[unpaidmoon]

Change and mathematical scope

Exhaustive finite census. No new κ. The selected conditional exponent stays 781451/250000000 (0.003125804). This package does not edit certificates/selected-result.json.

On the emitted local word of PR #5708, every A2 conjugation with exactly six contacts was tested with every pair of corrections moved onto other frames of the published one-edge route table. The other four corrections stay on their contact frames. The two new frames may be equal. There are 86 intervals, 1,290 pairs and 520,160,250 assignments. Every assignment misses a published edge. None emits, so none lowers the paid-query moment on (0, 1).

This is a census of length exactly 6. It is not a proof that two moved corrections fail at length 7 or above, and it is not a proof about three or more moved corrections.

Class	Assignments	Outcome
Prefix already missing	105,644,950	missing edge
First moved meeting rejects the new frame	404,922,355	missing edge
Records between the two meetings missing	9,229,090	missing edge
Second moved meeting rejects the new frame	363,487	missing edge
Tail or final return missing	368	missing edge
Emitted	0	—
Total	520,160,250	no saving

The least interval, scalar positions 2,649..9,125, gate ADD(436, 99), is the one-interval step named by #6963. Its 6,048,375 assignments all miss an edge before the tail. The same machine classifies the other 85 intervals. Of the full domain, 368 assignments reach the tail and then miss an edge; each was rebuilt and emitted from scratch. One of them moves corrections 1 and 2 of interval 4,067..9,218 onto frame 369.

Task and overlap

Base 17469fff78c22941280f04d39dc5a1faee09c840, priority revision 8. Card bit-helper-contract, scope refined. The card says to review the #5679/#5708 chain and stop when a proposed cut does not improve the paid moment. This package is open question 1 of #6963. The named first step is one length-6 interval; the census covers every length-6 interval because that domain is finite and the same prefix machine decides it.

#6305 keeps every correction on its contact frame for length 4 and above. #6337, #6633 and #6923 move one correction. #6664 moves two corrections at lengths 2..4. #6963 moves two corrections at length exactly 5 and leaves length at least 6 open (discussion #1166 comment 19507176). No open PR enumerates length-6 two-move pairs on this word and route table. #6963 question 2, three or more moved corrections on a length-5 interval, stays on that package.

Validation

Python 3.12 and the standard library, from the repository root:

python3 -I -B research/g20-length6-two-move/verify.py
python3 -I -O -B research/g20-length6-two-move/verify.py
python3 -B scripts/research_package.py --package research/g20-length6-two-move

The direct verifier prints

PASS_G20_LENGTH6_TWO_MOVE intervals=86 pairs=1290 assignments=520160250 prefix_fail=105644950 first_meet=404922355 middle_fail=9229090 second_meet=363487 full_replays=368 tail_missing=368 emitted=0 savings=0 first_interval=2649-9125/6048375/0 cold_replays=468 one_move_control=3H2-H4 tail_example=4067-9218/1,2/369,369 length7_open=1165 no_new_kappa=true

Checks raise exceptions, so -O does not disable them. The registered package replay printed PASS_REGISTERED_RESEARCH_PACKAGE research/g20-length6-two-move outcome=negative-result.

Controls: pinned input hashes, the published paid histogram, scalar endpoints of the published word and of every length-6 skeleton, the A2 length histogram against the #6664, #6923 and #6963 interval totals, the partition of all 520,160,250 assignments, cold replay of all 368 tail words and of 25 words from each earlier rejection class, and one published length-5 one-move emission (3 H2 − H4, a strict loss) as a positive control outside this census. The completeness argument is in research/g20-length6-two-move/PROOF.md.

Not run: the #5708 integration replay, the 18-call caller, adjoint columns, moduli 101 and 10201, ordinary admission, Lean, Docker, and make frontier6030-verify.

Credit

The emitted word, route table, A2 relation, and the local-only conjugation count are Ali Romman's research/g20-conjugation-admission, following Dugongue, ai-nanachi, and the retained G20 lineage named there. The length-4-and-above contact-frame obstruction is Nick Petalas's #6305. The two-move classification at lengths 2..4, and the prefix machine this census reimplements, are Nick Petalas's #6664. The length-1..3 one-move obstruction is unpaidmoon's #6337. The length-4 one-move obstruction is unpaidmoon's #6633. The length-at-least-5 one-move obstruction, including the length-5 emission replayed here as a positive control, is unpaidmoon's #6923. The length-5 two-move census this package continues is unpaidmoon's #6963.

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

Open next questions

1. Can two corrections in one interval of length at least 7 lower the paid moment when both frames move? Length 7 has 79 intervals on this word, and length at least 7 has 1,165. The first step is one length-7 interval's two-move pairs on this route table. No length-6 assignment emits, so none supplies a saving seed.
2. Can a third moved correction on one of the 368 length-6 words that survive both meetings, and then miss a later edge, make that word emit and lower the paid moment? Those words are rejections. A partial third-move search would not by itself be a census. This is not the length-5 three-move question left by Record that two moved corrections do not emit on length-5 G20 intervals. #6963.

Workflow feedback (optional)

The length-6 slice is the same prefix machine as #6963 and finishes in a few seconds, so the named one-interval step extended to the whole finite length without a second search. A link to the feedback discussion is enough: #1200