[unpaidmoon]

Change and mathematical scope

No new κ. The selected conditional exponent stays 781451/250000000. This package does not edit certificates/selected-result.json.

On one pinned D6 slice of E8, low_weight_words returns exactly the weight-at-most-2 words of the F2 incidence code of the orthogonal 6-frames. Width 30, kernel dimension 20, weight bound 2. The sets are equal, not merely the same size.

The root list is pinned in research/d6-punctured-frame-code/ROOTS.json. The anchors are the orthogonal E8 lines (2, 2, 0, 0, 0, 0, 0, 0) and (2, -2, 0, 0, 0, 0, 0, 0). The 30 stored lines are the E8 lines orthogonal to both, and they equal the coordinate lines ±2e_i ± 2e_j on axes 2, 3, 4, 5, 6, 7. Line-list SHA256 bd3d7efd8a94a7d0a6a7339cfd95805bb6907f3951ff67e9669b317655869538.

Two lines are orthogonal exactly when their supports are equal or disjoint. Those supports are the 15 edges of K_6. The 15 orthogonal 6-frames are the both-sign lifts of the perfect matchings of the six axes (5·3·1 = 15). A clique search returns the same set. Each line lies in 3 frames, and the sum of the frame rows is the all-one word, so every kernel word has even weight. Incidence rank 10. Free coordinates of the kernel basis: (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24).

Every vector in F_2^30 of weight at most 2 was tested against the frame rows (1 + 30 + 435 vectors). The words that pass are zero and the 15 partner-pair indicators. A binary-reflected Gray walk visits all 2^20 kernel words and checks the free bits against index XOR (index >> 1) at every index. A half-split after 10 generators returns that same 16-word set. low_weight_words at batch sizes 16 and 8 returns it, with no repeated yield. Weight bound 1 returns only zero.

The sorted positive supports are

3, 24, 36, 768, 1152, 2112, 98304, 147456, 270336, 528384,
50331648, 75497472, 138412032, 270532608, 537919488

Support-set SHA256 23a7b374a6bc62bc2aca47843d52a01fa8e791ed3a98085133829d816c5094e8.

The even-weight distribution of the whole code is 0:1, 2:15, 4:105, 6:1095, 8:10965, 10:59067, 12:170125, 14:282915, 16:282915, 18:170125, 20:59067, 22:10965, 24:1095, 26:105, 28:15, 30:1.

This is an exhaustive finite census of those two finite domains, plus a set comparison. It is not a proof that the iterator is correct for every generator matrix, and it is not an unrestricted nonexistence result.

Remaining obligations: transport to another orthogonal anchor pair; the P112 deletion; the intersection-counter engine on this basis. None is run here.

Task and overlap

Base 7c49fe32c55de02c2c873655c804b16e4c3fef0a. Task card replay-runtime, priority revision 8. Scope status refined: the card asks for a measured speedup, and the revision-8 verification row says faster output is not coverage until checked. The merged E7 comparison and the E6 4-frame comparison (discussion comment 19492511) left this D6 slice open.

Overlap refresh at 2026-11-10T02:05:29Z: 885 open pull requests and 6934 discussion records. The phrases "D6 punctured frame", "d6 frame code" and "orthogonal 6-frame" had no matches. Comment 19003654 / PR #3266 is a D6 frame-puncture support-capacity obstruction, a different object, not replayed. Open #6632 partitions the E7 weight-12 words. This package does not rerun the E6 census, build a P112 code, load research/e7-intersection-counters/engine.py, or time the engine.

Fork PR base is the pin cursor/crocswap-main-7c49fe32-1dbb of that upstream commit, so the diff is this package. No upstream write.

Validation

Python 3.12, standard library, from the repository root:

python3 -B scripts/research_package.py --package research/d6-punctured-frame-code --check-only
python3 -I -B research/d6-punctured-frame-code/verify.py
python3 -I -O -B research/d6-punctured-frame-code/verify.py
python3 -B scripts/research_package.py --package research/d6-punctured-frame-code

Observed direct line:

PASS_D6_PUNCTURED_FRAME_CODE width=30 frames=15 dimension=20 minimum=2 supports=15 codewords=1048576 batches=16,8 split=10 e6_census_replayed=false p112_built=false no_new_kappa=true

PASS_PACKAGE_METADATA_AND_PINS and PASS_REGISTERED_RESEARCH_PACKAGE research/d6-punctured-frame-code outcome=completed also ran. Controls: a dropped support compares unequal, a weight-1 injection is rejected, lines 0 and 2 are a weight-2 word outside the set, and a repeated generator is rejected.

Not run: the #5729 timing harness, the E6 census, the E7 kernel, the intersection-counter engine, any P112 root list, Lean, Docker, and scripts/research_selected_baseline.py as a scientific replay.

Credit

The D6 model as the lines orthogonal to an orthogonal E8 pair is the geometry in Nick Petalas's mixed-support arguments, including PR #3266. The coordinate lines match D(6) in research/char2-threshold/lib/roots.py. The bit-lane engine is Ali Romman's PR #5729. The request is the first open question of the E6 4-frame coverage check, discussion comment 19492511.

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 one other orthogonal E8 anchor pair induce the same set equality after the coordinate permutation that carries it to this pair? First reflect one pinned anchor by one simple E8 root and compare the transported partner supports with the hash above. This package does not apply that reflection.
2. Does the same set equality hold for one P112 punctured frame code, at a named width and weight bound? First pin the 112-line complement of one orthogonal 8-frame and compare one half-split with low_weight_words on that basis alone. No P112 list is pinned here.
3. Does the opt-in intersection-counter engine return this same 16-word set? First run research/e7-intersection-counters/engine.py on this 20-generator basis at one batch size and compare it with support hash 23a7b374a6bc62bc2aca47843d52a01fa8e791ed3a98085133829d816c5094e8. This is not the E6 64-word hash, and this package does not load that engine.

Workflow feedback (optional)

The predecessor named the missing root list as the blocker. Pinning that list in the package, and comparing the partner masks rather than the counts, made the equality checkable without another census of E6.