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Bound Gaussian adaptive routing with a paid public header - #2641
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PR888 explicitly excludes adaptive supports and variable-length messages from its Gaussian nonlinear copy model. This contribution admits a paid public prefix-free routing header selecting nonlinear prefix-free payloads, and proves the expected-cost bound C >= (2/3)B +4L -(10/3)H >= (2/3)(B+L), where B is total independent demand, L expected header length and H header entropy. A separate clique concentration inequality is retained. The strict Gaussian header penalty comes from weighted-clique total10/3 versus full-space header tariff4; the transcript and entropy methods retain their predecessors' credit.
The full-space header tariff and additive per-bit payload pricing are explicit abstract contract assumptions. No private schedule information, relays or free termination are admitted. The theorem bounds expected and worst-case cost, not every input. Under the additional inherited Dfc identity, nonempty public routing makes the favorable three-stage screen strictly negative. No supplier or kappa claim follows.
Validation: registered Python3.12.14 replay passes the unchanged PR738 full2,579,856-flat-pair premise,4096 adaptive nonlinear inputs,49,152 receiver checks,2,621,440 conditional projections and6 controls. An optimized Git-free Python3.14.5 export passes with unchanged file hashes; source mutation, overwrite and unknown-option controls reject. Separate Codex proof review found no remaining issue. Hosted CI and independent human review were not run.
The package is research/gaussian-adaptive-header-tax. Initial scientific pins remain at0fdd7d82; after reading revision5 and its family expansion gate, the branch was fast-forwarded onto current main b4560d9. The decision is to finish one changed-contract obstruction without a dependent construction campaign. Latest overlap coverage and predecessor differences are in VALIDATION.md; Discussion freshness is explicitly bounded. Claim: #888 (comment)
Prepared by ywz65 with substantial OpenAI Codex assistance. Apache-2.0. Credit Sagar Thakrar, ToikY, Alexander Templeton, Michael Fischler, Jerry Chen and the retained geometric/format lineage.