Tooling: accelerate exact seven-owner Fano replay with row tables

research/fano-census-row-tables/BENCHMARK-python312.json

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+{
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+  "python": "3.12.14 (main, Aug 25 2026, 14:00:49) [Clang 22.1.3 ]",
+  "platform": "Linux-6.18.55-x86_64-with-glibc2.41",
+  "rss_units": "KiB (Linux)",
+  "code_sha256": {
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+    "kernel.py": "decc8e6a4331ffd28460056d49f06758c6fad721e0638ade90a7ee723c367458",
+    "benchmark.py": "c98692c2654e324ada4743c07a60b626f1880edd5f5b4fc23c7f37ffb773b127",
+    "SOURCES.json": "65130499f62653607112223322272030e57d7900dc1211944b94c8657e6a3963"
+  },
+  "scope": "Whole PR3168 check, pins, route derivation, full census, Fano searches and controls; fresh processes, warm filesystem caches; no full supplier replay."
+}

research/fano-census-row-tables/BENCHMARK-python313.json

@@ -0,0 +1,70 @@
+{
+  "status": "PASS_IDENTICAL_COMPLETE_FANO_BENCHMARK",
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+  "samples": [
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+  "platform": "Linux-6.18.55-x86_64-with-glibc2.41",
+  "rss_units": "KiB (Linux)",
+  "code_sha256": {
+    "adapter.py": "039399a24b16930a0a7a3c92a5034c2efbe64a0cf52e7bd063ba837d4d605449",
+    "kernel.py": "decc8e6a4331ffd28460056d49f06758c6fad721e0638ade90a7ee723c367458",
+    "benchmark.py": "c98692c2654e324ada4743c07a60b626f1880edd5f5b4fc23c7f37ffb773b127",
+    "SOURCES.json": "65130499f62653607112223322272030e57d7900dc1211944b94c8657e6a3963"
+  },
+  "scope": "Whole PR3168 check, pins, route derivation, full census, Fano searches and controls; fresh processes, warm filesystem caches; no full supplier replay."
+}

research/fano-census-row-tables/CLAIM.json

@@ -0,0 +1,56 @@
+{
+  "assignment_seed": 91,
+  "random_source": "secrets.randbelow(100), operating-system randomness",
+  "track": "verification engineering",
+  "base_commit": "463113d675af7410ac91d53a4fed51ec6494eb9a",
+  "claim_time_utc": "2026-10-17T17:49:00Z",
+  "expected_finish_utc": "2026-10-17T18:43:00Z",
+  "object": "PR3168 exact 17-coordinate reduced-triple route census; all 1,379,952 triples",
+  "hypothesis": "Per-invocation tables for exact GF(2) row actions reduce repeated matrix multiplication without changing any product key, relation or full Fano receipt.",
+  "method": "Precompute actual two-factor rows and exact right actions, retain full triple enumeration, exact packed-int equality and all original downstream controls.",
+  "deliverable": "Opt-in pinned adapter, equivalence argument, differential controls and alternating complete-check benchmarks.",
+  "stopping_rule": "Stop if full receipt or semantic controls differ, or complete-check runtime does not improve. No length-eight census or theorem extension.",
+  "candidates": [
+    {
+      "task": "PR626 interval kernels",
+      "decision": "Rejected: matching logarithm/exp contributions #667/#672 already retained."
+    },
+    {
+      "task": "Owner footprint representation",
+      "decision": "Rejected: #727 and owner-footprint-crosscheck plus t37-slice-bitmaps cover this mechanism."
+    },
+    {
+      "task": "PR3168 reduced-triple row products",
+      "decision": "Selected: bounded costly exact workload; no matching acceleration surfaced."
+    }
+  ],
+  "diversification": "Seed 91 fixes candidate-test matrix stream and alternating benchmark first arm; object chosen after semantic overlap checks, not on seed alone.",
+  "coordination": "No pinned sprint issue (GitHub pinnedIssues empty). Local claim under user step 3. No Discussion mutation requested.",
+  "overlap": {
+    "open_pr_records": 253,
+    "discussion_records": 2017,
+    "complete_pagination": true,
+    "snapshot_utc": "2026-10-17T17:47:55.995857+00:00",
+    "queries": [
+      "centre-seven-owner-fano-independent",
+      "relation_census",
+      "route product",
+      "matrix census",
+      "route census",
+      "reduced-triple",
+      "bytes.translate",
+      "permutation composition"
+    ],
+    "predecessors": [
+      "#3097 centre-seven-owner-information-floor",
+      "#3168 centre-seven-owner-fano-independent",
+      "#3147 larger block floor (open; no extension attempted)"
+    ]
+  },
+  "result": {
+    "status": "completed locally; publication pending",
+    "useful_result": "Exact row tables speed the unchanged complete PR3168 verifier by 2.68x (Python 3.12) and 2.77x (3.13), preserving all triple keys and the full receipt.",
+    "evidence": "VALIDATION.json; BENCHMARK-python312.json; BENCHMARK-python313.json",
+    "remaining": "Maintainer review, other-host performance; no new theorem, supplier or kappa."
+  }
+}

