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Prove triple-source connector steps keep the 72-query floor. - #24
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The five-source paired-readout batch still needs a closed prefix set of size at least 10 when steps may have weight 3, 4, or 5. Two censuses of all 7,888,725 nine-point sets agree that none cover F_2^5, so the query count stays at least 72 and the length-10 leaf bill stays at least 120. Co-authored-by: unpaidmoon <unpaidmoon@users.noreply.github.com>
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Change and mathematical scope
Negative bound. No new κ and no selected-frontier change. Selected κ stays
0.001672660197076918.On the five-source paired-readout connector, every closed source walk whose prefix differences include all 31 nonzero masks has length at least 10, whether steps have weight 1, 2, 3, 4, or 5. A charged triple-source call
B_{jkℓ}(one query and three source accesses, not free) therefore does not lower the query count below62 + 10 = 72, which weight-at-most-2 pair calls already attain. On any covering closed walk of length 10 that uses a step of weight at least 2, the source-leaf bill at prices(1, 4, 10, 16, 28)is at least 120.Counting gives
|P| >= 9becauseC(8, 2) = 28 < 31. Two scans of allC(31, 8) = 7,888,725nine-point sets containing 0 find no difference basis ofF_2^5. The maximum is 28 nonzero differences, or 29 masks including 0.Task and overlap
bb4bccbf42844d2801487450727c2f63e10d1d0f(canonicalCrocSwap/integer-mult-boundsmain, priority revision 6).connector-alphabet-change, scope refined. The catalogue has 21 cards in track-weight order. Item index(30-1) mod 21 = 8is this card. The piece is the triple-source question left byresearch/connector-pair-source-path-seed2cdb, not the card's generic one-operation search.bit-helper-contract,bit-new-register-model,p104-side-correction,complex-rank-shape-decoder,complex-new-helper-inventory,joint-query-controller,centre-path-sharing,coverage-law-change,connector-alphabet-change, then the remaining twelve cards throughscalar-to-moment.research/connector-pair-source-path-seed2cdb, open question 1. The fixed alphabet and 74-query baseline are Ross Richardson,research/universal-connector-boundary.Validation
CPython 3.12. Registered replay:
Passed locally as
PASS_REGISTERED_RESEARCH_PACKAGE research/connector-triple-query-floor outcome=negative-result.verify.pychecks the counting bound, runs an odometer census and anitertoolscensus that must agree, checks the published 10-point prefix set and every one-point deletion, and enumerates source-leaf bills for every admissible multiplicity type with total weight 12 through 50.Not run: Lean, Docker, the 945 weight-1 pairing census, a length-10 triple witness search, and the selected cold replay. The query floor does not use the 945 census.
Credit
Ross Richardson for the five-source paired-readout model. Aaron Wang for the 72-query pair-call word, the nine-point census target, and the triple-source question. Adam Gall for the fixed-alphabet all-tariff formula. New census and leaf comparison by unpaidmoon, with substantial AI assistance (Cursor Grok 4.7). Apache-2.0. No independent human or proof-kernel review is claimed.
Open next questions
(4, 2, 2, 2, 2)with exactly one weight-3 step. A negative search would not reopen length 9.F_2^6have a 12-point difference basis? Counting already gives|P| >= 12at every step weight. The unrestricted binomial count blocks a direct copy of this census.Workflow feedback (optional)
The pair-source open question named the prefix-set method, so the session could stop at the nine-point obstruction instead of searching walks. No separate workflow note.