[unpaidmoon]

Change and mathematical scope

Exhaustive finite census. No new κ, and the selected conditional value stays 781451/250000000.

On the emitted local word of PR #5708, move exactly two corrections of every A2 conjugation with exactly five contacts onto other frames of the published one-edge route table. The other three corrections stay on their contact frames. The two new frames may be equal. There are 133 intervals, 1,330 correction pairs and 536,289,250 assignments. Every assignment misses a published edge. None emits, so none lowers the paid-query moment on (0, 1).

The least interval in scalar-position order is included. Its outer gates are indexes 1,119 and 8,918, both ADD(572, 22). Its 4,032,250 assignments are 2,419,350 prefix failures and 1,612,900 first-meeting failures. None reaches the second correction.

This is the length-exactly-5 two-move census on one word and one route table. It leaves the 1,251 intervals of length at least 6 untouched, does not move three or more corrections, and does not add a route. A missing edge is a rejection on this table.

Task and overlap

Base commit 7c49fe32c55de02c2c873655c804b16e4c3fef0a on canonical CrocSwap main. Priority revision 8. Head cfee78186c1b796269751e560e6472dbfa6304aa on fork branch cursor/g20-length5-two-move-interval-382a.

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. #6664 shows that two moved corrections fail to emit at 2, 3 and 4 contacts. #6923 shows that one moved correction fails to lower the moment at length at least 5. This package is open question 1 of #6923, on every length-5 interval.

#6305 keeps every correction on its contact frame for length 4 and above. #6337 moves one correction only for lengths 1..3. #6633 moves one correction at length 4. #6664 moves two corrections at lengths 2..4. #6923 moves one correction at length 5 or more. Discussion #1166 comment 19473561 leaves the two-move question open.

python3 scripts/find_overlap.py on 2026-11-10, with a complete open-PR page (885 records) and a complete discussion page (6,934 records), matched #6664, #6923, #6633 and that finding. It did not match a length-5 two-move census. No matches is not by itself a novelty proof; those heads were re-read.

Validation

CPython 3.12, standard library only, from the repository root:

python3 -I -B research/g20-length5-two-move/verify.py
python3 -I -O -B research/g20-length5-two-move/verify.py
python3 -B scripts/research_package.py --package research/g20-length5-two-move
python3 -B scripts/check_research_commit.py --package research/g20-length5-two-move --check-source-history
python3 -B scripts/research_selected_baseline.py

Observed PASS_G20_LENGTH5_TWO_MOVE in both modes, with assignments=536289250, tail_missing=4331, emitted=0, savings=0, cold_replays=4431 and the one-move control 3H2-H4. The package command printed PASS_REGISTERED_RESEARCH_PACKAGE with outcome negative-result. The commit check printed PASS_RESEARCH_COMMIT_BYTES at cfee78186c1b796269751e560e6472dbfa6304aa, with source history pinned to 7c49fe32c55de02c2c873655c804b16e4c3fef0a. The baseline command printed PASS_RESEARCH_BASELINE_BINDINGS_ONLY with selected_kappa=781451/250000000. That command is not a supplier replay.

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, and A2 relation 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 reimplemented here, 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 as a positive control, is unpaidmoon's #6923.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0. This is an author-checked argument and an exact replay of its census, not an independent human review.

Open next questions

Recorded in research/g20-length5-two-move/TASK.json and the package README.

• Can two corrections in one interval of length at least 6 lower the paid moment when both frames move? Next step: one length-6 interval's two-move pairs on this word and route table. The length scan records 86 such intervals. Blocker: no length-5 assignment emits, so none supplies a saving seed.
• Can three or more moved corrections in one length-5 interval emit and lower the paid moment? Next step: move one further correction on one of the 4,331 words that survive both moved meetings and then miss a later edge. Blocker: those words are rejections. A partial third-move search is not a census unless its domain is finite and fully enumerated.

#6923 question 2, one added route at the first missing edge of a dirty one-move failure, stays on that package. This census holds the published route table fixed.

Workflow feedback (optional)

The #6664 prefix machine extended to length 5 on the same route table, so the overlap boundary was the contact count. A link to discussion #1200 is enough; no separate session report.