Mister-Meeseeks · Oct 16, 2026 · Oct 16, 2026
diff --git a/research/four-flat-maximal-masks/README.md b/research/four-flat-maximal-masks/README.md
@@ -0,0 +1,158 @@
+# Exact maximal-mask setup for the four-flat decoder checker
+
+**Tooling improvement with a scoped equivalence proof.** The four-flat search
+constructs, for each active direction and first flat, the inclusion-maximal
+masks `Off(h) \ X1` intersected with candidate 7-flats. Its original setup tests
+every candidate against every other candidate. This adapter uses cardinality
+buckets and compares only against already retained, strictly larger maxima.
+It restores the original ascending mask order before the search resumes.
+
+This answers a separate setup bottleneck in
+[Discussion2954](https://github.com/CrocSwap/integer-mult-bounds/discussions/2954#discussioncomment-18977655).
+It composes with PR2975's faster requirement enumeration. Both benchmark builds
+use that same predecessor option generator; the only mathematical computation
+changed here is maximal-mask filtering. No new pruning of pairs or directions,
+new decoder exclusion, supplier, or kappa is claimed.
+
+## Result and evidence
+
+| Same-input workload | Reference | Accelerated | Speedup |
+| --- | ---: | ---: | ---: |
+| Maximal-mask filtering, both representatives | 104.85 s | 11.26 s | 9.31x |
+| Complete per-representative setup | 107.28 s | 13.55 s | 7.92x |
+| Full bounded run, shared catalogue/orbits included | 156.74 s | 61.42 s | 2.55x |
+
+Final registered Python 3.12 replay passes. The earlier complete serial trial
+measured 9.14x filtering and 2.58x total speedup, with identical exact outputs.
+
+See [RESULT.json](RESULT.json) for the serial same-input measurements and exact
+receipt hashes. The benchmark runs complete setup for representatives **46 and
+94** of the source's `a=4,b=6,c=4,d=5` configuration, and the predecessor's fixed
+12 pairs for representative 46. The second representative is selected by OS
+assignment seed 94. An additional `a=b=6,c=4,d=0` case preserves the known relaxed
+span-five witness at representative 82, V2 index 103676.
+
+The comparisons cover every active-direction index, residual mask, cap, maximal
+mask and its order, all eleven downstream requirement records, the complete output/histogram
+reporting 5,509 closure leaves, and the positive witness.
+Temporary binary setup records contain the complete arrays, not a sampled
+checksum. The verifier compares their bytes; only compact hashes/counts are
+committed. The timings measure this verifier on the recorded host, not integer
+multiplication or the entire class-C campaign. Benchmark wall time includes
+setup-state serialization and requirement exports, excludes compilation and
+additional controls. Filter/setup phase times use process CPU time and exclude
+setup-state serialization. A speed threshold is deliberately not a correctness
+predicate.
+
+Independent explicit-set controls cover all **65,536** families of subsets of a
+four-point universe, 2,000 deterministic wide-mask families, and 128 cases covering
+every bit position. Six implementation mutants must fail, including wrong bucket
+order, reversed containment, omitted high bits and lost canonical order. The
+same cases run under undefined-behavior/bounds sanitizer traps. Source-byte and
+missing/ambiguous adapter controls fail closed. This is a representation-level
+argument and finite replay, not a second independent proof of the outer decoder
+search or a formal multiplication theorem.
+
+## Reproduce
+
+From a checkout containing the seven declared predecessor files:
+
+```sh
+python3 -I -B research/four-flat-maximal-masks/verify.py --work /tmp/four-flat-masks
+```
+
+Use a fresh output directory, Python 3.12+ and a `cc` supporting GNU C11,
+unsigned 128-bit integers, `-fsanitize=undefined,bounds` and
+`-fsanitize-undefined-trap-on-error`. No Python third-party dependencies, network,
+Git metadata or cached scientific results are needed by this command.
+Expected: `PASS_MAXIMAL_MASK_CONTROLS` and `PASS_MAXIMAL_MASK_FULL`.
+`--controls-only` and `--full-only` select the separately bounded obligations.
