-bounds/pull/5550) checked that contract on the
+[#5545](https://github.com/CrocSwap/integer-mult-bounds/pull/5545) word. The same checker passes on
+both #5561 words when only the word and its invoice are swapped in.
+
+Base: canonical main `5e0052ca0aa3036a3afa8b0438927377c8d97d53`. Audited source: #5561 head
+`452d27dde67ee9f772dbbd3be129db97a8ecb9c1`. The words are byte copies in `inputs/` (SHA-256 in SOURCES.json).
+
+## What is checked
+
+| Check | Result |
+|---|---|
+| #5545 word (audited by #5550) | 192 of 527 helpers start at a nonzero frame (dims 1, 4, 5); 65 end below FULL; 40 distinct endpoint pairs |
+| Positive control | The patched #5550 checker on the #5545 word and invoice reproduces #5550's complete frozen output, SHA-256 `b51a7d19c10faea7d569a48e9536db8ba1e7418f8dd8dfb25646cc87cc9c4009`, byte for byte |
+| #5561 headline word | PASS: 527 helper endpoints, 272 exact signed-Pauli and phase-anchor checks, invoice 66,852 paid / 12,814 productive, ordinary passes 124,232,680 ≤ 184,647,552 |
+| #5561 starts-only word | PASS: 278 exact checks, invoice 67,374 / 12,814, ordinary passes 124,754,680 ≤ 184,647,552 |
+| Negative controls | Changed helper endpoint rejected; changed invoice rejected; all ten #5550 controls reject on each word |
+
+For comparison, the #5561 headline word has fewer nonzero helper starts (58) than the already audited #5545 word (192).
+Its 44 below-FULL finals are also fewer than #5545's 65. The starts-only word has 59 and 65.
+
+## Why this is the existing contract
+
+`native()` in `research/p104-productive-controller/local.py` credits each helper with the rank of
+`chart(initial)⁻¹·chart(final)` for any nested pair of frames. It also charges two normalizers per helper as
+ordinary routes. #5550 ([PROOF.md](../p104-caller-independent-audit/PROOF.md), "Helpers, scratch and
+paid jobs") makes the mechanism explicit. Each endpoint lowers to U = M_left·G_r·M_right. M_right⁻¹ acts on the
+fresh helper input before its LOCAL call and M_left⁻¹ after it. This relies on the local all-input ABI, which
+`replay()` checks row by row. A helper from E to B therefore delivers the native Gaussian G_r, with
+r = dim B − dim E, on an arbitrary fresh input. Only r is credited. Starting higher lowers the credited rank by
+exactly the climb it removes.
+
+The same wrapper mechanism appears in the T74 lineage. Entering helpers use paid residual wrappers
+R_E⁻¹/L_E⁻¹ (#458, Lemma A in `hpe_emit_local.py`). Hyperplane-ended helpers use pair wrappers R_(E,U), L_(E,U)
+([review](../../docs/research/community-hyperplane599-review.md)). The canonical start rule cited in #5561 belongs to the
+#4610/#5413 neutral caller, whose helper adapters J are pure coordinate permutations. It is not a
+predicate of the P104 contract. [PROOF.md](PROOF.md) gives the argument.
+
+## What the verifier changes
+
+`verify.py` copies the authenticated #5550 capsule to a temporary directory. It then replaces exactly four literal lines of
+its checker, each of which must occur once:
+
+1. Read the word from the given path, not the pinned #5545 word.
+2. Take the expected helper profile as a parameter, not the #5545 literal.
+3. Take the invoice from `inputs/INVOICE.json`, a byte extract of #5561's `RESULT.json`. The checker
+   recounts paid MOVEs and native target ranks and requires equality.
+4. Recompute `local_routes` from the MOVE count with the source formula (paid + 2·527 + 208 + 4·104 + 4·8)·1000.
+
+The canonical capsule is never edited. The positive control shows the four changes are faithful.
+
+## Reproduce
+
+Python 3.12+, standard library only:
+
+```sh
+python3 -B research/p104-free-endpoint-contract-audit/verify.py
+```
+
+The run takes about three minutes and should end with the marker `PASS_P104_FREE_ENDPOINT_CONTRACT_AUDIT`. `RESULT.json` holds the complete result.
