Tooling: 2.09x faster exact single-intersection Gram replay

certificates/affine-vector-screens.json

@@ -146,7 +146,7 @@
     "scripts/experiments/affine_vector_screens.py": "756778eeca27f490adc7354a122dc50c40375156259991469c47a90949118ea1",
     "scripts/experiments/affine_vector_witnesses.json": "672a4318c48f5286ce088d34736c38957b7f662a5f753d440dbc638e7da5f62a",
     "scripts/experiments/cube_core_family.py": "e58f1f4067bda2d4838343f42ec2505316f006561f0702e869847d88b85413a8",
-    "scripts/experiments/single_intersection.py": "08ddae46e5621a5b4c525b504e67ae655abe9b49461d894feaa7abc89a51847d"
+    "scripts/experiments/single_intersection.py": "6874d41b75590369182ed61e0c6da5b547e035e0e43b50ea2b39e1f3861dca6d"
   },
   "status": "NINE SPECIFIED CENTRAL MATRICES REJECTED; NO NEW KAPPA",
   "upstream_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a"

certificates/single-intersection.json

@@ -52854,7 +52854,7 @@
   "source_sha256": {
     "docs/research/single-intersection.md": "c3a9be97b38f4ac1e7983842d9f23656671e877ad5144f41894818f4551aa4dd",
     "scripts/audit_single_intersection.py": "1de7f9a62edc93c624ff2693ae9bb725cf6dc9735ff1caad56f6913aae9448ee",
-    "scripts/experiments/single_intersection.py": "08ddae46e5621a5b4c525b504e67ae655abe9b49461d894feaa7abc89a51847d",
+    "scripts/experiments/single_intersection.py": "6874d41b75590369182ed61e0c6da5b547e035e0e43b50ea2b39e1f3861dca6d",
     "scripts/experiments/single_intersection_witnesses.json": "c2308a3d21991f5828b0519b191b470f48b2fbbcaa5af0f7aed3986cc7534185"
   },
   "status": "BOUNDED TWO-FIELD RANK SCREEN; NO COMPETITIVE SIDE CIRCUIT OR NEW KAPPA",

