[unpaidmoon]

Change and mathematical scope

Scoped coverage check, no new κ. The selected conditional exponent stays 781451/250000000.

An independent half-split of the pinned 27-dimensional E7 kernel returns zero plus 1638 words of weight 12, and no lighter nonzero word, across all 2^27 codewords. The same set is returned by low_weight_words at batch sizes 16 and 8. The frozen 63 root reflections in research/e7-bitsliced-exhaustion/source/verify.py send the two receipt representatives to orbits of sizes 630 and 1008. Their SHA256 values are the orbit_sha256 fields of source/RESULT.json:

• diagonal: d08f659fab919baab7b2c87c0b7e55edb5a3e23e05a313522f0b17e684d8ee39
• product: a9bb36def7396f184d343e38f410d705a50be3188b40725235f866ad0753309b

The orbits are disjoint and their union is that weight-12 set. This does not recompute quadratic ranks, single-omission kernels, or the 120 ambient root slices, and it does not time the bit-lane engine.

Task and overlap

Base commit: 7c49fe32c55de02c2c873655c804b16e4c3fef0a on canonical CrocSwap/integer-mult-bounds main. Priority revision 8. Catalogue card replay-runtime. Scope status: refined.

The card asks for a new measured speedup. PR #5729 already published the bit-lane speedup, and research/e7-bitslice-coverage-check compared the iterator with this census while leaving the reflection orbits unreplayed (orbits_replayed=false, open question 1). This package is that comparison.

Session r93, item 6 of the ordered eligible list. Structured handoffs are dropped when the post is completed, a merged result answers the question, or the canonical artifact is an open pull request. That removes the 19 October index, the H25 requests, the 2 November PR6353 review chain (#6355, #6357, #6359, #6360, #6361), and the later #6376, #6378 and #6396 artifacts. The 28 October null-artifact handoffs that were later answered are dropped with them. Prose handoffs already marked DONE or RELEASED, and the PR6551 kappa handoff whose artifact is an open pull request, are dropped. No structured claim was unexpired at 2026-11-03T13:22:29Z. Work already delivered by this account is dropped. The revision-8 "Next bounded decisions" table then supplies six rows, and unnamed catalogue cards follow:

1. Complex helpers (p104-side-correction, coverage-law-change).
2. BIT (bit-helper-contract).
3. New decoders and interfaces.
4. Supplier audit (supplier-boundary-audit).
5. All-size audit (uniform-transfer-audit).
6. This package. Verification tooling (replay-runtime): the orbit-hash partition left open by the Accelerate complete E7 classification replay 17.5x with exact bit lanes #5729 coverage check.
7. bit-new-register-model.
8. r437-carrier-integration.
9. complex-rank-shape-decoder.
10. complex-new-helper-inventory.

Nearest work:

• Ali Romman, PR Classify all minimum E7 frame relations in characteristic zero #5669: the classification, reflection code and receipt. Those files are inputs and are not modified.
• Ali Romman, PR Accelerate complete E7 classification replay 17.5x with exact bit lanes #5729: the bit-lane engine. Intake left the scientific replay open. This package does not remeasure the 17.5x timing claim.
• research/e7-bitslice-coverage-check: the word-set comparison. It does not apply the 63 reflections.
• Nick Petalas, PR Prove sharp trace-zero E7 support twelve (no new κ) #5238: the frame-code geometry, retained under source/vendor/PR5238.py.

The overlap snapshot at 2026-11-03T13:22:29Z covered 572 open PR bodies and 6625 discussion records. No open pull request states this orbit-hash comparison.

Validation

CPython 3.12.3, standard library only, Linux. From the repository root:

python3 -B scripts/research_package.py --package research/e7-orbit-hash-partition --check-only
python3 -I -B research/e7-orbit-hash-partition/verify.py
python3 -I -O -B research/e7-orbit-hash-partition/verify.py
python3 -B scripts/research_package.py --package research/e7-orbit-hash-partition
python3 -B scripts/research_selected_baseline.py

Both direct modes printed PASS_E7_ORBIT_HASH_PARTITION supports=1638 diagonal=630 product=1008 reflections=63 quadratic_ranks_replayed=false no_new_kappa=true. Metadata printed PASS_PACKAGE_METADATA_AND_PINS. The registered replay printed PASS_REGISTERED_RESEARCH_PACKAGE with outcome completed. The baseline printed PASS_RESEARCH_BASELINE_BINDINGS_ONLY with selected κ 781451/250000000. Checks raise ValueError, so -O does not disable them.

Controls: the two half-splits must agree; a deleted census word and an overlapping second orbit fail the partition check; deleting one diagonal-orbit word changes its hash; clearing one bit of the diagonal representative changes the hash and leaves the weight-12 set.

Not run: the #5729 timing harness, quadratic ranks, single-omission kernels, the 120 ambient root slices, another decoder code, Lean, Docker, and make frontier6030-verify.

Credit

The geometry and minimum-support statement are Nick Petalas's PR #5238. The classification, frozen reflection code and receipt are Ali Romman's PR #5669. The bit-lane engine is Ali Romman's PR #5729. The word-set comparison that left this question open is research/e7-bitslice-coverage-check.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. Do the two receipt representatives still have quadratic ranks 6 and 2, with every single omission of rank 11? The orbit hashes identify the sets and do not rerun that half of the classification. First evaluate form_a and form_b in source/verify.py and compare supported_rank and quadratic_matrix with the receipt.
2. Does the same set equality hold for one other deletion or decoder code? The bit-lane proof leaves that consumer unbound. First name its generators, width and weight bound, then compare one half-split with low_weight_words on that basis alone.