+
+## Scope and limits
+
+This addresses only hypothesis (c) of #5561, and therefore also the mid-frame start hypothesis of
+[#5553](https://github.com/CrocSwap/integer-mult-bounds/pull/5553). It does not check the retime
+legality (#5561's own `retime.py`), the pricing or strictification, the outer conjunction, or the
+validity of the #5551 parent word. Those checks belong to #5561's verifier and the pending #5551 admission.
+The certified endpoints of the source are its checker constants KAPPA = .00308142 (headline) and
+.003076879 (starts-only), as noted in the intake record. Inherited local all-input native semantics,
+the five framework assumptions and maintainer acceptance remain. This is an agent check, not human
+or proof-kernel acceptance.
+
+## Open next questions
+
+- Admission of the #5551 parent word, on which #5561 and #5553 build (pending, with #5548/#5550/#5557 support).
+- Correction of #5561's claim lines to its certified endpoints .00308142 and .003076879.
+- A deterministic generator for the #5561 retime, so that a checker is not the only reproduction route.
+
+## Credit
+
+Chris R / Clear1nsight (#5550 checker, used unchanged except the four input lines). DreamingOfClouds
+(#5561, #5553). thu-nmrc (#5551). Ali Romman (#5544/#5545 and the P104 caller). chafreaky (#458
+wrappers). The P104 lineage (#2305, #2152, #2219) and all retained native, Clifford, compiler and analytic
+contributors are credited in the cited packages. This package was prepared for Matarener with Claude (Anthropic), via
+Claude Code. Apache-2.0.
diff --git a/research/p104-free-endpoint-contract-audit/RESULT.json b/research/p104-free-endpoint-contract-audit/RESULT.json
new file mode 100644
index 0000000000..ecdda8483b
--- /dev/null
+++ b/research/p104-free-endpoint-contract-audit/RESULT.json
@@ -0,0 +1,77 @@
+{
+ "headline": {
+  "census": {
+   "below_full_finals": 44,
+   "distinct_endpoint_pairs": 32,
+   "final_dims": {
+    "4": 27,
+    "5": 5,
+    "8": 12,
+    "9": 483
+   },
+   "helpers": 527,
+   "nonzero_starts": 58,
+   "start_dims": {
+    "0": 469,
+    "1": 2,
+    "5": 56
+   }
+  },
+  "certified_kappa_of_source": "154071/50000000",
+  "exact_native_checks": 272,
+  "ordinary_allowance": 184647552,
+  "ordinary_passes": 124232680,
+  "output_sha256": "e7bc506894359007b38552e99c93346a67fc3c754b8982595c7ae79b678bb3f4",
+  "paid_jobs": 66852,
+  "productive_fields": 12814
+ },
+ "negative_controls": {
+  "changed_helper_endpoint": "rejected",
+  "changed_invoice": "rejected"
+ },
+ "pr5545_census": {
+  "below_full_finals": 65,
+  "distinct_endpoint_pairs": 40,
+  "final_dims": {
+   "4": 27,
+   "5": 4,
+   "8": 34,
+   "9": 462
+  },
+  "helpers": 527,
+  "nonzero_starts": 192,
+  "start_dims": {
+   "0": 335,
+   "1": 136,
+   "4": 32,
+   "5": 24
+  }
+ },
+ "starts_only": {
+  "census": {
+   "below_full_finals": 65,
+   "distinct_endpoint_pairs": 35,
+   "final_dims": {
+    "4": 27,
+    "5": 4,
+    "8": 34,
+    "9": 462
+   },
+   "helpers": 527,
+   "nonzero_starts": 59,
+   "start_dims": {
+    "0": 468,
+    "1": 2,
+    "4": 1,
+    "5": 56
+   }
+  },
+  "certified_kappa_of_source": "3076879/1000000000",
+  "exact_native_checks": 278,
+  "ordinary_allowance": 184647552,
+  "ordinary_passes": 124754680,
+  "output_sha256": "a4d61875640bad3ca3c82ea08c764381f275bb6fa798b5c2c6db3f4d80275e60",
+  "paid_jobs": 67374,
+  "productive_fields": 12814
+ }
+}
diff --git a/research/p104-free-endpoint-contract-audit/SOURCES.json b/research/p104-free-endpoint-contract-audit/SOURCES.json
new file mode 100644
index 0000000000..255d538d0b
--- /dev/null
+++ b/research/p104-free-endpoint-contract-audit/SOURCES.json
@@ -0,0 +1,87 @@
+{
+  "schema_version": 1,
+  "base_commit": "5e0052ca0aa3036a3afa8b0438927377c8d97d53",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446",
+      "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "research/p104-caller-independent-audit/CAPSULE-INVENTORY.json",
+      "usage": "input",
