Research/seed42 decoder

[CubeJerry]

Change and mathematical scope

PR785's nonlinear Hurwitz copy floor excludes input-dependent supports. This research note / scoped negative result proves that a public prefix-free routing header preserves the floor when every header bit pays full-space rank two and payloads retain explicit additive per-bit pairing pricing:

E[2 × header length + payload charge] >= sum_t demand_bits.

The proof conditions the predecessor's transcript injection on the header and pays its information cost. It allows nonlinear encoding, input-dependent source/reader supports and widths, and variable-length prefix-free headers. The bound is sharp; it is an expected-cost and hence worst-case statement, not a pointwise one. Under the additional inherited Dfc accounting, even granting every other expense zero leaves D/T <= -40b at every stage count. No new kappa or physical supplier is claimed.

The package also exhausts all 65,536 Boolean headers on two mate pairs: exactly 30 nonconstant headers attain cost four, including 16 nonlinear ones. They are precisely one pair's parity XOR an arbitrary Boolean function of the other pair. Every attaining header includes explicit two-source-bit decoder witnesses. A separate conflict-graph implementation independently reconstructs that witness family.

Only research/hurwitz-adaptive-routing/ is added. Base: f567884. Selected PR799 and upstream/ are unchanged. Credit Douglas R. Colkitt's PR703 (358383e2f1b0f292d4d6eb897c06fd8558a4f5e6) for geometry/charges/transversals and Alexander Templeton's PR785 (83e78085ae9c110a34bff87e71387292d85e47c0) for the fixed-support nonlinear theorem. Their proofs are retained verbatim with SHA256 and Git-blob pins; no predecessor code is imported. Further lineage is credited in NOTICE.md.

The pricing and Dfc identities are explicit premises. Private/localized metadata, interactive payload relays and a cheaper physical realization remain outside scope. Inherited all-size/compiler, hosting, precision/tape and analytic obligations remain. This is a written argument with finite certificates, not proof-assistant verification of multiplication.

Seed 42, structural decoder track. The local claim records three candidates and the chosen scope; no pinned coordination issue exists. A full refresh covered 695 open PRs through #904, followed by an immediate submission check through #907; both consumed predecessor heads stayed unchanged. The new work specifically addresses the adaptive-support exclusion in PR785/814/888.

Validation

Offline, Python 3.10+ and the standard library:

python3 -I -B research/hurwitz-adaptive-routing/verify.py
python3 -I -B research/hurwitz-adaptive-routing/independent_census.py
python3 -I -B research/hurwitz-adaptive-routing/test_package.py

Expected main marker: PASS_HURWITZ_ADAPTIVE_ROUTING ... optimal_nonconstant_headers=30 floor=10b no_new_kappa.

• CPython 3.12.14: reconstructed 240 roots, all 100 singleton pairings and 45 spans; checked all 1,048,576 support pairs, all 65,536 headers, and attaining decoders.
• Five protocol rejection controls and three independent graph controls pass. Correct-code boundary examples expose free/underpriced headers and free termination; a valid low-cost branch prevents overclaiming a pointwise bound.
• All five package tests pass, including source/receipt/witness corruption and isolated optimized relocation to a path containing spaces.
• A staged Git-blob export passes both checkers under -I -O -B and regenerates a byte-identical receipt.
• make selected-record-check and staged whitespace checks pass. Full supplier/repository-wide suites were not repeated for this standalone research package; no hosted CI pass is claimed.

Prepared for ** @CubeJerry** with substantial OpenAI Codex assistance. Apache-2.0;

[Mister-Meeseeks]

100-PR batch review at 945b3da1f1dd87cebd456b3a0459601b15f7ea8b.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Paid public-header adaptive Hurwitz routing floor in expectation, with nonlinear finite controls; not a per-execution lower bound.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.