docs/research/single-intersection-packing.md

@@ -0,0 +1,97 @@
+# Exact packed Gram replay
+
+This verification tooling contribution targets `minor_rows` in
+`scripts/experiments/single_intersection.py`. It changes neither the historical
+single-intersection search domain nor the selected multiplication bound.
+
+The matrix entry is `C[S,T] = [S == T or popcount(S & T) == j]` over F2.
+Distinct labels make every diagonal entry one. The intersection relation is
+symmetric, so one exact popcount determines both off-diagonal entries.
+Byte buffers store bit `b` at byte `b // 8`, bit `b % 8`; little-endian integer
+conversion preserves the packed-row convention consumed by binary elimination.
+The final partial byte has zero padding. Every matrix entry is retained.
+
+The baseline at commit `66849e1475c930fd7732b1a0067ffee7e1e95f60` builds each
+row by summing shifted arbitrary-precision integers. Profiling all 5,257 cases
+and four committed orbit witnesses took 39.151 seconds, with 30.878 seconds
+inside `minor_rows` (profiling overhead included). This motivated switching
+from the initial feature-construction hypothesis to matrix packing. No rank,
+feature-basis independence, transposition-closure, or input rejection check
+is removed. No persistent cache is introduced.
+
+The contribution is by merramil with substantial OpenAI Codex assistance,
+under Apache-2.0. It builds on Douglas R. Colkitt's preserved historical
+single-intersection audit (`d55bcd62ceb8f322bcf311a5a66e94c3ac7724f0`) and
+retains that audit's mathematical scope and attribution. Assignment seed 86
+selected verification engineering; the three candidates were gather schedules,
+coded-carry controls, and single-intersection replay (86 modulo 3 selects the
+last). The initial open-PR snapshot had 582 entries and no title claiming this
+engine. The only open issue was #650, so the scope was claimed locally.
+
+## Verification contract
+
+Tests compare complete packed rows with the predecessor's directed formula,
+including permutations, negative controls, and byte-boundary sizes. The bounded
+benchmark compares every entry of all four committed orbit Gram matrices
+and the complete audit output. Only the changed implementation's source hash
+may differ from the committed certificate. Existing malformed orbit witnesses
+still fail, including with Python optimization enabled.
+
+The full matrices remain quadratic in space and time. This is an implementation
+speedup for finite verification, not a new construction, rank theorem, expanded
+search, or proof of the conditional multiplication theorem.
+
+## Reproduce and measured result
+
+From the repository root, using standard-library Python 3.11 or newer on
+macOS or Linux:
+
+```sh
+python3 -B research/single-intersection-packing/benchmark.py --rounds 3 --output /tmp/single-intersection-packing.json
+```
+
+Use a fresh output path. Expected final status:
+`PASS_IDENTICAL_GRAM_ROWS_AND_COMPLETE_CERTIFICATES`. Timing is descriptive,
+not a pass threshold. The benchmark imports the preserved, hash-pinned complete
+predecessor module, compares all 100,203,737 Gram entries, then runs three
+alternating baseline/packed pairs in fresh, sequential interpreters. Each
+worker recomputes the complete 5,257-case certificate, including feature-basis
+independence, every adjacent-image closure check, exact Gram ranks, and all
+other controls. Its full serialized output must have the original certificate
+SHA256 after restoring exactly the implementation-source binding. The matrix
+comparison happens outside the timing workers; it does not warm their caches.
+
+[RESULT.json](../../research/single-intersection-packing/RESULT.json) records
+every sample and source pin. On CPython 3.13.1 / macOS arm64, median full-audit
+time was **13.766 to 6.597 seconds (2.087x faster)**. This trades memory for
+speed: median process peak RSS increased from **49,266,688 to 68,845,568 bytes**
+(about 40%). In-place buffer conversion avoids explicitly retaining two full
+matrix lists, but Python allocator behavior still raises observed peak RSS.
+These timings cover this historical finite audit, not supplier cold replay
+or integer multiplication runtime.
+
+Run the focused tests with:
+
+```sh
+python3 -B -m unittest discover -s tests -p 'test_single_intersection*.py' -v
+python3 -B -O -m unittest discover -s tests -p 'test_single_intersection*.py' -v
+```
+
+The 16 tests include changed-source, changed-rank, changed-screen-row,
+changed-other-source-binding, and wrong-matrix-entry rejection controls.
+Only two generated certificate bindings change: `single-intersection.json`
+and `affine-vector-screens.json`. Tests reconstruct and hash each complete
+predecessor certificate after restoring that one binding. No selected-frontier
+artifact or `upstream/` source changes.
+
+The complete `make verify-tests` run passed **557 tests in 86 isolated
+interpreters and 20 patch-application checks**. Both affected certificate
+producers, selected-record integrity, and `git diff --check` passed.
+[VALIDATION.json](../../research/single-intersection-packing/VALIDATION.json)
+records the exact commands and scope. The broad `make verify-research` target
+would regenerate unrelated certificates, so only its two affected producers
+were rerun. Full `make verify`, selected-supplier cold replay, Lean builds, and
+remote Linux CI are outside this local validation.
+
+The final pre-submission overlap refresh covered 594 open PRs through #775;
+none claimed this single-intersection packing change.

