Research audit: binary cover order and exact finite invoice guards

research/orthogonal-cover-invoice-audit/CERTIFICATE.json

@@ -0,0 +1,221 @@
+{
+  "status": "PASS_ORTHOGONAL_COVER_INVOICE_AUDIT",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "assignment_seed": 65,
+  "scope": "Binary dot-product cover order and finite invoice only; no new kappa or full theorem proof.",
+  "selected_kappa_unchanged": "51110230636731/31250000000000000",
+  "enumeration": [
+    {
+      "dimension": 1,
+      "complete_bases": 1,
+      "prefix_counts": [
+        1,
+        1
+      ],
+      "first_column_completion_histogram": {
+        "1": 1
+      },
+      "characteristic_vector_completions": 1
+    },
+    {
+      "dimension": 2,
+      "complete_bases": 2,
+      "prefix_counts": [
+        1,
+        2,
+        2
+      ],
+      "first_column_completion_histogram": {
+        "1": 2
+      },
+      "characteristic_vector_completions": null
+    },
+    {
+      "dimension": 3,
+      "complete_bases": 6,
+      "prefix_counts": [
+        1,
+        4,
+        6,
+        6
+      ],
+      "first_column_completion_histogram": {
+        "0": 1,
+        "2": 3
+      },
+      "characteristic_vector_completions": 0
+    },
+    {
+      "dimension": 4,
+      "complete_bases": 48,
+      "prefix_counts": [
+        1,
+        8,
+        32,
+        48,
+        48
+      ],
+      "first_column_completion_histogram": {
+        "6": 8
+      },
+      "characteristic_vector_completions": null
+    },
+    {
+      "dimension": 5,
+      "complete_bases": 720,
+      "prefix_counts": [
+        1,
+        16,
+        120,
+        480,
+        720,
+        720
+      ],
+      "first_column_completion_histogram": {
+        "0": 1,
+        "48": 15
+      },
+      "characteristic_vector_completions": 0
+    },
+    {
+      "dimension": 6,
+      "complete_bases": 23040,
+      "prefix_counts": [
+        1,
+        32,
+        512,
+        3840,
+        15360,
+        23040,
+        23040
+      ],
+      "first_column_completion_histogram": {
+        "720": 32
+      },
+      "characteristic_vector_completions": null
+    },
+    {
+      "dimension": 7,
+      "complete_bases": 1451520,
+      "prefix_counts": [
+        1,
+        64,
+        2016,
+        32256,
+        241920,
+        967680,
+        1451520,
+        1451520
+      ],
+      "first_column_completion_histogram": {
+        "0": 1,
+        "23040": 63
+      },
+      "characteristic_vector_completions": 0
+    }
+  ],
+  "dimension_73": {
+    "exact_group_order": "88055447129748213099772773138986247571255042612072591674225283308028684371120843328012160052393152527232914014288489818688809961936816670640083409439382433171031243906547760371818869073538416126076656782695792682453482806912643430535775039142420588510522358113551513811666116187287324377802034479488864420323400940604907630584384722731975858354648334415461784223587007406274343722056702999013519051565035640715216081796349147473651840479245483695654253901532871494454113952288727044052531881069342514232455091429630737092047517685965106058714054953066900424219349387329299169409559363267460270558762270126564878116036572334698547529778107107730613024527066352193202984895478814351821651183238272958917221207575904540573250955207812277015748415513176772283677218766323712000000000000000000000",
+    "group_bits": 2628,
+    "finite": {
+      "physical_stock_bits": 2641,
+      "router_bits": 7985,
+      "literal_bits": 35282,
+      "physical_row_coefficient": 16467,
+      "retained_row_coefficient": 20161,
+      "required_C0_bits": 200012,
+      "halving_integer_inequality": [
+        5329,
+        4608
+      ],
+      "G_exponent": 30000,
+      "E_exponent": 100000,
+      "C0_exponent": 210000
+    },
+    "strict_checks": {
+      "local_primitive_bound": true,
+      "logical": true,
+      "router": true,
+      "literal": true,
+      "mass": true,
+      "precision": true,
+      "tape": true,
+      "row": true,
+      "halving": true
+    },
+    "guard_bits": {
+      "local_primitive_bound": {
+        "actual_bits": 44,
+        "bound_exponent": 48
+      },
+      "logical": {
+        "actual_bits": 2680,
+        "bound_exponent": 6050
+      },
+      "router": {
+        "actual_bits": 7985,
+        "bound_exponent": 30000
+      },
+      "literal": {
+        "actual_bits": 35282,
+        "bound_exponent": 100000
+      },
+      "mass": {
+        "actual_bits": 100001,
+        "bound_exponent": 100001
+      },
+      "precision": {
+        "actual_bits": 200012,
+        "bound_exponent": 210000
+      },
+      "tape": {
+        "actual_bits": 100002,
+        "bound_exponent": 210000
+      }
+    }
+  },
+  "negative_controls": {
+    "omit_cover_multiplicity": {
+      "cover_binding_rejected": true,
+      "group_bits": 1,
+      "failed_guards": [],
+      "physical_row_coefficient": 11211
+    },
+    "use_even_dimension_72": {
+      "cover_binding_rejected": true,
+      "group_bits": 2556,
+      "failed_guards": [],
+      "physical_row_coefficient": 16323
+    },
+    "omit_last_symplectic_pair": {
+      "cover_binding_rejected": true,
+      "group_bits": 2485,
+      "failed_guards": [],
+      "physical_row_coefficient": 16181
+    },
+    "omit_powers_of_two": {
+      "cover_binding_rejected": true,
+      "group_bits": 1332,
+      "failed_guards": [],
+      "physical_row_coefficient": 13875
+    },
+    "use_all_invertible_matrices": {
+      "cover_binding_rejected": true,
+      "group_bits": 5328,
+      "failed_guards": [
+        "row"
+      ],
+      "physical_row_coefficient": 21867
+    }
+  },
+  "cover_only_inflation": {
+    "last_passing_power_of_two": 1846,
+    "last_passing_row_coefficient": 20159,
+    "first_failing_power_of_two": 1847,
+    "first_failing_row_coefficient": 20161,
+    "first_failed_guards": [
+      "row"
+    ],
+    "scope": "All other admitted invoice quantities fixed; not a construction or supplier improvement."
+  }
+}