+The registered command is:
+
+```sh
+python3.12 scripts/research_package.py --package research/four-flat-maximal-masks
+```
+
+Both builds authenticate all external inputs by SHA256. Source adapter anchors
+must occur exactly once. Source files and the inherited circuit/checker remain
+unchanged; generated C, executables and large records live only in the work
+directory. `SOURCES.json` pins the baseline main commit, exact predecessor and
+all live bytes; `VERIFY.json` declares those inputs for CI selection.
+
+## Equivalence proof
+
+Let `F` be a finite collection of **distinct** bit masks, ordered by set
+inclusion. The frozen source sorts and deduplicates `tmp` immediately before
+the replaced block. Its output is the ascending list
+
+`Max(F) = {x in F : there is no y != x in F with x subset y}`.
+
+Process masks in descending cardinality, with an arbitrary order within each
+bucket. Maintain the retained maxima of the already processed, larger buckets.
+For a candidate `x`, any proper superset has strictly larger cardinality and has
+already been processed. If such a superset was discarded, it was contained in
+an earlier retained mask. By transitivity that retained mask also contains `x`.
+Consequently `x` is nonmaximal if and only if a retained larger mask contains it.
+Distinct masks of equal cardinality cannot contain one another, so comparisons
+within a bucket are unnecessary. No future smaller mask can invalidate an
+accepted maximum. This proves the invariant and exact maximal-set equality by
+induction over the buckets. Empty input returns the empty list; the zero mask
+is handled by the same argument. Sorting the retained masks with the original
+integer comparator gives the **same ordered array** as the predecessor.
+
+The C implementation uses all 128 bits for cardinality and containment. Bucket
+indices lie in 0..128, their sizes sum to the input count, and the permutation
+contains each input index exactly once. At the start of a bucket, `larger` fixes
+the count of earlier maxima; newly appended equal-size masks are intentionally
+not tested. Input and output buffers are distinct and each holds at least the
+input count, as provided by the original `tmp`/`mx` allocation. Additional space
+is one integer index per input mask and three 129-element arrays. Worst-case
+containment work remains quadratic; the claim is the measured reduction on the
+named workload, not a universal subquadratic bound.
+
+Every other setup calculation is unchanged. Thus identical `mx` implies
+identical `LG`, `LGn`, `capr`, `act` and `R1` for each direction. The unchanged
+outer search receives exactly the same arrays and order; its branch sequence,
+requirements, closure and reports are preserved, conditional on the inherited
+implementation. Source authentication and exact-once replacement prevent silently
+applying this argument to an unrelated future source version.
+
+## Scope, provenance and credit
+
+Scientific base: `b3f3ee0392b71b118fd086a6eaf6b4cab54ef455` (priority revision 5).
+Submission refresh: `836b19bfa309ceafbc8ee32a15e8c4b10dde7e11` (revision 6).
+The revised guidance, family record and priority log were read; the replay-runtime
+card, selected record and all runtime inputs are unchanged. This is bounded
+replay acceleration, not a larger static-cover census.
+Predecessor PR2975: `1d7b491c9efad451d49dbfd36a3be7443999bf17`.
+Original DreamingOfClouds help package:
+`1b25759bff5486293a9083ebbe0097b5f6642e08`, `research/k2-class-c-help`.
+The selected maintainer-reviewed conditional kappa remains
+`0.001672660197076918`; merged archive status does not certify newer claims.
+
+Credit **DreamingOfClouds** for the four-flat engine, original maximal-mask
+construction, help request and #2816/#2826/#2862 lineage, and Tekalign's PR2975 for
+the separately retained requirement-enumeration improvement. PR2985's newer
+residue-closure work is complementary; its claims are not prerequisites of this
+filter equivalence. Prepared by **Tekalign (@tekuuu)** with substantial **OpenAI
+Codex assistance** in analysis, implementation, checking and writing.
+Apache-2.0, as the repository and predecessors. No independent human review is
+claimed.
