[unpaidmoon]

Change and mathematical scope

On the 112 lines left by one simple reflection of the pinned P112 puncture, one half-split returns exactly the transported images of the seven weight-16 supports recorded in #7007. The reflected frame is a different orthogonal 8-frame. The code is again 36-dimensional, the least positive weight is 16, and those seven words are the whole weight-at-most-16 set.

This is an exhaustive finite census of one reflected code, and a set comparison. It is not a timing claim, not a consumer installation, and no new κ is claimed. The selected value stays 781451/250000000.

The reflection is the first pair, in the pinned E8 simple-system order and then the punctured-line order, that moves a line. Simple root α = (1, -1, -1, -1, -1, -1, -1, 1) sends punctured line (2, -2, 0, 0, 0, 0, 0, 0) to (1, -1, 1, 1, 1, 1, 1, -1). The same reflection fixes four punctured lines and moves four. The rebuilt complement, in increasing line index, has SHA256 a2ac7049d9eef1cff8af1eec35b084e6d261efad5311625e5356cceafe260da7.

The transported supports, in the recorded order, are

12726038110963558112484457976320
61084916320812443394843581087904
2433889152476423258413102440464394
6363012028601310481939177671680
954453281446482856702353473856
580303949270928947429810196
2677278706012631304342476888735745

Their SHA256, of json.dumps of that sorted list, is 9ce7e5edc72ee3104d62cb068146b73840e9a3c42c4132403dece70c8146cccb.

The seven untransported integers fail a frame parity of this new code. The half-split visits all 2^36 kernel words. Its weight distribution equals the distribution recorded for the unreflected frame. That is a comparison of enumerators from two different bases, not a replay of the unreflected census.

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 published faster replay is not equivalent coverage until checked. Open #7007 recorded the unreflected P112 equality and left this reflection as its first open question. This package answers that question for one pair. It does not rerun the unreflected census, the D6 equality of #6959, or the E6 equality of #6948, and it does not run the intersection-counter comparison.

scripts/find_overlap.py --refresh on 2026-11-10 read 317 open pull requests (fetched 2026-11-10T08:51:47Z, pagination complete) and 10180 local notes at this base, with a complete local inventory. The only match was #7007, which poses the question and does not build the reflected frame. The discussion refresh returned HTTP 504 and left no usable discussion snapshot. A search for the recorded support hash found that same pull request and no second item.

Validation

Python 3.12, gcc, and the standard library. The registered command measured about 73 seconds here, including a 70-second half-split on 4 cores.

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

check_research_commit.py --check-modes passed at 11af08b8ff57dc26492501b4efaffdb34d298a00. --check-source-history was not run: this checkout is shallow.

The registered replay printed

PASS_P112_REFLECTED_FRAME_CODE width=112 frames=1260 dimension=36 minimum=16 supports=7 codewords=68719476736 split=18 simple=0 punctured=1 moved_lines=4 same_frame=false unreflected_census=false engine=false no_new_kappa=true

Not run: a second split, the unreflected half-split, low_weight_words, research/e7-intersection-counters/engine.py, the E6 and D6 censuses, any other simple root's frame, Lean, Docker, and scripts/research_selected_baseline.py as a scientific replay. The selected record is provenance only.

This census does not cover every simple reflection, and it is not an unrestricted nonexistence result.

Credit

The 120-line order and the unreflected puncture are the model in research/p112-rank6-frame-coverage, from the PR1226/PR1323 listing used by Cinna Davis. The simple system is the one in research/p112-a3-six-flat/geometry.py, from Nick Petalas's PR3161/PR3162 lineage. The seven supports, their hash, and the unreflected weight distribution are recorded in open #7007. The doubling half-split follows that package's scanner and reads the reflected basis. The question is open question 1 of #7007.

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. Does the next simple root, in this same pinned order, that moves a punctured line induce the same set equality on its own rebuilt list? This census is the first moving pair only. First continue the lexicographic scan and compare one half-split with that pair's transported supports.
2. Does low_weight_words on this reflected 36-generator basis return the same seven transported supports? This is the bit-lane iterator on the reflected basis, compared with hash 9ce7e5edc72ee3104d62cb068146b73840e9a3c42c4132403dece70c8146cccb. It is separate from the intersection-counter comparison on the unreflected basis and hash ff8861dab18040c03d403a860773218df7c120d03770d701afb61b78c941e3d3.

Workflow feedback (optional)

One half-split of this 36-dimensional length-112 code fits in the 600-second command limit. The bit-lane scan that #7007 measured at about 494 seconds does not fit beside it, which is why that comparison stays a separate question. A link to the feedback discussion is enough: #1200