research: audit exact T74 moment endpoints

research/moment-endpoint-boundary/EXTERNAL-SOURCES.json

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+{
+  "schema_version": 1,
+  "pull_request": 3576,
+  "head_commit": "1630afea0fc1083717b5b2799b8de7a819a6ea02",
+  "base_commit": "20ecf2891d80b5acf18f980b2164fb44ea7faa90",
+  "files": [
+    {
+      "source_path": "research/t74-retuned-ordinary-layer/PROOF.md",
+      "local_path": "inputs/PR3576-PROOF.md",
+      "git_blob": "055c093ffd09b38eebb78e50e179909f007e25f4",
+      "sha256": "e393df9aaf1a2a1027377cf30e27ea16255d4d2fbefffeef0857f31a64ba7378"
+    },
+    {
+      "source_path": "research/t74-retuned-ordinary-layer/rate.py",
+      "local_path": "inputs/PR3576-rate.py",
+      "git_blob": "99983e724d5faa0828d6508bba18b43f3774881c",
+      "sha256": "a66e97da03752c72ffabe57048eab80b0fbe00b0d4c4b5a0c7debca845b81d53"
+    }
+  ]
+}

research/moment-endpoint-boundary/README.md

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+# Exact moment endpoint acceptance audit
+
+This is a bounded arithmetic audit of the moment acceptance boundary in
+[PR #3576](https://github.com/CrocSwap/integer-mult-bounds/pull/3576), head
+`1630afea0fc1083717b5b2799b8de7a819a6ea02`. The moment uses the complete T74
+profile and order from the source archive in
+[PR #2979](https://github.com/CrocSwap/integer-mult-bounds/pull/2979).
+
+The original `independent-moment` card proposed reconstructing a frame group,
+single-change control, and invoice. Live overlap found that PR #3576 already
+supplies the complete moment through two exact interval engines, together with
+the direct ordinary-rate and one-extra-rank-one controls. This package changes
+scope to the uncovered endpoint-consumption question: are the inequalities,
+strict boundary, and decimal rounding direction used correctly when accepting
+those intervals?
+
+## Result
+
+No endpoint-direction or rounding defect was found in the audited acceptance
+code. The pinned source tests `upper < 1` for the accepted sigma moment and
+`lower > 1` for the two rejected alternatives. It floors the lower endpoint and
+ceils the upper endpoint using integer arithmetic.
+
+The independent `Fraction` check reads the three intervals from the exact
+PR3576 proof bytes and verifies these strict comparisons:
+
+| Case | Exact interval over `10^30` | Exact comparison used |
+| --- | --- | --- |
+| `sigma = 998271/1000000` | `[999999903535664027556833879161, 999999903535664027556833879162]` | upper `< 1`, with `1 - upper > 9/10^8` |
+| ordinary exponent `tau` | `[1000003022093731739239177793276, 1000003022093731739239177793277]` | lower `> 1` |
+| sigma with one extra rank-one child | `[1000000111677363244276477808366, 1000000111677363244276477808367]` | lower `> 1` |
+
+The test uses no floating point and imports neither enclosure engine. Its
+canaries put a rational one third of a 30-place unit above and below one, verify
+floor/ceiling enclose both values, and show that the corresponding inward
+rounding mutations fail. Equality-at-one and intervals straddling one catch
+non-strict and wrong-endpoint comparator mutations. The exact proof and rate
+source bytes, their Git blob ids, and their SHA256 hashes are retained in
+`inputs/` and `EXTERNAL-SOURCES.json`. The rate source's profile/order hashes are
+also checked against the live #2979 inputs pinned in `SOURCES.json`.
+
+These checks validate how the published intervals are consumed. They do not
+rederive either enclosure, replay the full T74 package, or establish a supplier
+or multiplication theorem. The source claim retains its physical, production,
+and outer-transfer limits; the selected frontier is unchanged.
+
+## Reproduce
+
+From the repository root:
+
+```sh
+python3 -I -B research/moment-endpoint-boundary/verify.py
+python3 scripts/research_package.py --package research/moment-endpoint-boundary --check-only
+python3.12 scripts/research_package.py --package research/moment-endpoint-boundary
+```
+
+The first command runs only the independent endpoint arithmetic and controls.
+The package replay runs the same bounded verifier after metadata validation.
+The captured PR source bytes can be checked against its exact commit with:
+
+```sh
+git show 1630afea0fc1083717b5b2799b8de7a819a6ea02:research/t74-retuned-ordinary-layer/PROOF.md | sha256sum
+git show 1630afea0fc1083717b5b2799b8de7a819a6ea02:research/t74-retuned-ordinary-layer/rate.py | sha256sum
+```
+
+## Open next questions
+
+- **Does a future production T74 call path consume this same complete profile and strict moment contract?** This matters because the endpoint check covers the numeric acceptance step only. The first step is to trace the actual retuned constructor into the production T74 call and bind its profile to the pinned `ORDER.json` and `PROFILE.json`. The full production GL64/T74 payload was not run in PR #3576 and remains a blocker to resolving this question here.
+
+## Credit
+
+Credit Hiroki Kumazaki and PR #3576 for the rate transfer and its source-pinned
+two-engine certificate; Douglas Colkitt and Nick Petalas for the retained
+interval engines; Jose Manuel for PR #3562 and the PR #3477 T74 layer; Marius-Paul
+Dumitrean and the cited predecessor authors for PR #2979 and its T74 profile.
+This audit reuses their interval claims and does not claim a new enclosure
+method. New audit code is Apache-2.0.

