Mister-Meeseeks · Oct 14, 2026 · Oct 14, 2026
diff --git a/research/pr1407-complex-moment-audit-seed39/CLAIM.json b/research/pr1407-complex-moment-audit-seed39/CLAIM.json
@@ -0,0 +1,36 @@
+{
+  "run": 4,
+  "assignment_seed": 39,
+  "track": "complex supplier",
+  "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "started_utc": "2026-10-14T00:18:11Z",
+  "planned_finish_utc": "2026-10-14T01:08:11Z",
+  "verification_start_utc": "2026-10-14T00:55:41Z",
+  "status": "completed",
+  "candidate_tasks": [
+    {
+      "scope": "PR1094 neutral-then-strict two-bin whole-helper path search.",
+      "overlap": "Dropped after live refresh found PR1407 covering neutral whole-helper hosting paths."
+    },
+    {
+      "scope": "PR1387 operator-preserving subset of simultaneous idle-axis optimum.",
+      "overlap": "Open PR #1387 and completed discussion #1339 already cover this optimum and counterexample."
+    },
+    {
+      "scope": "Independent arithmetic audit of PR1407 complex profile and kappa receipts.",
+      "overlap": "Selected as explicitly complementary second audit; no separate arithmetic-audit claim found at refresh."
+    }
+  ],
+  "object": {
+    "pr": 1407,
+    "head": "d8640f5b7ae99b43f5d56146cb94ca62b8b3835d",
+    "candidate_profile_delta": "+e1 - 7e7 + 3e16"
+  },
+  "method": "Third code-disjoint exact interval implementation using binary-reduced atanh log bounds and positive Taylor exponential with geometric tail; verify primary and conservative complex endpoint signs, exact kappa grid, rank mass/deficit, unchanged bit endpoint and failure controls. Does not replay the construction.",
+  "expected_deliverable": "Small registered research package and one focused independent-verification PR if the final replay remains green.",
+  "finish_time_utc": "2026-10-14T01:08:11Z",
+  "coordination": "No pinned sprint issue exists; local claim recorded. PR #1407 itself has two exact moment engines and pending cross-vendor/fresh-context review; this audit uses an independent third implementation.",
+  "completed_utc": "2026-10-14T00:42:32Z",
+  "result": "The exact Fraction replay certified the selected and PR1407 primary and conservative complex root endpoint signs, profile delta and conservation, unchanged bit endpoint, and primary/conservative kappa grids; four deliberate mutation controls rejected.",
+  "reproduction": "python3.12 scripts/research_package.py --package research/pr1407-complex-moment-audit-seed39"
+}
diff --git a/research/pr1407-complex-moment-audit-seed39/README.md b/research/pr1407-complex-moment-audit-seed39/README.md
@@ -0,0 +1,108 @@
+# Independent arithmetic audit of PR #1407's complex profile
+
+**Status: completed, scoped independent verification. No new construction or κ claim.**
+
+PR #1407 proposes a neutral whole-helper hosting construction for the selected
+PR1094 owner map. I do not repeat its search or replay its owner paths. This
+package independently checks the resulting profile arithmetic with a third,
+code-disjoint exact interval engine: the primary and conservative complex root
+brackets, the unchanged bit ceiling, and the published κ grid. The upstream PR
+reports two exact moment engines; this audit adds a separate rational
+atanh/Taylor implementation while leaving its construction proof and native
+admission as inherited claims.
+
+## Frozen data and exact result
+
+The research/source base is
+`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. Before publication, `main`
+advanced to `410026dc5513b87db92ae98571d1d5984c69a983` through three
+reconciliation commits. The selected certificate and the seven other pinned repository
+inputs/provenance files have identical Git blobs at both commits; the audit
+branch is based on the refreshed `main`, while `TASK.json` and `SOURCES.json`
+retain the exact research base. The selected record binds at
+`κ = 836330098538459/500000000000000000`, with complex endpoint
+`67018507072324140917/40000000000000000000000` and bit endpoint
+`1733427039589844234749/10^24`. The source construction and maintainer review
+are pinned by `SOURCES.json`.
