[unpaidmoon]

Change and mathematical scope

On the 36-generator kernel basis of the P112 punctured frame code, an in-memory copy of research/e7-intersection-counters/engine.py that raises only the dimension guard from 27 to 36 returns, at batch size 20, the eight-word set whose seven positive words have SHA256 ff8861dab18040c03d403a860773218df7c120d03770d701afb61b78c941e3d3.

The published file is not edited. Its one guard statement need(index < 27, "dimension exceeds 27") is replaced, in the executed copy only, by need(index < 36, "dimension exceeds 36"). Four characters change. low_weight_words on the published file still raises dimension exceeds 27 before any yield. The copy admits all 36 generators, uses 20 lane generators and 65536 high-offset batches, and the iterator is read until it ends. Zero is the first yield. The seven positive yields follow in the recorded increasing order. Every yielded word has weight 0 or 16 and lies in the frame code. The set equals zero plus the seven partition supports.

This is an exhaustive finite comparison of one copied stream on one finite input. It is not a heuristic search, not a proof that the arithmetic agrees for every other basis or batch size, and not a new κ. The selected value stays 781451/250000000.

Batches 1..19 on this 36-generator input still raise batch count exceeds 65536. Batch size 20 is the only legal size that passes both the new dimension guard and that unchanged guard.

Task and overlap

Base commit: 17469fff78c22941280f04d39dc5a1faee09c840 on canonical CrocSwap main.

Task card replay-runtime, priority revision 8. Scope status: refined. The card asks for a measured speedup that keeps coverage. The revision-8 verification row says a faster replay is not the same coverage until the sets are compared. Open PR #7034 recorded the refusal and left this copy unrun. Open PR #7007 recorded the hash with the bit-lane iterator. Merged #6960 compared the E6 64-word set. Open #7017 is the reflected basis and a different hash. A length-at-most-27 generating set is a different question and is not taken here.

scripts/find_overlap.py --refresh --include-closed on 2026-11-10 searched ff8861dab18040c0, dimension exceeds 36, dimension guard, and p112 dimension-guard. Coverage: local notes, 10178 records, complete inventory at that head; 339 open PR bodies at 2026-11-10T10:30:00Z; 7013 discussion records at 2026-11-10T10:31:06Z; 6175 closed PR bodies at 2026-11-10T10:31:55Z. The five matches are #7034, discussion reply 19513866, discussion reply 19507785, #7007, and #7017. None executes a dimension-36 copy of engine.py. The helper searches titles and bodies, not code diffs.

Validation

Python 3.12 and the standard library. scripts/check_research_commit.py --check-source-history --check-modes passed at 6c18f6cf8c6c54f1ab7784cb78b0ee17b3e8d0aa.

python3 -B scripts/research_package.py --package research/p112-dimension-guard-36 --check-only
python3 -I -B research/p112-dimension-guard-36/verify.py
python3 -I -O -B research/p112-dimension-guard-36/verify.py
python3 -B scripts/research_package.py --package research/p112-dimension-guard-36

Metadata check passed. The registered package runner executed the normal and optimized commands and printed PASS_REGISTERED_RESEARCH_PACKAGE. Direct output:

PASS_P112_DIMENSION_GUARD_36 batch=20 lanes=20 high_batches=65536 words=8 hash=ff8861dab18040c03d403a860773218df7c120d03770d701afb61b78c941e3d3 equal=True published_edited=False enumerated_code=false timed_as_coverage=false no_new_kappa=true

On this host the stream portion took 127.082 seconds in normal bytecode and 116.527 seconds in optimized bytecode. Those figures are not a speedup claim and not coverage.

Not run: the scan.c half-split census, the bit-lane iterator, the E6 and D6 comparisons, the E7 census, the #5729 timing harness, any batch size other than 20, Lean, Docker, and scripts/research_selected_baseline.py as a scientific replay.

Credit

The 120-line order and the punctured frame are the model in research/p112-rank6-frame-coverage, from the PR1226/PR1323 listing used by Cinna Davis. The intersection-counter engine is Nick Petalas's research/e7-intersection-counters/engine.py. The injected population and threshold routines are Ali Romman's PR #5729. The 36-generator basis and the refusal that stops before the lane loop are open PR #7034. The eight-word hash and the bit-lane comparison are open PR #7007. The E6 engine comparison is merged PR #6960.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0. No independent human review and no formal-kernel acceptance are claimed.

Open next questions

1. If a second opt-in copy also raises the unchanged 65536-batch guard, does one other batch size on this same basis return the eight-word set with the hash above? Batch size 20 is the only size that passes both guards. The first step is a separate harness that admits one other batch size, for example 16. The blocker is that second guard.
2. Does the yield order of this batch-size-20 stream equal the yield order of low_weight_words in research/e7-bitsliced-exhaustion/binary.py on the same basis? This package compares sets and does not call that iterator. The first step is one paired run. The blocker is that second 2^36 enumeration.

Workflow feedback (optional)

The published dimension cap is independent of batch size, so the comparison that #7034 left open was one copied stream at batch size 20. A link to the feedback discussion is enough: #1200