+      "git_blob": "07c7b818f02c2aabab4798c3e8203ffd2fe1e827",
+      "sha256": "c3e525f5d42ad5b274b039db42f97a2b6e372b583d382c73f59dcb3142f1960d"
+    },
+    {
+      "path": "research/p104-caller-independent-audit/expected/caller.json.gz",
+      "usage": "input",
+      "git_blob": "812ef403ffb149c6230e4a58f29bea75c38f9ba2",
+      "sha256": "383509fce75e2d364138775a4fc96181c9c4cf2608eda0819a7c0c6236faa679"
+    },
+    {
+      "path": "research/p104-full-frame-contact/WORD.json.gz",
+      "usage": "input",
+      "git_blob": "1ce96b0130daeea46ef53fdbd32bca2727aa6b35",
+      "sha256": "a1e416add9d2bb44fce923111ebc50513e5d845e56aabe214f2f0bc7d5f2b45d"
+    },
+    {
+      "path": "research/p104-native-channel/vendor/clifford_exact.py",
+      "usage": "input",
+      "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2",
+      "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+    },
+    {
+      "path": "research/p104-native-channel/vendor/native_verify.py",
+      "usage": "input",
+      "git_blob": "2c209dfa9cfade3bc20ac5fc9d876b433a147f8c",
+      "sha256": "3049471905b47b385c88378a1a3be7a18b8858aadd035b8a6da2f4a03b470f38"
+    },
+    {
+      "path": "research/pr4359-p7-padding/native_inventory.py",
+      "usage": "input",
+      "git_blob": "8d2d96e3998254c2333c43fe47cdfd074cbd811e",
+      "sha256": "65539acaf45bdfe8c5aee6830f9c9b3d1107c442a60842ef803fdd7688de8f32"
+    },
+    {
+      "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json",
+      "usage": "input",
+      "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70",
+      "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa"
+    },
+    {
+      "path": "research/p104-caller-independent-audit/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "3a74b71a55753a6e7cb372d98b0074cf98dc8708",
+      "sha256": "d73ff9587a85db8063391919ffc4a17521ccd5759cdaf6338ba036703239d839"
+    },
+    {
+      "path": "research/p104-productive-controller/local.py",
+      "usage": "provenance",
+      "git_blob": "dbb3d56a4f5b733bb0c32a91249d1f6a7e1ab5d2",
+      "sha256": "878734dfd64c4b9d362d0ae476cc5c2a19fe93e48b7378763b23f3e0dd0a5a71"
+    }
+  ],
+  "package_inputs": {
+    "INVOICE.json": "703d91eb2bb19caa22367c3b84dc7f7c666b3b94341981284e46cf998bbe7d84",
+    "pr5561-WORD.json.gz": "b3701d78bee3661382ebe5414e678dfc9ee292e254cb9dc56339c2d2f45fdf44",
+    "pr5561-WORD-STARTS-ONLY.json.gz": "c9d978ba90a3ddf6d50529a010ddb5dadc56554c99a15c36378b999deb6d6a20"
+  },
+  "external_sources": {
+    "pr5561": {
+      "head": "452d27dde67ee9f772dbbd3be129db97a8ecb9c1",
+      "files": {
+        "research/p104-free-endpoint-retime/WORD.json.gz": "inputs/pr5561-WORD.json.gz",
+        "research/p104-free-endpoint-retime/WORD-STARTS-ONLY.json.gz": "inputs/pr5561-WORD-STARTS-ONLY.json.gz",
+        "research/p104-free-endpoint-retime/RESULT.json": "inputs/INVOICE.json (extract)"
+      }
+    }
+  }
+}
diff --git a/research/p104-free-endpoint-contract-audit/TASK.json b/research/p104-free-endpoint-contract-audit/TASK.json
new file mode 100644
index 0000000000..f1508dff3d
--- /dev/null
+++ b/research/p104-free-endpoint-contract-audit/TASK.json
@@ -0,0 +1,112 @@
+{
+  "schema_version": 1,
+  "task_id": "scalar-to-moment",
+  "priority_revision": 7,
+  "base_commit": "5e0052ca0aa3036a3afa8b0438927377c8d97d53",
+  "original_card": {
+    "id": "scalar-to-moment",
+    "question": "Can a changed frame itinerary remove a paid transition beyond the already covered scalar A2 contractions?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "research/staged544-a2-graph-rewrite/README.md",
+      "research/staged544-separated-a2/README.md",
+      "research/staged544-a2-composition-audit/README.md",
+      "research/staged544-a1858-contraction-audit/README.md"
+    ],
+    "methods": [
+      "Derive the changed legal frame itinerary and exact child histogram.",
+      "Prove a scoped obstruction showing why that scalar gain cannot change the paid contract."