+
+The external candidate snapshot is PR #1407 at exact head
+`d8640f5b7ae99b43f5d56146cb94ca62b8b3835d`. `REFERENCE.json` contains the
+candidate profile, endpoint receipts and the original SHA256 and Git blob
+identifiers for PR #1407's `PROFILE.json`, `RESULT.json` and `ASSEMBLY.json`.
+I fetched that exact PR commit through the upstream pull ref and independently
+recomputed all three Git blob IDs and content SHA256 values; all six matched
+the recorded pins. Its snapshot hash is also pinned in `SOURCES.json`.
+
+The candidate profile changes from the selected
+`{1:349604, 2:60192, 3:62585, 4:20448, 5:11808, 7:7, 8:1152, 48:4866}`
+to
+`{1:349605, 2:60192, 3:62585, 4:20448, 5:11808, 8:1152, 16:3, 48:4866}`.
+The exact delta is `+e1 - 7e7 + 3e16`: rank mass and deficit stay fixed,
+while the positive-rank call count drops by three. The priced parameters are
+`m=73`, `W=14336`; the primary complex moment has no added surcharge. The
+conservative check includes the inherited term
+`32*m*N/(10^16*W) * m^a`.
+
+| profile and moment | lower endpoint (`M(a)-1` scaled by `10^32`) | upper endpoint (`M(a)-1` scaled by `10^32`) |
+|---|---:|---:|
+| selected primary | `[-130421533, -130421532]` accepted | `[162472375, 162472376]` rejected |
+| PR #1407 primary | `[-159548291, -159548290]` accepted | `[133342011, 133342012]` rejected |
+| selected conservative | `[-281245180, -281245179]` accepted | `[11648729, 11648730]` rejected |
+| PR #1407 conservative | `[-171561767, -171561766]` accepted | `[121328535, 121328536]` rejected |
+
+Each displayed integer interval is divided by `10^32`. The exact brackets
+reproduce the receipts. The candidate's primary and conservative complex
+brackets both move above the selected brackets, and both remain below the
+unchanged bit endpoint. Exact flooring of `a/(1+a)` to the repository's
+`10^-18` κ grid reproduces the candidate and conservative κ values. The
+primary κ difference is exactly `161104813/7812500000000000`.
+
+## Independent interval method
+
+`verify.py` uses only Python's standard library and `Fraction` arithmetic. It
+computes logarithms after binary range reduction with 48 positive atanh terms
+and the explicit geometric tail
+`2*z^(2N+1)/((2N+1)*(1-z^2))`, where `0 <= z <= 1/3`. It encloses each
+positive exponential with 32 Taylor terms and a geometric bound on the
+remaining tail. The verifier does not import either moment engine used by
+PR #1407 or the selected assembly.
+
+Failure controls mutate one rank-16 count, swap accepted and rejected endpoint
+labels, change κ by one grid unit, and omit the conservative surcharge. Every
+mutation is rejected. The saved exact replay is [RESULT.json](RESULT.json).
+
+Reproduce from the repository root with Python 3.12:
+
+```sh
+python3.12 scripts/research_package.py --package research/pr1407-complex-moment-audit-seed39
+```
+
+Expected: `PASS_REGISTERED_RESEARCH_PACKAGE research/pr1407-complex-moment-audit-seed39 outcome=completed`.
+
+## Scope and limits
+
+This confirms the finite arithmetic receipts derived from the two histograms.
+It does not verify PR #1407's 24 owner moves, its all-input dirty-state
+argument, strict source-event windows, native T16 execution, controller,
+invoice, all 47 outer inequalities, or full ancestry. The audit does not
+establish that the published reassignment realizes the candidate histogram.
+PR review and hosted-workflow status are mutable. This package pins the
+candidate content at the exact head above and makes no claim that its
+construction, CI or review gates are approved.
+
+## Open next questions
+
+The next useful step is a fresh, independent replay of PR #1407's native path
+and a role-by-role check of its eleven neutral-then-concentrating paths. That
+matters because profile arithmetic alone cannot establish physical admission.
