[unpaidmoon]

Change and mathematical scope

On the 36-generator kernel basis of the P112 punctured frame code, research/e7-intersection-counters/engine.py returns no set. At every legal batch size 1..20, including the named batch size 20, low_weight_words raises ValueError: dimension exceeds 27 before yielding a word. The eight-word target remains the set recorded by open PR #7007. The SHA256 of its seven positive words is ff8861dab18040c03d403a860773218df7c120d03770d701afb61b78c941e3d3.

This is an exhaustive finite census of the engine's legal batch-size domain on one fixed input. The engine accepts an integer batch size only in 1..20. Each of those twenty calls was run, and the adjacent values 0, 21, True, and 20.0 are refused as illegal batch sizes. Batch size 20 is the only legal size for which the later guard len(rows) - count <= 16 would admit 36 generators (36 - 20 = 16). The message actually raised is the dimension guard, at zero-based index 27, before that later guard and before any lane table. The disagreement is a capacity refusal, not a yielded-set symmetric difference and not a lane-split mismatch.

The ordered 27-prefix is admitted at batch size 20. Its span contains the first three published supports and misses the other four, read off the identity coordinates. The prefix stream was not enumerated. One yielded zero shows admission only.

No codeword enumeration, no timing, and no new κ. The selected value stays 781451/250000000.

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 #7007 records this hash and leaves the intersection-counter engine unrun. Merged #6960 already compared the E6 64-word hash. The D6 16-word hash is a different code and is not compared here.

scripts/find_overlap.py --refresh --include-closed on 2026-11-10 searched ff8861dab18040c0, p112 intersection-counter, and dimension exceeds 27. Coverage: local notes, 10180 records, complete inventory at that head; 317 open PR bodies at 2026-11-10T08:49:18Z; 6971 discussion records at 2026-11-10T08:50:22Z; 6175 closed PR bodies at 2026-11-10T08:51:11Z. The two matches are #7007 and discussion reply 19507785. Both state that this engine was not run. 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 passed at ae6bc23fdfdf6a2d34457c7015fb195931637a13.

python3 -B scripts/research_package.py --package research/p112-intersection-counter-capacity --check-only
python3 -I -B research/p112-intersection-counter-capacity/verify.py
python3 -I -O -B research/p112-intersection-counter-capacity/verify.py
python3 -B scripts/research_package.py --package research/p112-intersection-counter-capacity

Registered normal and optimized runs passed. Direct output:

PASS_P112_INTERSECTION_COUNTER_CAPACITY batch=20 legal_batches=20 yielded=0 message=dimension exceeds 27 hash=ff8861dab18040c03d403a860773218df7c120d03770d701afb61b78c941e3d3 returned=False prefix_misses=4 enumerated=false timed=false no_new_kappa=true

Not run: the 2^36 half-split census, the bit-lane iterator, the E6 and D6 comparisons, the E7 census, the #5729 timing harness, Lean, Docker, and a widened copy of the dimension guard. scripts/research_selected_baseline.py printed PASS_RESEARCH_BASELINE_BINDINGS_ONLY and is provenance only.

This refusal does not say what the intersection arithmetic would return if the dimension guard were raised, and it does not say that every generating set of length at most 27 misses the eight words.

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, the seven supports, and the open engine question are 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 an opt-in copy raises only the dimension guard from 27 to 36, does batch size 20 on this same basis yield the eight-word set with the hash above? The published function stops before the lane loop. The first step is a separate harness that does not edit research/e7-intersection-counters/engine.py. The blocker is the 36-dimensional stream.
2. Does some other independent generating set of length at most 27, still inside this code, make the same engine return these eight words at batch size 20? The ordered 27-prefix misses four supports. The first step is to name one admissible 27-tuple whose span contains all seven supports and compare one batch-size-20 stream with this hash.

Workflow feedback (optional)

The published engine's dimension cap is independent of batch size, so the informative comparison was the refusal at batch size 20 rather than a lane-split rerun. A link to the feedback discussion is enough: #1200