Independent verification: targetwise audit of PR966 decoder certificates

research/prescribed-triple-decoder/AUDIT.json

@@ -0,0 +1,72 @@
+{
+  "cases": [
+    {
+      "group_elements": 8,
+      "labelled_target_triples": 4,
+      "orbits": 1,
+      "p": 2,
+      "ports": 4,
+      "retained_decoder_equations": 9
+    },
+    {
+      "group_elements": 48,
+      "labelled_target_triples": 220,
+      "orbits": 9,
+      "p": 3,
+      "ports": 12,
+      "retained_decoder_equations": 141
+    },
+    {
+      "group_elements": 384,
+      "labelled_target_triples": 2024,
+      "orbits": 16,
+      "p": 4,
+      "ports": 24,
+      "retained_decoder_equations": 537
+    },
+    {
+      "group_elements": 3840,
+      "labelled_target_triples": 9880,
+      "orbits": 18,
+      "p": 5,
+      "ports": 40,
+      "retained_decoder_equations": 1119
+    },
+    {
+      "group_elements": 46080,
+      "labelled_target_triples": 34220,
+      "orbits": 19,
+      "p": 6,
+      "ports": 60,
+      "retained_decoder_equations": 1941
+    }
+  ],
+  "format": "pr966-targetwise-independent-audit-v1",
+  "independent_rref": [
+    {
+      "p": 3,
+      "subspaces": 155,
+      "target_triples": 220
+    },
+    {
+      "p": 4,
+      "subspaces": 11811,
+      "target_triples": 2024
+    }
+  ],
+  "negative_controls": [
+    "source_sha256",
+    "zero_decoder",
+    "wrong_target_decoder",
+    "delete_target",
+    "nonport",
+    "duplicate_deletion",
+    "surviving_inventory",
+    "collapse_partition",
+    "port_inventory",
+    "histogram_preserving_target_swap_p3",
+    "histogram_preserving_target_swap_p4"
+  ],
+  "source_commit": "7eaf5665ac246310293fda06a3cf245fe72f6012",
+  "source_sha256": "ab75a0a3506f66053ad0b7f693738e45db06ff9befdeed4484b9dffaa7f687dc"
+}