research/single-intersection-packing/NOTICE.md

@@ -0,0 +1,22 @@
+# Attribution and scope
+
+Contributor: merramil, with substantial OpenAI Codex assistance. Apache-2.0.
+
+`baseline.py` is an exact, unmodified copy of
+`scripts/experiments/single_intersection.py` at
+`66849e1475c930fd7732b1a0067ffee7e1e95f60`, SHA256
+`08ddae46e5621a5b4c525b504e67ae655abe9b49461d894feaa7abc89a51847d`.
+It was introduced in Douglas R. Colkitt's historical research preservation
+commit `d55bcd62ceb8f322bcf311a5a66e94c3ac7724f0`. The benchmark retains it
+only as a pinned comparison implementation, under the repository's Apache-2.0
+license. All original construction, rank-screen, and orbit-proof credit remains
+with that work and its cited mathematical sources.
+
+The closest concurrent tooling PRs inspected were #707 (Bareiss determinant
+prefixes for selected R420 frames) and #756 (balanced-Fano meet-in-the-middle
+replay). Neither supplies code or a dependency here; this contribution packs
+the historical single-intersection binary Gram matrix.
+
+See [the engineering note](../../docs/research/single-intersection-packing.md)
+for the equivalence argument and verification scope. No new multiplication
+exponent, broader negative result, or full theorem verification is claimed.

research/single-intersection-packing/RESULT.json

@@ -0,0 +1,92 @@
+{
+  "status": "PASS_IDENTICAL_GRAM_ROWS_AND_COMPLETE_CERTIFICATES",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "assignment_seed": 86,
+  "python": "3.13.1 (main, Dec  3 2024, 17:59:52) [Clang 16.0.0 (clang-1600.0.26.4)]",
+  "platform": "macOS-26.5.1-arm64-arm-64bit-Mach-O",
+  "machine": "arm64",
+  "source_pins": {
+    "research/single-intersection-packing/baseline.py": "08ddae46e5621a5b4c525b504e67ae655abe9b49461d894feaa7abc89a51847d",
+    "scripts/experiments/single_intersection_witnesses.json": "c2308a3d21991f5828b0519b191b470f48b2fbbcaa5af0f7aed3986cc7534185",
+    "scripts/audit_single_intersection.py": "1de7f9a62edc93c624ff2693ae9bb725cf6dc9735ff1caad56f6913aae9448ee"
+  },
+  "packed_source_sha256": "6874d41b75590369182ed61e0c6da5b547e035e0e43b50ea2b39e1f3861dca6d",
+  "row_comparisons": [
+    {
+      "h": 20,
+      "k": 6,
+      "j": 2,
+      "rows": 1140,
+      "entries_compared": 1299600,
+      "packed_rows_sha256": "f230204454368c722bb34307e0daf1356126df03208a2531277516b4ad41fb2d"
+    },
+    {
+      "h": 32,
+      "k": 6,
+      "j": 2,
+      "rows": 4960,
+      "entries_compared": 24601600,
+      "packed_rows_sha256": "ee09dd3c8190623f7f0e518a48fc2726ce905fb8eeb24cd0e7bddc692005e0e2"
+    },
+    {
+      "h": 38,
+      "k": 6,
+      "j": 2,
+      "rows": 8436,
+      "entries_compared": 71166096,
+      "packed_rows_sha256": "3a53896a8f14e3384a283e0530865c190e1631d25e2f81f9c9c5ae212d914049"
+    },
+    {
+      "h": 23,
+      "k": 7,
+      "j": 3,
+      "rows": 1771,
+      "entries_compared": 3136441,
+      "packed_rows_sha256": "9b1919d552c6fb54798470ba193a7ebe8a4d4cc2210737667dd77cb495d10957"
+    }
+  ],
+  "samples": [
+    {
+      "engine": "baseline",
+      "audit_seconds": 14.628344791941345,
+      "peak_rss_bytes": 49266688,
+      "certificate_sha256_with_original_source_binding": "59bca430c5cda9050b346f0f89ff980c9e610a30786cd19677911a1eb433d5b8"
+    },
+    {
+      "engine": "packed",
+      "audit_seconds": 6.6083968337625265,
+      "peak_rss_bytes": 66437120,
+      "certificate_sha256_with_original_source_binding": "59bca430c5cda9050b346f0f89ff980c9e610a30786cd19677911a1eb433d5b8"
+    },
+    {
+      "engine": "packed",
+      "audit_seconds": 6.596809957176447,
+      "peak_rss_bytes": 71843840,
+      "certificate_sha256_with_original_source_binding": "59bca430c5cda9050b346f0f89ff980c9e610a30786cd19677911a1eb433d5b8"
+    },
+    {
+      "engine": "baseline",
+      "audit_seconds": 13.502197874709964,
+      "peak_rss_bytes": 48578560,
+      "certificate_sha256_with_original_source_binding": "59bca430c5cda9050b346f0f89ff980c9e610a30786cd19677911a1eb433d5b8"
+    },
+    {
+      "engine": "baseline",
+      "audit_seconds": 13.766040291637182,
+      "peak_rss_bytes": 51019776,
+      "certificate_sha256_with_original_source_binding": "59bca430c5cda9050b346f0f89ff980c9e610a30786cd19677911a1eb433d5b8"
+    },
+    {
+      "engine": "packed",
+      "audit_seconds": 6.383586917072535,
+      "peak_rss_bytes": 68845568,
+      "certificate_sha256_with_original_source_binding": "59bca430c5cda9050b346f0f89ff980c9e610a30786cd19677911a1eb433d5b8"
+    }
+  ],
+  "median_audit_seconds": {
+    "baseline": 13.766040291637182,
+    "packed": 6.596809957176447
+  },
+  "speedup": 2.0867723007029437,
+  "scope": "Four committed orbit witnesses and 5,257 historical cases; no new kappa."
+}