+The open blocker is the draft PR's pending review and workflow approval.
+
+## Credit
+
+PAI (@pai-scaffolde) supplies PR #1407's candidate profile and receipts. Rohan
+Arun's PR #1094 supplies the selected owner map; Jeremy Kothe and Hao Yan / FanPUYen
+supply the retained packing and controller lineage. The selected construction
+and its maintainer review remain the pinned baseline. Prepared by Cinna Davis
+(@1337isnot1337) with substantial OpenAI Codex assistance in review, exact
+arithmetic design, implementation and writing. This is a code-disjoint audit,
+not independent human review. New material is Apache-2.0.
diff --git a/research/pr1407-complex-moment-audit-seed39/REFERENCE.json b/research/pr1407-complex-moment-audit-seed39/REFERENCE.json
@@ -0,0 +1,91 @@
+{
+  "schema_version": 1,
+  "source": {
+    "repository": "CrocSwap/integer-mult-bounds",
+    "pr": 1407,
+    "head": "d8640f5b7ae99b43f5d56146cb94ca62b8b3835d",
+    "files": [
+      {
+        "name": "profile",
+        "path": "research/astra-ultra-hosting-20261013/data/PROFILE.json",
+        "git_blob": "54c3e1076c6cccbe6c6a90b39b2aba7b800762e6",
+        "sha256": "e3f778d24ce02c1ddc21b4632c3e0d99e064d8db359b03b019fd8b37baf815b5"
+      },
+      {
+        "name": "result",
+        "path": "research/astra-ultra-hosting-20261013/RESULT.json",
+        "git_blob": "6505aafdcafeb1bcd37aa2ccbf0bd9c5eeab99e0",
+        "sha256": "6be31e95e41bcc83577b364b01a0339d16a8f6f09277b9d8d964c0ea4c1f158c"
+      },
+      {
+        "name": "assembly",
+        "path": "research/astra-ultra-hosting-20261013/receipts/ASSEMBLY.json",
+        "git_blob": "997cce16c3362b27250c3d0de0a29192c9dd4376",
+        "sha256": "fe9dd283cdc5034b74fcca6d2f344da08a876ef1fde6a4db35626a680a12183f"
+      }
+    ]
+  },
+  "candidate_profile": {
+    "1": 349605,
+    "2": 60192,
+    "3": 62585,
+    "4": 20448,
+    "5": 11808,
+    "8": 1152,
+    "16": 3,
+    "48": 4866
+  },
+  "result": {
+    "kappa": "836340409246491/500000000000000000",
+    "kappa_decimal": "0.001672680818492982",
+    "baseline_kappa": "836330098538459/500000000000000000",
+    "delta": "161104813/7812500000000000",
+    "complex_lower": "837741683691654218469/500000000000000000000000",
+    "complex_decimal": "0.001675483367383308436938",
+    "bit_lower": "1733427039589844234749/1000000000000000000000000",
+    "conservative_complex_lower": "837741682260907314779/500000000000000000000000",
+    "conservative_kappa": "1672680815641053/1000000000000000000",
+    "conservative_kappa_decimal": "0.001672680815641053",
+    "profile": {
+      "1": 349605,
+      "2": 60192,
+      "3": 62585,
+      "4": 20448,
+      "5": 11808,
+      "8": 1152,
+      "16": 3,
+      "48": 4866
+    },
+    "live": 14336,
+    "rank_mass": 1041408,
+    "deficit": 5120
+  },
+  "complex_moments": [
+    {
+      "surcharge": false,
+      "endpoint": "837741683691654218469/500000000000000000000000",
+      "accept": true
+    },
+    {
+      "surcharge": false,
+      "endpoint": "1675483367383308436939/1000000000000000000000000",
+      "accept": false
+    }
+  ],
+  "conservative_complex_moments": [
+    {
+      "surcharge": true,
+      "endpoint": "837741682260907314779/500000000000000000000000",
+      "accept": true
+    },
+    {
+      "surcharge": true,
+      "endpoint": "1675483364521814629559/1000000000000000000000000",
+      "accept": false