research/prescribed-triple-decoder/README.md

@@ -0,0 +1,119 @@
+# Independent targetwise audit of PR #966
+
+**Independent verification; no new kappa.** This package audits the exact
+prescribed-triple certificate from [PR #966](https://github.com/CrocSwap/integer-mult-bounds/pull/966)
+at `7eaf5665ac246310293fda06a3cf245fe72f6012`. It checks the identity of
+every labelled target in the independent comparison, rather than comparing
+only cost histograms. It also verifies the certificate's orbit multiplicities
+by explicitly applying the matching automorphism group, without importing
+the predecessor's first-occurrence canonicalization or verifier.
+
+The result is a positive audit of a concurrent contribution. PR #966
+published the same deletion theorem while this sprint was running, with
+broader finite coverage than our initial experiment. We therefore changed
+the deliverable to this independent certificate audit and credit that work.
+The new evidence is a targetwise cross-check, an independent group-action
+inventory and literal witness checks, with a histogram-preserving adverse
+control. No new deletion theorem is claimed here.
+
+## Reproduce
+
+Python 3.9 or later, standard library only. From the repository root:
+
+```sh
+python3 -I research/prescribed-triple-decoder/audit.py
+```
+
+Expected final line:
+
+```text
+PASS PR966 targetwise audit: 46348 triples; 63 orbits; 59 witnesses; 2244 targetwise minima; 11 controls
+```
+
+The audit checks the committed [receipt](AUDIT.json) and all **46,348** labelled
+target triples represented by the certificate at `p=2,...,6`, all **63**
+matching orbits, and all **59** feasible orbit witnesses. At `p=3,4`, it
+compares each of **2,244** labelled target budgets against **11,966**
+independently enumerated rank-three cut-code subspaces. Run with `-O`
+after `-I` to check optimized-mode failure detection. The replay is offline
+and leaves the checkout unchanged. `--write` explicitly regenerates only
+this package's deterministic audit receipt.
+
+## What is checked
+
+The port graph is `K_(2p)` with the `p` original matched edges removed.
+For every certificate representative, `audit.py` explicitly permutes the
+original pairs and flips their signs. The resulting set of labelled target
+triples must have exactly the recorded multiplicity. Different orbit sets
+must be disjoint and their union must equal all three-edge target sets.
+This independently checks the geometric inventory instead of trusting
+the predecessor's canonical keys or histogram totals.
+
+For every feasible orbit, the audit checks deletion membership, uniqueness,
+count and target exclusion. It evaluates each published decoder vertex set
+as a literal symmetric difference of incidence-star supports; after removing
+deleted coordinates its support must be exactly the corresponding retained
+target singleton. Every retained non-target input stays unrestricted.
+
+`independent_check.py` imports no predecessor or audit implementation. It
+enumerates all RREF rank-three subspaces of the full binary cut code at
+`p=3,4`, fixing the final vertex coefficient to zero to remove the constant
+kernel. It computes an exact minimum for every labelled target triple,
+including spaces with five through eight distinct vertex labels. The audit
+compares each target individually to the expanded PR #966 certificate.
+
+The published PR #966 replay at this pin compares deletion histograms
+between its partition and independent engines. A histogram alone does not
+identify which target receives which budget. Our adverse control exchanges
+an ordinary and exceptional target's budgets, preserving the histogram,
+and requires the targetwise comparison to reject the exchange. This is a
+test of the additional comparison's failure detection, not a reported
+counterexample to PR #966's theorem or its own primary checks.
+
+At `p=2,5,6`, this audit verifies inventory and attaining witnesses. It does
+not independently enumerate every cut subspace there. The unrestricted
+optimality claim for those parameters remains with PR #966's written proof
+and its own independent checks. This finite audit is not a formal proof of
+the general deletion theorem or of integer multiplication.
+
+## Provenance and sprint scope
+
+Base: `007664306fff84fbb1c9a1b4053b69f439764034`. Seed **42**, drawn from OS
+randomness at `2026-10-13T14:53:15.619448+00:00`, selected structural decoder
+research. The initial three candidates were nonempty-star prescribed
+triples, empty-allowed triangle targets, and prescribed targets in the
+exceptional `k=4,q=2` cube. Seed modulo three selected the first. The
+initial experiment completed all triples at `p=3,4,5`; refreshing overlap
+then found concurrent PR #966, published at `15:07:03 UTC`. The one
+evidence-driven pivot retained the exact same mathematical object and
+added independent verification of that submission.
+
+A local claim records the initial scope and final result. The open issue
+search found #650 and #913, neither a sprint coordination issue. PR #669
+was the only prescribed-triple submission found before selection. The
+experiment has fixed exhaustive stopping domains, not a randomized search.
+
+The exact source pins are in [SOURCES.json](SOURCES.json). The vendored
+certificate is byte-identical to its Git blob, checked by SHA-256 on each
+run; its retained attribution is in [vendor/NOTICE.md](vendor/NOTICE.md).
+Sam Sung's [PR #669](https://github.com/CrocSwap/integer-mult-bounds/pull/669)
+at `7d526020fc368ce4157cd436995c2f4fcf683318` supplies the signed-port model
+and selectable versus prescribed distinction. PR #966 credits that work,
+Joel Pulikkan / GamingPuzzled, icekylinx and eumemic. Their credit is retained.
+
+The observation model is binary nonempty singleton stars at `k=2`, three
+retained targets and unrestricted surviving non-target inputs. Empty-star
+observations, higher `k`, other target counts and physical suppliers are
+outside this audit. Source access, totals, helpers, frames, copies,
+restoration, recursive children and assembly remain unpriced.
+
+Current main selects conditional PR #890 at
+`kappa=1661957774647029/10^18`. We inspected its source manifest, certificate
+and review and checked selected-record integrity. Its unrelated cold
+construction was not rerun. No existing file, selected record or `upstream/`
+file is changed.
+
+Contributor: Eva Ayala / ToikY, with substantial OpenAI Codex assistance,
+including separate bounded workers for mathematical and implementation
+checks. No independent human review is claimed. Apache-2.0, under the
+repository's [license](../../LICENSE).