+    ],
+    "acceptance_gate": "An unchanged histogram is not a kappa gain; record any separate runtime or proof benefit explicitly.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the A2 and separated-A2 constructions and their composition/contraction audits. Scalar contractions can preserve the complete recursive histogram; fewer ADDs alone do not justify further scans.",
+      "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+    },
+    "first_experiment": "Identify an actual paid transition to remove and construct a legal replacement frame itinerary, charging restoration, source windows and changed helpers. Compare complete before/after histograms. Stop if only scalar count changes; report that benefit honestly, without expanding the same scalar-only census.",
+    "bottleneck_link": "A legal change to the histogram, not addition count alone, is the bridge to an exponent gain.",
+    "allowed_variations": [
+      "One existing scalar simplification and one proposed frame-path change."
+    ],
+    "scope_change_triggers": [
+      "Submitting only another scalar count as completion of a paid-profile task."
+    ],
+    "overlap_terms": [
+      "scalar simplification",
+      "paid profile",
+      "R439",
+      "3998",
+      "4019",
+      "4112",
+      "4152",
+      "staged544-a2-graph-rewrite",
+      "staged544-separated-a2",
+      "staged544-a2-composition-audit",
+      "staged544-a1858-contraction-audit"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #3998: consecutive A2 scalar contraction",
+        "evidence": "research/staged544-a2-graph-rewrite/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "status": "author-checked",
+        "source_commit": "389268a6b5e0373a3125d5c6fcd6995f4ea324f5",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4019: separated A2 sites with unchanged recursive histogram",
+        "evidence": "research/staged544-separated-a2/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "status": "author-checked",
+        "source_commit": "f408e09df300b575235f7f77f81948071397e16d",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4112: composition audit",
+        "evidence": "research/staged544-a2-composition-audit/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "status": "author-checked",
+        "source_commit": "205b7380656ba4b6316a8a493b1a3c679b8f7a0e",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4152: A1858 contraction audit",
+        "evidence": "research/staged544-a1858-contraction-audit/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "status": "author-checked",
+        "source_commit": "caaa14cde5962adc372fdca71f63d0f29e73c8b2",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Audit hypothesis (c) of PR5561 (free helper start/final frames) against the P104 helper-endpoint contract audited in PR5550; rerun the PR5550 checker on both PR5561 words.",
+  "scope_change_reason": "Audit of a changed frame itinerary already proposed in PR5561; no new itinerary or kappa.",
+  "bottleneck_link": "PR5561 removes paid MOVE stops (69,912 -> 66,852 paid calls) by retiming helper endpoints; this audit decides whether that changed itinerary needs an extra premise.",
+  "budget_minutes": 120,
+  "stop_rule": "Stop after the PR5550 checker passes or fails on both PR5561 words with positive and negative controls.",
+  "outcome": "completed",
+  "evidence": "research/p104-free-endpoint-contract-audit/RESULT.json",
+  "author": "Matarener",
+  "ai_assistance": "Prepared with Claude (Anthropic) via Claude Code.",
+  "open_questions": [
+    {
+      "question": "Is the PR5551 parent word admitted?",
+      "why_it_matters": "PR5561 and PR5553 build on it; this audit takes it as given.",
+      "first_step": "Follow the pending PR5551 admission with PR5548/PR5550/PR5557 support.",
+      "blocked_by": "Maintainer admission queue"
+    },
+    {
+      "question": "Do PR5561 claim lines match its certified endpoints?",
+      "why_it_matters": "Intake records KAPPA=.00308142 and .003076879 as certified, not the raw crossings.",
+      "first_step": "Author correction of README/receipt claims.",
+      "blocked_by": "PR5561 author"
+    }
+  ]
+}
diff --git a/research/p104-free-endpoint-contract-audit/VERIFY.json b/research/p104-free-endpoint-contract-audit/VERIFY.json
new file mode 100644
index 0000000000..9f5a551cdb
--- /dev/null
+++ b/research/p104-free-endpoint-contract-audit/VERIFY.json
@@ -0,0 +1,26 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/p104-caller-independent-audit/CAPSULE-INVENTORY.json",
+    "research/p104-caller-independent-audit/expected/caller.json.gz",
+    "research/p104-full-frame-contact/WORD.json.gz",
+    "research/p104-native-channel/vendor/clifford_exact.py",
+    "research/p104-native-channel/vendor/native_verify.py",
+    "research/pr4359-p7-padding/native_inventory.py",
+    "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 600,
+      "checks": "Authenticated PR5550 capsule; PR5545 endpoint census; patched checker reproduces the complete PR5550 output on PR5545 byte for byte; PASS on both PR5561 words; changed endpoint and changed invoice rejected; result equals RESULT.json."