+
+The direction catalogue, group/orbit reduction, real-rank arithmetic, RRC,
+complete decoder floor, native/supplier admission and all-size multiplication
+interfaces remain inherited or unresolved. This package does not audit or
+silently accept those obligations. The seeded finite fixtures are performance
+measurements, not a new impossibility theorem. It does not launch a larger
+construction/search campaign or alter the selected frontier.
+
+## Open next questions
+
+- A stronger common-flat gate or exact orbit reduction is still needed before
+  the full campaign is affordable. First profile the transformed search, then
+  prove any proposed reduction cannot discard a possible span witness.
+- Measure other representatives/configurations with the same complete setup
+  comparison. The present timing evidence covers only the named inputs and host.
+
+Structured questions, stopping rule and the three candidate tasks considered
+are retained in [TASK.json](TASK.json).
diff --git a/research/four-flat-maximal-masks/RESULT.json b/research/four-flat-maximal-masks/RESULT.json
@@ -0,0 +1,126 @@
+{
+  "status": "PASS_FOUR_FLAT_MAXIMAL_MASKS",
+  "registered_python": "3.12.14 (main, Sep  1 2026, 14:16:52) [Clang 22.1.3 ]",
+  "platform": "Linux-7.2.8-200.fc44.x86_64-x86_64-with-glibc2.43",
+  "compiler": "cc (GCC) 16.2.1 20260819 (Red Hat 16.2.1-2)",
+  "controls": {
+    "status": "PASS_MAXIMAL_MASK_CONTROLS",
+    "explicit_set_cases": 67664,
+    "all_four_point_families": 65536,
+    "seeded_wide_families": 2000,
+    "all_bit_position_cases": 128,
+    "oracle_sha256": "eb9522da30e3696e33249b9cd9ba8f363538149ad65e1eb1bf44e24a71887280",
+    "implementation_mutants": [
+      "reverse_bucket_order",
+      "skip_larger_masks",
+      "reverse_containment",
+      "discard_high_word",
+      "drop_last_maximum",
+      "omit_canonical_order"
+    ],
+    "invalid_inputs_rejected": 6,
+    "adapter_anchor_controls": 2,
+    "source_byte_control": "PASS",
+    "setup_export_controls": 6
+  },
+  "full": {
+    "status": "PASS_MAXIMAL_MASK_FULL",
+    "benchmark": {
+      "reference": {
+        "wall_seconds": 156.7442173870004,
+        "representatives": [
+          {
+            "rep": 46,
+            "calls": 1332,
+            "input_masks": 2206610,
+            "maximal_masks": 1191638,
+            "filter_cpu_seconds": 52.570777,
+            "setup_cpu_seconds": 53.788808
+          },
+          {
+            "rep": 94,
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+            "input_masks": 2200160,
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+            "filter_cpu_seconds": 52.275135,
+            "setup_cpu_seconds": 53.486273
+          }
+        ]
+      },
+      "accelerated": {
+        "wall_seconds": 61.422050555998794,
+        "representatives": [
+          {
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+        ]
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+    "filter_speedup": 9.313900087670447,
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+    "wall_speedup": 2.5519209464375647,
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+    "positive_setup_sha256": "cae33d73c21527f325275578e3606520d7b29866fd9accfb2c69e89143a5eda3",
+    "pairs": 12,
+    "closure_leaves": 5509,
+    "positive_span_five": "PASS",
+    "generated_c_sha256": {
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+  },
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+    "accelerated_wall_seconds": 58.26836285900026,
+    "filter_speedup": 9.139422924950882,
+    "wall_speedup": 2.579534700343525,
+    "note": "Same final C filter; preliminary Python3.14 harness, before extra export-parser controls."
+  },
+  "portability": {
+    "status": "PASS",
+    "mode": "read-only Git-free source export, optimized (-OO) interpreter",
+    "python": "3.14.7 (main, Aug 10 2026, 00:00:00) [GCC 16.1.1 20260515 (Red Hat 16.1.1-2)]",
+    "controls_equal": true
+  }
+}
diff --git a/research/four-flat-maximal-masks/SOURCES.json b/research/four-flat-maximal-masks/SOURCES.json
@@ -0,0 +1,112 @@
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