research/moment-endpoint-boundary/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    },
+    {
+      "path": "research/rank7-joint-endframes/allocation/ORDER.json",
+      "usage": "input",
+      "git_blob": "7409c4df1092241729739596c7648bda504e6aad",
+      "sha256": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1"
+    },
+    {
+      "path": "research/rank7-joint-endframes/allocation/PROFILE.json",
+      "usage": "input",
+      "git_blob": "46a83eeda67ab67cccbffe8b7ad8e44368b40ea7",
+      "sha256": "94a819747f3ced41f1544ada0036c983fc0c92847b9644380f877a06cd7931cf"
+    }
+  ]
+}

research/moment-endpoint-boundary/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "independent-moment",
+  "priority_revision": 6,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "original_card": {
+    "id": "independent-moment",
+    "question": "Does one changed supplier or assembly claim lack a source-bound independent check of a specific new implication?",
+    "starting_points": [
+      "certificates/selected-result.json",
+      "research/rank7-joint-endframes/README.md",
+      "docs/research/research-family-status.md"
+    ],
+    "methods": [
+      "Independently reconstruct a coordinated frame/circuit change and its single-change control, then derive the complete rank and physical ledger.",
+      "Implement certified moment inequalities through a different exact enclosure method."
+    ],
+    "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read #2979 joint rank-7 end-frame proposal and the revision-6 evidence status. Its claimed kappa is not selected. Compare coordinated changes with the losing single-change controls and locate the complete physical ledger; an aggregate moment alone does not validate the mechanism.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Prioritize a bounded independent audit of #2979: reconstruct one joint group and its single-lowering control, check the declared frames/chronology, then trace changed children, idle widths and cleanup buffers into the complete invoice and both supplier caps. Choose one still-missing implication after checking existing audits. Stop with exact unresolved dependencies if full admission exceeds the session; do not launch a new lowering census on an unvalidated premise or substitute extra root digits for mechanism checking.",
+    "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.",
+    "allowed_variations": [
+      "Reconstruct either a source ledger or a numeric enclosure with a different method."
+    ],
+    "scope_change_triggers": [
+      "Importing the primary function and calling its output independent verification.",
+      "Promoting #2979 from merged source archive to validated supplier solely from author PASS receipts or aggregate pricing."
+    ],
+    "overlap_terms": [
+      "independent moment",
+      "rank histogram",
+      "exact enclosure",
+      "2979",
+      "rank7 joint endframes",
+      "paired extraction",
+      "joint lowering"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "For PR3576's complete T74 moment intervals over the PR2979 profile and order, independently check the exact inequality direction, strictness, and 30-place outward-rounding boundary with rational endpoint substitutions and corruption controls.",
+  "scope_change_reason": "Live overlap showed open PR3576 already supplies the full T74 moment computation through two exact engines plus direct-rate and extra-rank-one controls. I narrowed the card to the nonduplicative acceptance boundary and did not reconstruct frames, repeat the invoice, or build another enclosure engine.",
+  "bottleneck_link": "The T74 moment is the strict gate used to turn the complete paid profile into a layer-rate bound. An endpoint-direction or inward-rounding error could invalidate that local rate step.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after exact rational checks of the three published intervals, both strict inequality directions, the stated sigma gap, and one-unit boundary/rounding canaries. Do not rederive the interval engines or extend into production payload and outer admission.",
+  "outcome": "completed",
+  "evidence": "verify.py checks the exact PR3576 proof/rate source bytes, their Git blob IDs, the source-pinned PR2979 PROFILE/ORDER inputs, strict endpoint comparisons, the sigma margin, equality and straddling controls, and outward floor/ceiling behavior near one.",
+  "author": "Cinna Davis",
+  "ai_assistance": "OpenAI Codex assisted with source discovery, exact-rational verifier implementation, and packaging.",
+  "open_questions": [
+    {
+      "question": "Does a future production T74 call path consume the same complete profile and strict moment contract that PR3576 certifies?",
+      "why_it_matters": "The endpoint audit confirms only the numerical acceptance boundary; source-to-production execution and the inherited physical and outer conditions remain separate.",
+      "first_step": "Trace the actual production entry point through the retuned constructor into the T74 call and bind its full profile to the pinned ORDER and PROFILE hashes.",
+      "blocked_by": "PR3576 records no full production GL64/T74 payload execution, and this session did not inspect or run that payload."
+    }
+  ]
+}

research/moment-endpoint-boundary/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/rank7-joint-endframes/allocation/ORDER.json",
+    "research/rank7-joint-endframes/allocation/PROFILE.json",
+    "research/moment-endpoint-boundary/inputs/PR3576-PROOF.md",
+    "research/moment-endpoint-boundary/inputs/PR3576-rate.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Pinned source bytes; exact rational moment endpoint directions and gap; strict equality, straddling, corruption, and outward-rounding controls"
+    }
+  ]
+}