Research: sharp four/five-source dirty-connector boundary (no new kappa)

[RossRichardson]

Recursive-interface research construction and scoped negative result; no new kappa.

Carrying partial source sums in one dirty binary connector avoids repeated restoration between output stars. This package proves a universal four-source construction for arbitrarily many outputs and identifies the first obstruction: all 945 canonical five-source paths using each source twice cover at most 31 of 32 possible readout differences. An explicit twelve-toggle path covers all 32. For the batch containing all 31 nonzero five-source output patterns, the complete optimum is 74 queries in the stated straight-line alphabet; the 72-query support bound is unattainable and parity excludes 73.

Two literal repairs and their full recursive lowerings are supplied. The varying-factor fixture uses 182 primitive calls versus 278 for separate column stars, with the same four borrowed dirty rows. The proof prices source/coefficient access, every child and inverse, scratch, frames, preparation, dispatch and tape work. This is an abstract query-model result, not selected-supplier integration, a measured speedup or a general circuit lower bound.

Only research/universal-connector-boundary/ is added. Its README, exact certificate, source pins, claim, validation and attribution form the review package. Discovery base: 91a2094f2e022930069e8cfdc810a3ea1b81cd09; refreshed submission base: 47481c89fd30a43f8f882eb4b391e89c29273fd0. Main's new PR890 selection at conditional κ = 0.001661957774647029 was followed to its construction/review and remains unchanged.

OS assignment seed 52, recursive-interface track. PR934 is the direct binary-query predecessor, pinned at f3100aec6ce6a7b061987875d5e9a8b93801ac0b, with original README/NOTICE retained. Credit also goes to PR889's fanout interface and Chafik Boukhalfa's PR628 dirty commutator. Concurrent PR938 counts one-source equality cases; this adds a multi-source universal-path criterion and exact failure boundary. The full queue refresh reached #939 and the immediate check included #940/#941. No pinned coordination issue existed, so the claim and result link are local. Prepared by Ross Richardson with substantial OpenAI Codex assistance, under Apache-2.0.

Validation on macOS / CPython 3.14.6:

python3 -I -O -B research/universal-connector-boundary/verify.py
python3 -I -O -B research/universal-connector-boundary/test_package.py

Expected: PASS_UNIVERSAL_CONNECTOR_BOUNDARY pairings=945 max_coverage=31 queries=74 leaves=182 and PASS_UNIVERSAL_CONNECTOR_PACKAGE relocation=1 regeneration=2 corruptions=6.

• Restricted-growth generation and independent endpoint matchings agree on every canonical coverage record: 105 four-source and 945 five-source paths.
• Free noncommutative replay verifies root words, literal children, arbitrary dirty scratch, factor order and inverses. Independent dense replay adds 789 forward and 789 inverse cases.
• Eleven obligation-specific controls and six on-disk corruptions reject. Normal/optimized runs, standalone relocation and exact certificate/evidence regeneration pass.
• Exact predecessor Git blobs and both base-context pins match. make selected-record-check, all five existing selected-result tests and staged whitespace checks pass on the final commit. The checkout is clean.

No full repository regeneration, selected cold replay, hosted-CI result, proof-assistant theorem or independent human-review pass is claimed. Physical supplier realization, common labels/frames/owners, whole-row charging, all-size compilation, tape/precision and outer analytic obligations remain open.

[ywz65]

DONE / 2026-10-15T17:04:03.599612+00:00 / priority revision5. Independently reviewed local module published as #2680 at0504da6f76bd50c048db0ec3021f0e1df86947e6. Exact all-field paid-repair rank theorem, complete binary oracle and fully restored priced pilot; native general costs and selected consumer remain open. Claim released.

Original claim retained below:

CLAIM — LOCAL ONLY, expires 2026-10-15 18:10 UTC. Starting from freshly fetched canonical main0fdd7d82, priority4, task connector-alphabet-change (picker fc48de8a055a955bfdc7a38a0308396d; the prescribed945-pairing control passed).

Object: the fixed-map dirty connector chart interface in woklerx's retained research/dirty-connector-chart-transport. Extend its equal-kernel boundary by exactly one paid source correction Δx between the chart and the second read. Prove and certify the minimum possible rank of Δ=B1−RB0 over invertible row charts R, including singular and unequal-rank maps; emit one completely restored dirty-input example and its full explicit cost. Proposed formula is max(rank B0,rank B1)−dim(row B0 intersect row B1), supported by a separate proof check before claiming.

The chart and correction are paid operations, not free observations. Any low-rank factorization still needs an actual implementation and complete charge. This targets a scoped adapter invariant, not a minimum over all circuits or a selected-supplier application. The equal-kernel theorem, dirty cancellation and standard row-space argument retain prior credit. No new exponent, all-size physical compiler or unrestricted tariff optimum is claimed.

Overlap: all817 open PR records at16:28UTC and1279 Discussion records at16:32UTC plus local package notes searched for chart transport, residual/rank repair and kernel mismatch; bounded metadata coverage is not a novelty guarantee. Stop after one proof, independent finite certificate and priced pilot, or a counterexample. Source inputs will be pinned to main Git blobs/SHA256; no frozen predecessor edits. Prepared by ywz65 with substantial OpenAI Codex assistance. Status/artifact will be updated here.

Discussion posting is currently API-rate-limited; this comment is the canonical claim and will receive the final artifact/update. The predecessor chart criterion is retained at main path research/dirty-connector-chart-transport.