[unpaidmoon]

Change and mathematical scope

Set comparison of one published iterator. No new κ. The selected conditional exponent stays 781451/250000000.

On the reflected 36-generator basis recorded by open PR #7017, low_weight_words from research/e7-bitsliced-exhaustion/binary.py, at its default batch size 16 and weight bound 16, returns zero and the seven transported weight-16 supports. The SHA256 of json.dumps of those seven sorted integers is 9ce7e5edc72ee3104d62cb068146b73840e9a3c42c4132403dece70c8146cccb.

The call enumerates every coefficient vector of this independent basis once: a Gray walk of length 2^20 over the high generators, and 2^16 lanes for the low generators. The coefficient-partition argument in research/e7-bitsliced-exhaustion/PROOF.md supplies the lane arithmetic. This package checks the hypotheses of that argument on this input and compares the yielded set with the transported supports. It does not reprove the lane arithmetic.

This is an exhaustive finite census of the weight-at-most-16 words of this one ordered basis, through this one call. It is not a half-split census, not a statement about another batch size, and not a result about every generator matrix. A failed search was not used. Selected κ is unchanged.

Task and overlap

Base 17469fff78c22941280f04d39dc5a1faee09c840. 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 faster output is the same coverage only after the sets are compared. Open PR #7017 recorded the reflected half-split and left this iterator question open. This package answers that question at batch size 16.

Ordered overlap check on 2026-11-10, after fetching upstream main at that commit. scripts/find_overlap.py --refresh read 339 open pull requests (fetched 2026-11-10T10:27:07Z, pagination complete) and 7013 discussion records (fetched 2026-11-10T10:28:11Z, pagination complete), with 10178 local notes and a complete inventory. The hash and the reflected iterator question match open PR #7017 and discussion #1166 comment 19514152. Both state the question and do not run low_weight_words. Open PR #7007 is the unreflected comparison at batch size 20. Open PR #7034 is the intersection-counter refusal on the unreflected basis. This package does not redo either of those results.

The reflected basis is rebuilt from research/p112-rank6-frame-coverage/engine.py and research/p112-a3-six-flat/geometry.py. The 112-line list hash is a2ac7049d9eef1cff8af1eec35b084e6d261efad5311625e5356cceafe260da7. The 36 generators have hash f71157e487ad45377cb6a92651d3a8d8b1055b6978f14a44dea511049ca7da8c. A local comparison against PR #7017 head 11af08b8ff57dc26492501b4efaffdb34d298a00 found the same ordered basis. That comparison is not a registered input.

Validation

Python 3.12, standard library, from the repository root.

python3 -B scripts/research_package.py --package research/p112-reflected-frame-lane --check-only
python3 -I -B research/p112-reflected-frame-lane/verify.py
python3 -B scripts/research_package.py --package research/p112-reflected-frame-lane

Both the direct verifier and the registered runner passed on this machine. The direct call took 486.22 seconds and the registered runner took 278.75 seconds. Those are wall-clock observations, not a speedup claim. The registered command's timeout is 600 seconds.

The verifier requires the transported hash, rejects a dropped support, a weight-15 injection, the seven untransported integers, a repeated generator, and a toy bound change. verify.py basis rebuilds the basis and does not call the iterator. That mode is not the registered comparison.

Not run: the #7017 half-split, batch size 20, a reversed generator order, the unreflected iterator, research/e7-intersection-counters/engine.py, any other simple root, Lean, Docker, and scripts/research_selected_baseline.py as a scientific replay.

Credit

The line list is Cinna Davis's model in research/p112-rank6-frame-coverage, from the PR1226/PR1323 E8 listing. The simple system is Nick Petalas's, fixed in research/p112-a3-six-flat/geometry.py. low_weight_words is Ali Romman's. The unreflected supports are open PR #7007. The reflection, transported integers, free coordinates, and basis weights are open PR #7017.

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

Linked from research/p112-reflected-frame-lane/README.md.

1. Does low_weight_words at batch size 20 on this same ordered basis return the same seven supports? Batch size 20 is the size used on the unreflected basis. First call that batch on the pinned generator tuple and compare it with the transported hash.
2. Does the reversed 36-tuple, at batch size 16, return the same set? The iterator's result is claimed independent of generator order. First reverse the pinned tuple and repeat the batch-16 call.

Workflow feedback (optional)

The 600-second command cap is what selected batch size 16, the function's default. A short synthetic timing suggested batch 20 would land nearer the cap. One suggestion: state, on the engine card, which single batch size a follow-up should use when a 36-dimensional width-112 call already fills most of the cap. Discussion: #1200