+    }
+  ]
+}
diff --git a/research/p104-free-endpoint-contract-audit/inputs/INVOICE.json b/research/p104-free-endpoint-contract-audit/inputs/INVOICE.json
new file mode 100644
index 0000000000..acd57323b4
--- /dev/null
+++ b/research/p104-free-endpoint-contract-audit/inputs/INVOICE.json
@@ -0,0 +1,107 @@
+{
+ "note": "Byte-for-byte extract of paid, targets and nonrecursive from the author receipt; the checker recounts paid MOVEs and native target ranks itself and requires equality.",
+ "parts": {
+  "headline": {
+   "kappa": "154071/50000000",
+   "nonrecursive": {
+    "fixed_scalar_growth_bound": "At most 2^(16*26000) before native factors; a declared constant, not an attained norm.",
+    "local_routes": 5164000,
+    "local_scalar": 217428,
+    "peak_owned_fields": 1,
+    "raw_budget": 1000000000,
+    "raw_scalar_upper": 184647552,
+    "tensor_native_growth_bound": "Each rank-r Gaussian has row l1 norm at most 2^(rf); sum of local ranks is 5894."
+   },
+   "paid": {
+    "1": 41340,
+    "16": 416,
+    "2": 8262,
+    "24": 416,
+    "3": 8928,
+    "32": 416,
+    "4": 1674,
+    "40": 416,
+    "48": 416,
+    "5": 2952,
+    "56": 416,
+    "6": 324,
+    "64": 416,
+    "7": 252,
+    "72": 208
+   },
+   "raw_root_interval": [
+    "15407121669/5000000000000",
+    "308142433381/100000000000000"
+   ],
+   "targets": {
+    "145": 208,
+    "17": 416,
+    "25": 416,
+    "33": 416,
+    "4": 1494,
+    "41": 416,
+    "49": 416,
+    "5": 90,
+    "57": 416,
+    "65": 416,
+    "73": 208,
+    "8": 252,
+    "9": 7650
+   }
+  },
+  "starts_only": {
+   "kappa": "3076879/1000000000",
+   "nonrecursive": {
+    "fixed_scalar_growth_bound": "At most 2^(16*26000) before native factors; a declared constant, not an attained norm.",
+    "local_routes": 5193000,
+    "local_scalar": 217428,
+    "peak_owned_fields": 1,
+    "raw_budget": 1000000000,
+    "raw_scalar_upper": 184647552,
+    "tensor_native_growth_bound": "Each rank-r Gaussian has row l1 norm at most 2^(rf); sum of local ranks is 5894."