research/prescribed-triple-decoder/SOURCES.json

@@ -0,0 +1,40 @@
+{
+  "base_commit": "007664306fff84fbb1c9a1b4053b69f439764034",
+  "source_role": "Independent audit of PR966's immutable certificate; no predecessor implementation is imported or executed",
+  "audited_submission": {
+    "pr": 966,
+    "repository": "woklerx/integer-mult-bounds",
+    "commit": "7eaf5665ac246310293fda06a3cf245fe72f6012",
+    "contributor": "woklerx, with substantial OpenAI Codex assistance",
+    "license": "Apache-2.0",
+    "certificate_path": "research/prescribed-three-port-decoders/CERTIFICATE.json",
+    "certificate_git_blob": "28d04184f1c7a4734ac14fdd577dd8429d29a716",
+    "certificate_sha256": "ab75a0a3506f66053ad0b7f693738e45db06ff9befdeed4484b9dffaa7f687dc",
+    "inspected_replay_path": "research/prescribed-three-port-decoders/reproduce.py",
+    "inspected_replay_git_blob": "a9b855caf33c4c49d519fd250402c111d8c6b7ee"
+  },
+  "predecessor": {
+    "pr": 669,
+    "repository": "the-missionary-company/integer-mult-bounds",
+    "commit": "7d526020fc368ce4157cd436995c2f4fcf683318",
+    "contributor": "Sam Sung / the-missionary-company",
+    "license": "Apache-2.0",
+    "files": {
+      "research/asymmetric-hypercube-decoder/HIGHER-GRAPH.md": {"git_blob": "46f3857025f4d1e2e970ce8f2d7a2607d6007006", "sha256": "b1fab5e859209b983ca6374e11f41988e2146e3ab843e649a668b49c6443d739"},
+      "research/asymmetric-hypercube-decoder/HIGHER-WEIGHTS.md": {"git_blob": "abf5be278d1bae25f131880ef1c49a894fb147e3", "sha256": "7dd0ea3eea0cb3f4ed4075da8a1648589aac995f4f7fda0674924368c5de40ff"},
+      "research/asymmetric-hypercube-decoder/HIGHER-COST.md": {"git_blob": "a0fe1fcc4ed34f27a2434972d7c6e1d56f227a42", "sha256": "23a68e4dfd772244021f8cfcabb39a05bd4bec38415376c6bffd197b55e9a278"}
+    }
+  },
+  "context_only": {
+    "selected_record": "certificates/selected-result.json",
+    "selected_pr": 890,
+    "selected_source_commit": "4b3bd8cbe8e3e81c44161017c9b72c905a8040a8",
+    "selected_kappa": "1661957774647029/1000000000000000000",
+    "selected_certificate": "research/community-frontier890-audit/ASSEMBLY.json",
+    "selected_certificate_sha256": "190110b509dc87d38b72ad37c3290efcc245ce26df4cae3d7e2d6dcf0bac2c43",
+    "review": "docs/research/community-frontier890-review.md",
+    "physical_construction_dependency": false
+  },
+  "assignment": {"seed": 42, "track": "structural decoder research", "randomness": "OS randomness via Python secrets.randbelow", "generated_at_utc": "2026-10-13T14:53:15.619448+00:00"},
+  "attribution": "Eva Ayala (GitHub ToikY), with substantial OpenAI Codex assistance; Apache-2.0"
+}