DONE: five-root minimum for eight-source paired-call connectors (PR2795)

[Arham-Tahir64]

DONE / FINDING — five dirty roots are exactly necessary at eight sources in the paired-call scalar-F2-frame interface.

Public artifact: PR2795, head fad52f9528cfea1c3bcfc0094ff56abf945d31a7; package research/eight-source-root-code/.

Established: a general root-code mask-intersection criterion and an all-ones-cut reduction to n! source orders. Complete independent Python span/prefix and C++ RREF/interval engines exclude all 40,320 × 11,811 = 476,219,520 eight-source/four-root cases and agree on the entire code inventory and both histograms. The credited PR2182 star attains five roots with 16 B + 510 A + 120 paid row XORs. Its full dirty-state forward/inverse replay passes, as do all 646 operation omissions; a constructive five-source root-code compiler and 130 omissions, small cut controls, known seven-source calibration and semantic/typed-receipt controls also pass. Registered CPython3.12.14 replay passed on macOS arm64. No hosted-CI or independent human/proof-kernel pass is claimed.

This settles Mason Hale PR2282 Open next question 1; its seven-source theorem is credited, not resubmitted. Credit conorholds PR2182 for axes/contracts/star, Ross Richardson PR934/943, Douglas Colkitt PR1185 and the retained root/compiler lineage. Substantial OpenAI Codex assistance, Apache-2.0.

HANDOFF / stop: no recursive caller or paid physical supplier is admitted. Identify one actual consumer and instantiate all complete-port, root-stock, preparation, routing, tape and precision costs before another construction campaign. Extra child calls and changed operations remain outside the root minimum. Selected frontier unchanged; no kappa claim. Claim released.

Canonical main refreshed to 12edc35a354c809e0ab01a3c093a2175450ec80c, with relevant instructions and scientific inputs unchanged. Final open PR coverage: 722; complete Discussion snapshot: 1,425 records. Full Discussion refresh failed on connection reset, supplemented by a fresh top-30 active-thread/last-ten-comments query. Full details and limitations are in TASK.json.

Original claim and bounded scope pivot

CLAIM UPDATE — eight-source / four-root minimum-incidence boundary (one bounded pivot).
The completed live Discussion index exposed Mason Hale PR2282 / Discussion2275, already settling my initial seven-source scope. My independent 135,135-word / 715-partition control corroborated it; no new seven-source result is claimed. Credit PR2282 at 74e5713 and conorholds PR2182 at dc252de.

Take PR2282 Open next question 1: can four arbitrary dirty roots realize every nonzero eight-source mask at exactly two calls per source/output map, under arbitrary paid invertible scalar F2 root frames and occurrence-varying ports?
New reduction: the all-ones output requires an interval containing each source exactly once; rotate that interval to the first half and rename it, leaving 8! = 40,320 source words. Enumerate the 11,811 four-dimensional binary root-code row spaces containing all ones, rather than labelled frame/source assignments. Prove a full mask-intersection feasibility criterion and test the complete reduced domain. Expected artifact: general reduction, exact census or literal witness, charged known upper construction and positive/failure controls. No supplier or kappa claim.
Base remains current-main 7788b59, priority revision 5. Stop after this one eight-source check; no adjacent expansion. Claim expires 2026-10-15T23:55:00Z. Arham Tahir, substantial OpenAI Codex assistance.

Initial claim, retained for history: seven-source three-root boundary, posted before completed indexing exposed the exact predecessor. Superseded and independently corroborated; scope released.