+   },
+   "paid": {
+    "1": 42204,
+    "16": 416,
+    "2": 8442,
+    "24": 416,
+    "3": 8442,
+    "32": 416,
+    "4": 1638,
+    "40": 416,
+    "48": 416,
+    "5": 2970,
+    "56": 416,
+    "6": 306,
+    "64": 416,
+    "7": 252,
+    "72": 208
+   },
+   "raw_root_interval": [
+    "76922002003/25000000000000",
+    "307688008013/100000000000000"
+   ],
+   "targets": {
+    "145": 208,
+    "17": 416,
+    "25": 416,
+    "33": 416,
+    "4": 1494,
+    "41": 416,
+    "49": 416,
+    "5": 90,
+    "57": 416,
+    "65": 416,
+    "7": 18,
+    "73": 208,
+    "8": 612,
+    "9": 7272
+   }
+  }
+ },
+ "schema": "p104-free-endpoint-invoice/1",
+ "source_head": "452d27dde67ee9f772dbbd3be129db97a8ecb9c1",
+ "source_path": "research/p104-free-endpoint-retime/RESULT.json",
+ "source_pr": 5561,
+ "source_sha256": "8a97218d94c149e7d5b62654cbf84ee8647bff99a9f8f6bd795b29ba0b02e70b"
+}
diff --git a/research/p104-free-endpoint-contract-audit/inputs/pr5561-WORD-STARTS-ONLY.json.gz b/research/p104-free-endpoint-contract-audit/inputs/pr5561-WORD-STARTS-ONLY.json.gz
new file mode 100644
index 0000000000..b0c13f48e9
Binary files /dev/null and b/research/p104-free-endpoint-contract-audit/inputs/pr5561-WORD-STARTS-ONLY.json.gz differ
diff --git a/research/p104-free-endpoint-contract-audit/inputs/pr5561-WORD.json.gz b/research/p104-free-endpoint-contract-audit/inputs/pr5561-WORD.json.gz
new file mode 100644
index 0000000000..c367d865a1
Binary files /dev/null and b/research/p104-free-endpoint-contract-audit/inputs/pr5561-WORD.json.gz differ
diff --git a/research/p104-free-endpoint-contract-audit/verify.py b/research/p104-free-endpoint-contract-audit/verify.py
new file mode 100644
index 0000000000..5e40382376
--- /dev/null
+++ b/research/p104-free-endpoint-contract-audit/verify.py
@@ -0,0 +1,180 @@
+#!/usr/bin/env python3
+"""Free helper endpoints of PR5561 under the audited P104 endpoint contract.  Apache-2.0.
+
+Prepared for Matarener with Claude (Anthropic), via Claude Code.
+The scientific checker is Chris R / Clear1nsight's byte-pinned PR5550 caller and
+target-binding audit (research/p104-caller-independent-audit, substantial OpenAI
+Codex assistance).  This file changes only four literal input lines of a temporary
+copy and never edits the canonical capsule.
+
+Steps:
+  1. authenticate every input by SHA-256 (canonical PR5550 capsule, PR5545 word,
+     package-local PR5561 words and invoice extract);
+  2. census of nonzero helper starts and below-FULL helper finals in the PR5545 word;
+  3. positive control: the patched checker on the PR5545 word with the PR5545 invoice
+     reproduces PR5550's complete frozen scientific output byte for byte;
+  4. the patched checker on both PR5561 words (headline and starts-only);
+  5. negative controls: a changed helper endpoint and a changed invoice are rejected.
+"""
+from collections import Counter
+from pathlib import Path
+import gzip
+import hashlib
+import json
+import os
+import shutil
+import subprocess
+import sys
+import tempfile
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+AUDIT = ROOT/'research/p104-caller-independent-audit'
+CAPSULE = AUDIT/'capsule'
+CHECK = 'outputs/p104-caller-route-audit-v2-20261025/check.py'
+PR5545_WORD = ROOT/'research/p104-full-frame-contact/WORD.json.gz'
+EXPECTED_5550 = 'b51a7d19c10faea7d569a48e9536db8ba1e7418f8dd8dfb25646cc87cc9c4009'
+
+REPLACEMENTS = (
+    ("    word = read(PRIOR/'sources/contact/WORD.json.gz')\n",
+     "    word = read(Path(os.environ['P104_WORD']))\n"
+     "    FREE = json.loads(Path(os.environ['P104_INVOICE']).read_text())\n"),
+    ("helper_profile == Counter({4:51, 5:36, 7:24, 8:122, 9:294})",
+     "helper_profile == Counter({int(k):v for k,v in json.loads(os.environ['P104_PROFILE']).items()})"),
+    ("    costs = source['complete_cost']\n",
+     "    costs = FREE\n"),
+    ("nr['local_routes'] == 5334000 and sum(paid_local.values()) == 3624",