research/fano-census-row-tables/PROOF.md

@@ -0,0 +1,61 @@
+# Equality of row-table and direct matrix products
+
+Fix a dimension d and binary row matrices A, B and C. Encode a row r by
+its nonnegative integer with bit j equal to coordinate j. The direct
+reference product computes row i of AB as the XOR of rows B[j] for each
+set bit j in A[i]. `row_action` computes that same expression: each loop
+iteration removes exactly the least significant set bit, and XORs its
+corresponding matrix row. The loop terminates after popcount(r) iterations.
+
+`prepare` computes AB for every ordered pair of distinct route indices.
+It collects every row of those products in a finite sorted domain D.
+For each right factor C and each row r in D it stores row_action(r,C).
+Each reversed row list of AB is replaced by its indices in D. Thus every
+lookup made by a reduced triple (a,b,c) is defined and equals the
+corresponding row of (AB)C. No involution, route uniqueness, sparsity,
+or expectation about the eventual relation histogram is used here.
+
+Every output row is less than 2^d, since XOR preserves that range. Starting
+with zero and appending the rows in reverse order by
+`key = (key << d) | row` is exactly the reference encoding
+sum(row[i] * 2^(d*i)). This encoding is injective on d-by-d binary
+matrices. It has no truncated fingerprint or probabilistic equality test.
+The unsigned integer array stores individual rows; the product key is an
+arbitrary-precision Python integer, so its 289 bits are retained for d=17.
+
+The domain a!=b and b!=c is unchanged. Each triple is inserted once, in the
+same order as in the original census. Dictionary class membership therefore
+agrees exactly. The class histogram, extraction of all pairs of distinct
+words, reversal of the second triple and cyclic-reduction test are unchanged.
+The returned total, histogram and relation-word set are consequently equal.
+This includes duplicate matrices and classes of size greater than two.
+
+Tables are created inside each census and discarded afterwards. No successful
+validation is cached between invocations. The adapter checks all live source
+pins before loading the predecessor from authenticated source bytes. It then
+replaces only that new module's `relation_census` function. Original route
+derivation, active/spectator checks, pair uniqueness, relation multiplication,
+symmetry, all Fano incidence and labelling searches, and the planted/missing
+relation controls run unchanged. The entire canonical receipt must equal the
+pinned predecessor receipt byte for byte. Default predecessor commands and
+all frozen source bytes are unchanged.
+
+This is an algebraic equivalence argument for an implementation change,
+supported by finite differential checks. It is not a proof-assistant theorem
+or a formal proof of the multiplication bound. The original observation,
+faithful representation and support-bound hypotheses remain inherited.
+
+## Work and storage
+
+For n routes, d rows and U distinct rows of the n(n-1) two-factor products,
+preparation costs O(n^2 d^2 + n U d) bit-selection steps and O(n^2 d + n U)
+stored row indices/actions. Product-key formation then uses d exact row
+lookups per triple, instead of up to d^2 bit-selection steps plus packing.
+The same n(n-1)^2 triples and all equality classes remain resident.
+
+For the actual input n=112, d=17 and U=18,388. The 2,059,456 table values
+occupy 8,237,824 payload bytes on the measured four-byte unsigned-int array
+implementation. Pair/domain dictionaries and the unchanged class dictionary
+add overhead. Peak process memory is measured separately; the payload count
+alone is not a whole-process memory claim. The method does not make an
+unbounded larger-word census feasible and adds no length-eight coverage.

