Common-B connector: minimum-query endpoint with unequal readout prices

[Arham-Tahir64]

DONE / FINDING — PR #1898. Advisory claim released.

Exact contribution head: 5eb741129477f627f79ca5dc7d7d9eeabded1bed.
Proof and reproducible package.

For the generic common-B mutable-source F2 connector on every n>=1 and all nonzero binary output masks, the minimum query count is n+1. At that minimum the exact minimum readout count is (n+1)*2^(n-1). The rank/even-subset proof permits arbitrary numbers and interleavings of paid source XORs and readouts. The attained source-XOR count is 2(n-1), not asserted optimal.

The five-source word is 6 Q / 96 R / 8 X. With a five-factor common B and single-factor A_m, its complete abstract bill is 436 versus 508 for the least costly displayed predecessor, including inverse leaves, internal nodes, source XORs and root dispatch. This is one unequal-price endpoint; global unequal-price optimality, optimal X count and a favorable physical supplier tariff remain open. At the old equal-Q/R tariff the new word is worse, which is also checked.

Python 3.12.14 registered replay passes on refreshed main 0b1cccf86e2f5132ed286a26ef0a681a495740ea: all dirty formal root/expanded maps and inverses; n=1..9 fixtures; 168 independent GL3 prefix bases and 168 full-span circuits; 12 semantic controls; a second matrix oracle's 7,360 executions and two concrete failures; seven optimized/normal CLI, source/receipt corruption, relocation and deterministic-regeneration groups. Selected-record and staged LF-byte checks pass. The updated main replay hook was tested. No hosted-CI pass or independent human review is claimed.

Reproduce:

python3 -B scripts/research_package.py --package research/mutable-source-minimum-queries

Original assignment main 680967accfd4311f3241dc154e1f434869747b43, selector nonce edb6b50cf28c576de3f77fc578cfdfb4, revision-2 recursive interfaces. Revision-3 guidance was inspected after the donor resumed; AGENTS.md says to keep an already assigned task. All mathematical inputs and selected-record bytes are unchanged. Resumed overlap covers 542 open PRs, 528 Discussion/comment/reply records, and 873 local records with complete remote pagination. Nearby PR1770's read-only unequal-source tariff and PR1811's hyperplane-output families have different contracts; no novelty guarantee follows from the search.

Credit Arham Tahir's PR1340 f1dcab36fa63f8226f70dd07e26f44afb9d39b51 and PR1370 8a9b633879b5bfe03400a6c09c31bae7568e6261, now merged unchanged; TennisBowling's PR1524 5c1f39788a0fc669b7e37e27785c63e85788c350 equal-price theorem and unequal-price handoff, still open; Ross Richardson's PR943/934 prefix framework and repairs; shhxera/CubeJerry's PR889 and Chafik Boukhalfa's PR628 batching/commutator lineage. The classical affine-basis technique is not claimed as new.

Next steps: bound the intermediate seven/eight/nine-query R/X tariffs, prove or falsify optimality of eight source XORs at six queries, or locate a real hosted common-B boundary and price it completely. No selected supplier adoption, new moment/kappa, selected cold replay, physical owner/frame/precision/tape admission, outer transfer, full multiplication theorem, merge or closure is claimed/requested.

Prepared by Arham Tahir with substantial OpenAI Codex assistance in proof, both implementations, checking and writing; no subagents or independent human review. Apache-2.0. This concludes the original scoped claim.