+     "nr['local_routes'] == (sum(paid_local.values())+2*527+208+4*104+4*8)*1000 and sum(paid_local.values()) == int(os.environ['P104_MOVES'])"),
+)
+
+PARTS = {
+    'headline': {'word': 'pr5561-WORD.json.gz', 'moves': 3454, 'paid': 66852, 'pairs': 32,
+                 'profile': {4: 83, 5: 5, 8: 14, 9: 425}},
+    'starts_only': {'word': 'pr5561-WORD-STARTS-ONLY.json.gz', 'moves': 3483, 'paid': 67374, 'pairs': 35,
+                    'profile': {4: 83, 5: 5, 7: 1, 8: 34, 9: 404}},
+}
+
+
+def need(ok, why):
+    if not ok:
+        raise ValueError(why)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def read(path):
+    raw = Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def authenticate():
+    pins = json.loads((HERE/'SOURCES.json').read_text())
+    for row in pins['files']:
+        need(sha(ROOT/row['path']) == row['sha256'], 'source pin '+row['path'])
+    for name, digest in pins['package_inputs'].items():
+        need(sha(HERE/'inputs'/name) == digest, 'package input '+name)
+    inventory = json.loads((AUDIT/'CAPSULE-INVENTORY.json').read_text())['files']
+    for name, digest in inventory.items():
+        if name.startswith('capsule/'):
+            need(sha(AUDIT/name) == digest, 'PR5550 capsule byte '+name)
+
+
+def endpoint_census(word):
+    frames = word['frames']
+    main = set(word['live']) | {r+112 for r in word['live']}
+    helpers = [r for r in range(word['public']) if r not in main]
+    starts = Counter(len(frames[word['initial'][r]]) for r in helpers)
+    finals = Counter(len(frames[word['final'][r]]) for r in helpers)
+    pairs = {(word['initial'][r], word['final'][r]) for r in helpers}
+    return {'helpers': len(helpers), 'start_dims': dict(sorted(starts.items())), 'final_dims': dict(sorted(finals.items())),
+            'nonzero_starts': sum(n for d, n in starts.items() if d), 'below_full_finals': sum(n for d, n in finals.items() if d < 9),
+            'distinct_endpoint_pairs': len(pairs)}
+
+
+def run(work, word_path, invoice, profile, moves):
+    inv = work/'invoice.json'
+    inv.write_text(json.dumps(invoice))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', P104_WORD=str(word_path), P104_INVOICE=str(inv),
+               P104_PROFILE=json.dumps(profile), P104_MOVES=str(moves))
+    env.pop('P104_TRACE_FILE', None)
+    command = [sys.executable, '-X', 'pycache_prefix='+str(work/'bytecode')] + (['-O'] if sys.flags.optimize else []) + \
+              ['-B', str(work/'capsule'/'outputs/p104-caller-route-audit-v2-20261025/check_free.py')]
+    done = subprocess.run(command, cwd=work/'capsule', env=env, capture_output=True, timeout=300)
+    return done.returncode, done.stdout, done.stderr.decode(errors='replace')
+
+
+def main():
+    authenticate()
+    print('PASS authenticated canonical PR5550 capsule, PR5545 word and PR5561 inputs', flush=True)
+    base = read(PR5545_WORD)
+    census_5545 = endpoint_census(base)
+    need((census_5545['nonzero_starts'], census_5545['below_full_finals'], census_5545['distinct_endpoint_pairs']) == (192, 65, 40),
+         'PR5545 already has 192 nonzero helper starts, 65 below-FULL finals and 40 endpoint pairs')
+    print('PASS PR5545 endpoint census', census_5545, flush=True)
+    invoice = json.loads((HERE/'inputs/INVOICE.json').read_text())
+    results = {'pr5545_census': census_5545}
+    with tempfile.TemporaryDirectory(prefix='p104-free-endpoint-contract-') as tmp:
+        work = Path(tmp)
+        shutil.copytree(CAPSULE, work/'capsule')
+        text = (work/'capsule'/CHECK).read_text()
+        need(hashlib.sha256(text.encode()).hexdigest() == sha(CAPSULE/CHECK), 'pinned PR5550 checker')
+        for old, new in REPLACEMENTS:
+            need(text.count(old) == 1, 'literal present once: '+old.strip()[:60])
+            text = text.replace(old, new)
+        (work/'capsule'/CHECK).with_name('check_free.py').write_text(text)
+        # Positive control: the PR5545 word and invoice give PR5550's frozen output byte for byte.
