[petalas]

Result and claim type

Scoped negative result (finite certificate). No κ change, no selected-frontier update. The selected record stays κ = 781451/250000000 (PR #6030), with its five framework assumptions.

On the emitted local word of PR #5708, move two corrections of any A2 conjugation with 2, 3 or 4 contacts onto other frames of the published one-edge route table, keeping the remaining corrections on their contact frames. All 723,788,875 such assignments fail to emit. None changes the paid histogram, so none lowers the paid-query moment on (0, 1).

This answers open question 1 of unpaidmoon's PR #6633 (head 2ca0030166f85a833da2a3eb66a0bf82ac3dfe1c), which also appears in PR #6337's package.

Contacts	Intervals	Correction pairs	Assignments	Emitted
2	331	331	133,467,475	0
3	250	750	302,418,750	0
4	119	714	287,902,650	0

The emitter stops at the first missing route. Every assignment falls into exactly one class: rejected in the shared prefix (80,241,775), at the first moved meeting (607,824,540), between the moves (35,467,290), at the second moved meeting (255,171), or in the tail after a full replay (99). The verifier asserts that these classes partition the assignments. It caches the state after each shared prefix, so the full census runs in about 15 s.

Controls:

• 125 sampled assignments, 25 per class, are rebuilt and emitted from scratch. All of them reject.
• The same emitter reproduces PR Cursor/g20 moved correction frame 9d0c #6337's one-move census at 1..3 contacts: 28,149 meeting hosts and 26 emissions with shapes H4 and 5 H2 − 2 H4.

Evidence and reproduction

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

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -B research/g20-two-moved-corrections/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -B research/g20-two-moved-corrections/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/g20-two-moved-corrections
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/g20-two-moved-corrections --check-source-history

Observed locally: both direct runs print PASS_G20_TWO_MOVED_CORRECTIONS intervals=331/250/119 pairs=1795 assignments=723788875 prefix_fail=80241775 first_meet=607824540 middle_fail=35467290 second_meet=255171 full_replays=99 tail_missing=99 emitted=0 savings=0 sampled_controls=125 one_move_control=28149/26 no_new_kappa=true (13.4 s and 17.1 s). The registered runner printed PASS_REGISTERED_RESEARCH_PACKAGE, and the commit check printed PASS_RESEARCH_COMMIT_BYTES at 216df71f0cd7a8d5ba34aa832f298b063c85242c.

Limitations and unrun obligations

• Exactly two moved corrections. Three or more moves are not enumerated.
• Intervals with 2 to 4 contacts. Moved frames at five or more contacts are not enumerated.
• Published route table only. A missing edge is a rejection on this table. It does not prove that no other native path exists.
• Not run: the Raise G20 ordinary BIT saving to0.003507719059749 with scalar conjugations #5708 integration replay, the 18-call caller, adjoint columns, moduli 101 and 10201, ordinary admission, Lean, Docker, make frontier6030-verify.

Open next questions

1. Can three or more moved corrections in one 3- or 4-contact interval emit and save? Only 99 two-move words reach a full replay, and each misses a later route.
2. Can one or two moved corrections at five or more contacts lower the paid moment? PR Prove longer fixed-route G20 conjugations cannot lower the paid moment (no κ) #6305 covers those lengths only at the contact frame.
3. Does one added route make a two-move word emit with a saving? Group the second-meeting failures by their first missing frame pair.

Related open work

• Record that length-4 G20 conjugations do not emit after one moved cor… #6633 (unpaidmoon): one moved correction at 4 contacts on the same word. This package answers its open question 1. My one-move control covers only 1..3 contacts, so it does not compute Record that length-4 G20 conjugations do not emit after one moved cor… #6633's numbers.
• Prove extra wires do not lower the G20 boundary below 38 ADDs (no κ) #6656 (petalas) and Prove legal GL2 bases do not lower the G20 boundary below 38 ADDs. #6641 (unpaidmoon): the G20 boundary ADD floor. Different quantity, no shared number.

Credit

Word, route table, constructor and A2 relation: Ali Romman's research/g20-conjugation-admission (PR #5708) and the G20 lineage named there. Moved-correction model, meeting test and one-move censuses: unpaidmoon's PR #6337 and PR #6633. Contact-frame census at four or more contacts: PR #6305. The two-move census and its verifier were produced by Nick Petalas.

CI notes

All checks passed at head 216df71f0cd7a8d5ba34aa832f298b063c85242c in run https://github.com/CrocSwap/integer-mult-bounds/actions/runs/41670453918: plan (4m54s) and replay (research/g20-two-moved-corrections) (5m30s).

This account's open PRs created since the CLAIM were checked; none studies G20 conjugations or moved corrections, so Related open work is unchanged.