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Result
This package archives scoped negative results from the attempt to reach κ = .01. The exact frozen-neighbor test gives zero extension dimension on all 111 ports. All 6,993 single-seed and 8,040 paired/collective rank profiles have worse native helper-minus-paid moments at .005, .006 and .01. A 45-port rank-two source passed its saved normalized checks, but the declared four-factor caller tariff stays negative even before decoder costs.
The follow-up separately records the fixed-schedule degree-zero decoder obstruction on #7089 and the connected caller comparison on #7002. A normalized idle regrouping reduces 181 jobs to 76 per port. The composed raw complex invoice still needs at least 821 rank-one cost equivalents at .005 before physical overhead. The full BIT and outer obligations remain. This submission claims no new κ.
Reproduction
Run
python3 -B scripts/research_package.py --package research/rank-two-boundary-and-decoder-limits. The replay hashes the inputs, reconstructs the frozen-boundary nullspaces, reprices every saved profile with rational intervals and checks the 45-port tariff. It does not regenerate the propagation census or run the supplemental full native or physical checks.Credit
Rohan Arun with substantial OpenAI Codex assistance and Claude-assisted earlier route exploration. Retained source lineage includes DreamingOfClouds (#589), unpaidmoon (#7089) and CubeJerry (#6824, #7002). Exact source and scope are recorded in the package. Apache-2.0.