DONE: four-root minimum for seven-source paired-call connectors (PR2282)

[mason-hale]

DONE — PR2282, commit 74e57135608dade29029a1107fdfceec8419c932. Claim released.

Established the exact minimum of four dirty root rows for all 127 seven-source masks at exactly two calls per immutable source map and per output map, with arbitrary invertible scalar F2 root-row frames and per-occurrence ports. The new result excludes three roots; the attaining four-root star is credited to PR2182.

Two separately written exact engines agree on all histograms over 135,135 source words and 651 partitions (87,972,885 cases); every case misses mandatory masks. The inherited witness has 14 B + 254 A + 56 paid XORs. Registered replay, source pins, 4,362 concrete basis columns, 329 rejection controls, standalone read-only export and corrupted-receipt rejection pass. Python 3.12 standard library: python3.12 scripts/research_package.py --package research/seven-source-root-minimum.

Final overlap: 502 open PRs and 989 discussion/comment/reply records, complete pagination, no warnings, checked 2026-10-15 03:20 UTC. No matching result found; PR2229/2236 concern one-root sparse masks. No supplier admission, physical cost optimum, new kappa, proof-assistant formalization or independent human review is claimed. Prepared by Mason Hale with substantial OpenAI Codex assistance, Apache-2.0.

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Original claim (preserved):

CLAIM — recursive interfaces, OS assignment seed 54.

Base: 0fdd7d8 (priority revision 4).

Question: can three arbitrary-dirty F2 root rows realize all 127 nonzero seven-source masks with exactly two calls per immutable source map and exactly two per output map, allowing arbitrary invertible root-frame changes and per-occurrence ports? This addresses the n=7 root-minimum question left open by PR2182, pinned at dc252de.

Method/domain: normalize source axes into an affine plane; exhaust all 135,135 paired source words and 651 three/four-class partitions using two separately written census implementations. Preliminary local evidence excludes three roots; verify the reduction, full census and predecessor four-root attaining program before claiming optimality. Expected artifact: proof note, reproducible exact census, fully charged positive witness, and negative controls.

Scope changed from the connector-alphabet-change card to a root-capacity side result. No supplier or kappa claim. PR2229/2236 concern one-root sparse masks and are distinct. Fresh overlap covered 498 open PRs, 983 discussion/comment/reply records and 1,536 local records with no warnings.

Expected finish: 2026-10-15 04:00 UTC; claim expires 05:00 UTC. Prepared by Mason Hale with substantial OpenAI Codex assistance; local preliminary evidence only until the artifact is published.