+        source = read(CAPSULE/'outputs/p104-contact-reassessment-20261025/sources/contact/RESULT.json')
+        code, out, err = run(work, CAPSULE/'outputs/p104-contact-reassessment-20261025/sources/contact/WORD.json.gz',
+                             source['complete_cost'], {4: 51, 5: 36, 7: 24, 8: 122, 9: 294}, 3624)
+        need(code == 0 and not err, 'positive control failed: '+err[-2000:])
+        need(hashlib.sha256(out).hexdigest() == EXPECTED_5550 == hashlib.sha256(gzip.decompress((AUDIT/'expected/caller.json.gz').read_bytes())).hexdigest(),
+             'patched checker reproduces the complete PR5550 output on PR5545')
+        print('PASS positive control: patched checker reproduces PR5550 output', EXPECTED_5550, flush=True)
+        for part, spec in PARTS.items():
+            word_path = HERE/'inputs'/spec['word']
+            word = read(word_path)
+            census = endpoint_census(word)
+            need(census['distinct_endpoint_pairs'] == spec['pairs'], part+' endpoint pairs')
+            code, out, err = run(work, word_path, invoice['parts'][part], spec['profile'], spec['moves'])
+            need(code == 0 and not err, part+' checker failed: '+err[-2000:])
+            res = json.loads(out)
+            need(res['status'] == 'PASS_SCOPED_CALLER_AND_TARGET_BINDING' and res['kappa_claim'] is None, part+' scoped status')
+            need(sum(res['paid'].values()) == spec['paid'] and sum(res['targets'].values()) == 12814, part+' invoice')
+            need(len(res['helper_normalizers']) == 527 and res['native_checks']['fresh_helpers'] == 9486, part+' helper coverage')
+            need(len(res['controls']) == 10, part+' all ten PR5550 controls reject')
+            o = res['ordinary']
+            need(o['abstract_address_phase_scalar_pass_upper'] <= o['retained_raw_scalar_upper'], part+' ordinary allowance')
+            results[part] = {'census': census, 'paid_jobs': spec['paid'], 'productive_fields': 12814,
+                             'exact_native_checks': res['native_checks']['distinct_signed_Pauli_and_independent_phase_anchors'],
+                             'ordinary_passes': o['abstract_address_phase_scalar_pass_upper'], 'ordinary_allowance': o['retained_raw_scalar_upper'],
+                             'certified_kappa_of_source': invoice['parts'][part]['kappa'], 'output_sha256': hashlib.sha256(out).hexdigest()}
+            print('PASS', part, results[part], flush=True)
+        # Negative controls on the headline word.
+        word = read(HERE/'inputs/pr5561-WORD.json.gz')
+        main_regs = set(word['live']) | {r+112 for r in word['live']}
+        h = next(r for r in range(735) if r not in main_regs and len(word['frames'][word['initial'][r]]))
+        zero = next(i for i, f in enumerate(word['frames']) if not f)
+        bad = json.loads(json.dumps(word))
+        bad['initial'][h] = zero
+        bad_path = work/'bad-endpoint.json.gz'
+        bad_path.write_bytes(gzip.compress(json.dumps(bad).encode(), mtime=0))
+        code, _, err = run(work, bad_path, invoice['parts']['headline'], PARTS['headline']['profile'], 3454)
+        need(code != 0 and 'ValueError' in err, 'changed helper endpoint rejected')
+        wrong = json.loads(json.dumps(invoice['parts']['headline']))
+        wrong['paid']['1'] += 1
+        code, _, err = run(work, HERE/'inputs/pr5561-WORD.json.gz', wrong, PARTS['headline']['profile'], 3454)
+        need(code != 0 and 'complete unchanged paid/target invoice' in err, 'changed invoice rejected')
+        results['negative_controls'] = {'changed_helper_endpoint': 'rejected', 'changed_invoice': 'rejected'}
+        print('PASS negative controls', results['negative_controls'], flush=True)
+    expected = json.loads((HERE/'RESULT.json').read_text())
+    if '--write' in sys.argv:
+        (HERE/'RESULT.json').write_text(json.dumps(results, indent=1, sort_keys=True)+'\n')
+    else:
+        need(json.loads(json.dumps(results)) == expected, 'complete result equals RESULT.json')
+    print('PASS_P104_FREE_ENDPOINT_CONTRACT_AUDIT')
+
+
+if __name__ == '__main__':
+    main()