research/orthogonal-cover-invoice-audit/CLAIM.md

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+# Sprint claim — seed 65
+
+- Track: adversarial mathematical audit (60–74).
+- OS-random assignment seed: **65**, from `secrets.randbelow(100)` at
+  2026-10-13 05:09:06 UTC (2026-10-12 22:09 PDT).
+- Exact base: `66849e1475c930fd7732b1a0067ffee7e1e95f60`.
+- Branch: `codex/orthogonal-cover-invoice-seed65`.
+- Budget: 60 minutes, with the final 15 minutes reserved for verification
+  and handoff; expected finish 2026-10-13 06:09 UTC (October 12, 23:09 PDT).
+
+## Three narrow candidates
+
+0. Cold-helper compensation admission in the selected #626 source; deferred
+   because #702 and #729 already cover related wrapper/frame obligations.
+1. Arbitrary private-center restoration in a selected scalar orientation;
+   deferred because #734/#745 already cover it by distinct forward/reverse methods.
+2. The order of the binary dot-product isometry group used in #626's finite
+   routing invoice, and the propagation of its multiplicity into finite guards.
+
+The seed selects candidate `65 % 3 = 2`. The other candidates are already
+crowded. The chosen mathematical object is the *bilinear* dot-product group,
+not a quadratic-form orthogonal group; in odd dimension its characteristic
+vector splits off and the complement is symplectic.
+
+## Exact scope and method
+
+Audit the group factor in `code/invoice_allcold.py` and `code/assemble.py`
+of `research/complex-k492-owner-repair`, bound to the reviewed #626 invoice.
+Derive the odd-dimensional order by counting symplectic bases; independently
+count complete binary orthonormal bases in dimensions 1 through 7 without
+using that formula. Recompute the group-dependent finite guards with integer
+arithmetic, and supply controls for a wrong group family or missing cover
+multiplicity. No new kappa, search for a new supplier, or selected-frontier
+edit is planned. Expected deliverable: a scoped proof, exact certificate,
+standalone verifier, source pins and meaningful negative controls.
+
+## Coordination and overlap
+
+GitHub reports no pinned issues; the sole open issue is #650 (Discussions),
+so this is the local claim. No separate reservation issue was opened.
+The full open queue was inspected (578 PRs), then latest arrivals through
+#762 were checked immediately before this claim. #717 studies moment/invoice
+sensitivity and pair-preserving program permutations, not the ambient cover
+cardinality and finite routing guards. Its scope was inspected. The selected
+review and prior negative-results index were read; no closed supplier search
+is reopened here. No pending PR supplies code or inputs to this audit.
+
+## Completed result and final overlap check
+
+The group factor and all nine finite invoice guards are corroborated.
+Exhaustive basis enumeration covers dimensions 1–7. Five wrong-order controls
+are rejected explicitly; four undercounts still pass every upper-bound guard,
+whereas using GL(73,2) violates the row cap. Exact cover-only inflation reaches
+its first failed guard at a factor of 2^1847. No construction defect or new
+kappa is claimed. See README.md, CERTIFICATE.json and VALIDATION.json.
+
+The final full-queue check covered 586 open PRs through #767, followed by
+an immediate pre-submission latest-arrival check through #769; no ambient
+cover-cardinality audit was found. #717 remains distinct (moment/invoice
+sensitivity and finite program permutations). Upstream main is still the
+recorded base. No coordination issue exists, so the result is recorded locally.
+
+Submitted: https://github.com/CrocSwap/integer-mult-bounds/pull/771
+Completion recorded: 2026-10-13 05:24:47 UTC.
+The contribution finished early; verification and packaging occupied the final
+portion of the session. No work remains on the claimed mathematical scope.