+    }
+  ],
+  "surcharge_model": {
+    "complex": false,
+    "bit": true
+  }
+}
diff --git a/research/pr1407-complex-moment-audit-seed39/RESULT.json b/research/pr1407-complex-moment-audit-seed39/RESULT.json
@@ -0,0 +1,101 @@
+{
+  "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "base_conservative_bracket": [
+    {
+      "accept": true,
+      "endpoint": "1675462673946628390003/1000000000000000000000000",
+      "moment_minus_one_interval_scaled_1e32": [
+        "-281245180",
+        "-281245179"
+      ]
+    },
+    {
+      "accept": false,
+      "endpoint": "418865668486657097501/250000000000000000000000",
+      "moment_minus_one_interval_scaled_1e32": [
+        "11648729",
+        "11648730"
+      ]
+    }
+  ],
+  "base_primary_bracket": [
+    {
+      "accept": true,
+      "endpoint": "67018507072324140917/40000000000000000000000",
+      "moment_minus_one_interval_scaled_1e32": [
+        "-130421533",
+        "-130421532"
+      ]
+    },
+    {
+      "accept": false,
+      "endpoint": "837731338404051761463/500000000000000000000000",
+      "moment_minus_one_interval_scaled_1e32": [
+        "162472375",
+        "162472376"
+      ]
+    }
+  ],
+  "bit_endpoint_unchanged": "1733427039589844234749/1000000000000000000000000",
+  "call_delta": -3,
+  "candidate_conservative_bracket": [
+    {
+      "accept": true,
+      "endpoint": "837741682260907314779/500000000000000000000000",
+      "moment_minus_one_interval_scaled_1e32": [
+        "-171561767",
+        "-171561766"
+      ]
+    },
+    {
+      "accept": false,
+      "endpoint": "1675483364521814629559/1000000000000000000000000",
+      "moment_minus_one_interval_scaled_1e32": [
+        "121328535",
+        "121328536"
+      ]
+    }
+  ],
+  "candidate_primary_bracket": [
+    {
+      "accept": true,
+      "endpoint": "837741683691654218469/500000000000000000000000",
+      "moment_minus_one_interval_scaled_1e32": [
+        "-159548291",
+        "-159548290"
+      ]
+    },
+    {
+      "accept": false,
+      "endpoint": "1675483367383308436939/1000000000000000000000000",
+      "moment_minus_one_interval_scaled_1e32": [
+        "133342011",
+        "133342012"
+      ]
+    }
+  ],
+  "conservative_kappa_grid": "1672680815641053/1000000000000000000",
+  "construction_scope": "Arithmetic only; no owner/window/path, native compiler, controller, all-47-outer-constraint or full ancestry replay.",
+  "exact_kappa_gain": "161104813/7812500000000000",
+  "external_head": "d8640f5b7ae99b43f5d56146cb94ca62b8b3835d",
+  "external_source_sha256": {
+    "assembly": "fe9dd283cdc5034b74fcca6d2f344da08a876ef1fde6a4db35626a680a12183f",
+    "profile": "e3f778d24ce02c1ddc21b4632c3e0d99e064d8db359b03b019fd8b37baf815b5",
+    "result": "6be31e95e41bcc83577b364b01a0339d16a8f6f09277b9d8d964c0ea4c1f158c"
+  },
+  "failure_controls": [
+    "added rank-16 child",
+    "swap accepted/rejected endpoint labels",
+    "one-grid-unit kappa mutation",
+    "omit conservative surcharge"
+  ],
+  "interval_method": "standard-library Fraction; 48-term binary-reduced atanh logarithm bounds and 32-term positive Taylor exponential with geometric tail",
+  "primary_kappa_grid": "836340409246491/500000000000000000",
+  "profile_delta": {
+    "1": 1,
+    "7": -7,
+    "16": 3
+  },
+  "rank_mass_delta": 0,
+  "status": "PASS_PR1407_COMPLEX_PROFILE_ARITHMETIC_INDEPENDENT_AUDIT"
+}