research/single-intersection-packing/VALIDATION.json

@@ -0,0 +1,59 @@
+{
+  "status": "PASS_SCOPED_VERIFICATION",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "assignment_seed": 86,
+  "checks": [
+    {
+      "command": "PYTHONDONTWRITEBYTECODE=1 make verify-tests",
+      "exit_code": 0,
+      "tests": 557,
+      "isolated_modules": 86,
+      "patch_checks": 20,
+      "log_sha256": "77c358c471a9a051ab3af9c228320ecaf19574c1ee90e784803e1baaac028ba2"
+    },
+    {
+      "command": "python3 -B -m unittest discover -s tests -p 'test_single_intersection*.py' -v",
+      "exit_code": 0,
+      "tests": 16
+    },
+    {
+      "command": "python3 -B -O -m unittest discover -s tests -p 'test_single_intersection*.py' -v",
+      "exit_code": 0,
+      "tests": 16
+    },
+    {
+      "command": "python3 -B scripts/audit_single_intersection.py",
+      "exit_code": 0,
+      "cases": 5257
+    },
+    {
+      "command": "python3 -B scripts/audit_affine_vectors.py",
+      "exit_code": 0,
+      "cases": 9
+    },
+    {
+      "command": "python3 -B scripts/verify_selected_result.py",
+      "exit_code": 0
+    },
+    {
+      "command": "python3 -B research/single-intersection-packing/benchmark.py --rounds 3 --output research/single-intersection-packing/RESULT.json",
+      "exit_code": 0,
+      "receipt": "RESULT.json",
+      "entries_compared": 100203737,
+      "fresh_process_samples": 6
+    },
+    {
+      "command": "git diff --check",
+      "exit_code": 0
+    }
+  ],
+  "regenerated_certificates": "Only the single_intersection.py source binding changes in single-intersection.json and affine-vector-screens.json. Tests hash the complete predecessor certificate after restoring that binding.",
+  "not_run": [
+    "Full make verify",
+    "Whole make verify-research target (would regenerate unrelated certificates)",
+    "Selected supplier cold replay",
+    "Lean builds",
+    "Remote Linux CI"
+  ],
+  "scope": "Historical finite verification tooling; no new kappa, mathematical search, or full theorem verification."
+}