Seven-source sparse connector boundary at 14 toggles (no new kappa)

[1337isnot1337]

Result

Adds a reproducible, exact finite result for one-root F2 dirty connectors with seven immutable source maps. The package enumerates all 135,135 canonical 14-toggle words in which each source is toggled exactly twice, testing the 63 output masks of weights 1, 2, and 3.

• No word covers all 63 masks; the exact maximum is 56, attained by two words.
• A displayed 14-toggle witness covers every singleton and pair mask plus 28 triples. It realizes those 56 arbitrary dirty outputs at the 126-complete-call floor.
• Compared with independent per-output stars, that shared schedule saves 252 complete source-map calls and 1,008 bits under the package's explicit event encoding. The invoice charges each complete call, shared input/preparation, event storage, and root dispatch. No new supplier or kappa is claimed.
• The 140-call floor for all 63 outputs is excluded only for the exact two-toggles-per-source schedule class. The parity lower bound then puts a generic full schedule at 142 or more calls; this PR does not claim a 142-call construction or exclude longer schedules.

The dirty-state identity is proved for arbitrary F2-linear maps and dimensions. The exact search and independent verifier are packaged with the complete histogram, witness readout boundaries, and three negative controls.

Pins and reproduction

Base commit: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2
Selected-record SHA-256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32

From the repository root:

python3 -I -B research/seven-source-weight123-connector-seed7db30a/search.py
python3 -I -B research/seven-source-weight123-connector-seed7db30a/verify.py
python3 -I -O -B research/seven-source-weight123-connector-seed7db30a/verify.py
python3 scripts/research_package.py --package research/seven-source-weight123-connector-seed7db30a --check-only

Observed markers:

SEVEN_SOURCE_WEIGHT123_SEARCH pairings=135135 targets=63 hits=0 best=56
PASS_SEVEN_SOURCE_WEIGHT123_PAIRING_BOUND pairings=135135 max=56 full_hits=0 subset_calls=126 controls=3
PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)

Local direct replay used CPython 3.14.7. CPython 3.12 is unavailable here, so the registered Python 3.12 package replay was not run. The search, verifier in normal and optimized modes, metadata/pin check, and git diff --check passed directly.

Scope and related work

This is a scoped positive construction for a 56-mask sparse batch plus a finite obstruction at the 140-call floor. It is not a universal-mask connector, recursive assembly, multiplication result, or frontier update. The live overlap scan covered 463 open PRs and 918 Discussion records with complete pagination and no warnings. Nearest work is #2128 (six-source universal DUO path), #2146 (six-source TRIO exclusion), and #2182 (fixed-port/two-root boundaries); each studies a different source count, support family, alphabet, or root count. The general dirty-connector and paired-prefix criterion are attributed to #934 and #943.

Seed: 7db30a45a4ca218f66c410637c8459f3; task connector-alphabet-change, refined scope key 6a70fd459cc03339ab38, track recursive-interfaces, priority revision 4.

Prepared by Cinna Davis with substantial OpenAI Codex assistance in scoping, proof derivation, exact search, verification, cost accounting, overlap checks, and writing. No independent human review or proof-assistant formalization is claimed.