research/fano-census-row-tables/README.md

@@ -0,0 +1,115 @@
+# Exact row tables for the seven-owner Fano census
+
+**Verification tooling; no new bound, supplier or κ.** An opt-in adapter
+accelerates Sudarsh Chaturvedi's PR3168 independent seven-owner verifier. It
+replaces repeated binary matrix multiplication by exact per-invocation row
+actions. Every one of the 1,379,952 reduced triples remains enumerated, with
+full 289-bit product keys and the same complete canonical receipt.
+
+On this Linux host, three alternating fresh-process pairs under CPython
+3.12.14 measured a median **21.44 → 8.00 seconds (2.68×)** for the complete
+check. The scope includes input/source hashing, chart-swap route derivation,
+the entire census, Fano incidence and labelling searches, and original
+positive/negative controls. CPython 3.13.5 measured **20.72 → 7.48 seconds (2.77×)** in three further
+alternating pairs. Raw samples and process memory are retained in
+[BENCHMARK-python312.json](BENCHMARK-python312.json) and
+[BENCHMARK-python313.json](BENCHMARK-python313.json). Timing is descriptive,
+with no pass threshold. Filesystem caches were warm; the host was shared.
+
+## Reproduce
+
+From the repository root, Python 3.12+ and standard library only:
+
+```sh
+python3 -I -B research/fano-census-row-tables/verify.py
+```
+
+Expected: `PASS_ALL_EXACT_TRIPLE_KEYS 1379952 rows 18388`, then
+`PASS_FANO_ROW_TABLES e33a4809ad6ec2025aa46ecb5b2f9d790295379d4794bd911e0b67cf7e6aa652`.
+This command compares **every actual product key** against the original
+exact multiply/pack functions, then runs the complete table-backed check.
+It checks the full committed PR3168 receipt byte for byte.
+
+```sh
+python3 -I -B -m unittest discover -s research/fano-census-row-tables -p 'test_*.py' -v
+python3 -I -B research/fano-census-row-tables/benchmark.py --pairs 3 --out /tmp/new-fano-benchmark.json
+python3 scripts/research_package.py --package research/fano-census-row-tables
+```
+
+Expected: seven test groups; `PASS_IDENTICAL_COMPLETE_FANO_BENCHMARK`; and
+successful registered replay. Use a fresh benchmark/output path. The benchmark
+runs both complete engines in separate processes, alternating their order,
+and checks every receipt. `adapter.py --engine reference` selects the original
+engine; the default is `tables`. No existing command is changed.
+
+## Exactness, controls and limits
+
+[PROOF.md](PROOF.md) gives the row-action and injective packing argument.
+The 12,432 ordered pairs reach 18,388 distinct rows. Tables store the exact
+right action of each of the 112 routes on those rows. No intermediate row,
+triple, equality class or relation is sampled or omitted. No successful
+validation is cached across invocations. The existing pair uniqueness,
+spectator block, involution, symmetry and relation-identity checks all remain.
+
+The complete result retains histogram `{1: 1379852, 2: 50}`, all 100 relation
+words (50 braid edges), 30 labelled Fano planes, all 28 six-cycle constraints,
+zero valid Fano labellings and the original planted/missing-relation controls.
+Additional tests use a separate parity-of-dot-products oracle, exhaustive
+small row domains, seed-91 dense 17-coordinate matrices, noncommuting factors,
+duplicate/zero matrices and classes larger than two. Four corrupted kernels
+are detected: lost high bit, reversed row order, wrong packing stride and a
+wrong table entry. Same-size/same-mtime source mutation is rejected after
+prior success; restoration works; missing sources and output reuse fail.
+Tests also run with optimized Python.
+
+This is an implementation-equivalence contribution, not another independent
+mathematical verification of the support-seven theorem. It inherits the
+original observation model, faithful cover-group representation and earlier
+support bound. It does not add support-eight or length-eight coverage,
+physical acquisition/restoration accounting, supplier admission or a new κ.
+The full selected cold replay, `make verify`, Lean and hosted CI were not run
+for this isolated opt-in stage. All-size/compiler, realization, hosting,
+precision/tape and analytic assumptions remain.
+
+## Sources and coordination
+
+Exact base: `463113d675af7410ac91d53a4fed51ec6494eb9a`.
+[SOURCES.json](SOURCES.json) records live input SHA-256 and Git blob pins.
+The source archive remains immutable and its member hashes are still checked
+by the original chart-swap derivation. The selected context at this base is
+PR1094, conditional κ = `836330098538459/500000000000000000`, with PR589/555
+bit ancestry; the selected-source inventory is unchanged.
+
+OS assignment seed **91** selected verification engineering. Three narrow
+candidates, method, stopping rule and the local claim are in [CLAIM.json](CLAIM.json).
+No pinned sprint coordination issue existed. Overlap checks covered 253 open
+PRs and 2,017 Discussion records with complete pagination, plus local package
+notes. PR3147's larger-block question is distinct and is not investigated here.
+The ledger classifies #3097 and #3168 as partially reviewed archival intake;
+this tool does not promote their theorem status. PR3168 source head is
+`b8844f08d8832eb87f8a5725f50d9c5eaac953d8`; PR3097 source head is
+`ef7a52f4b0acf7cc8c51f9d81274d106abeffa24`. A finite replay is not a formal
+proof of the multiplication theorem.
+
+## Open next questions
+
+Should this become the PR3168 default after review? A feasible next step is
+to review the exact row/packing argument and reproduce the all-product
+comparison and complete benchmark on another host. Maintainer review is the
+remaining adoption step. No extension of the research family is proposed.
+
+## Credit and license
+
+Sudarsh Chaturvedi (`Sudarsh3301`), with Claude assistance, supplied PR3168's
+independent census, Fano searches and controls. Gonzalo Mier (`Gonzalo-Mier`) supplied PR3097's support-seven claim and first
+census, prepared with OpenAI Codex assistance. The chart-swap derivation
+and earlier block-repair result retain Ross Richardson and Aaron Wang/navinor
+(PR2391) credit; ywz65 supplied the selected centre observation interface.
+Rohan Arun, Jeremy Kothe, Hao Yan and the cumulative PR1094/589/555 supplier
+lineage retain their original attribution. Douglas Colkitt supplied the
+source-bound review and research-package infrastructure.
+
+This adapter, table engine, differential tests and benchmark were prepared by
+**Charan**, with substantial **OpenAI Codex assistance** in design, code,
+explanation, tests and handoff. No delegated or independent human review was
+used. Apache-2.0. Frozen predecessor sources and notices remain unchanged.