[ToikY]

Result

NO VERIFIED GAIN. The κ change is exactly 0%. Exact #7244 remains the strongest independently reproduced comparable result at κ = 0.003645372367832. This package proves zero paid savings in a scoped one-input, one-retained-child decoder, even with any fixed finite number of ordinary monomial terms on its source and returned fields.

The full native census has 6,281 MOVEs and 2,602 ordered retained/omitted pairs. For 1,516 pairs the source, retained output, and requested output lie in three distinct chart cosets. The inherited all-column tensor lift makes their normalized row overlaps decay. The exact Gram bound excludes every fixed finite arm count as column multiplicity grows. The remaining 1,086 pairs reduce to a monomial source bypass. Every apparent source depends on the MOVE it would remove. No ordered pair remains unresolved. The whole 17-stage saving is zero and the raw target margin is at most −140.31183525084741, even with free ordinary work, holding, and routing.

Scope and overlap

Canonical e54523517d0f03e58352e647c403a5af3e525a57, changed p104-side-correction scope. The exact #7244 scientific head 4156504fa39efb51c550d218a9b94fe69dbce8f6 and live head 215f67247f395c0e15f5ea3980f6a3e4aed155af share science tree f201bc8b5d1402ca40e7aa419269a58b7724798d. The exact #7113 caller is 07a76c5e2738882c0cb322278e56f6cae3c9885d. Exact bytes and all-column contract citations are included. #7243 bounds paid chart-split capacity on #7161. #7245 concerns fixed whole-output pooling within a coset. Here the targets are in distinct cosets and the source is one exact projective row on #7244. The separate navigation prerequisite reuses the already verified CI documentation commit.

Replay

From a clean checkout with CPython 3.12 and assertions:

python3.12 -B scripts/research_package.py --package research/p104-finite-monomial-decoder-bound

Clean local replay passed. The wrapper authenticates and regenerates the full stock, one-arm availability and tensor receipts, checks two independent scientific audits, and reconstructs all 110,553 paid positions and 22,461 productive targets. The finite control gives a width-one signed success that fails at tensor multiplicity three. All 34 committed-byte, mode and source-history checks and six navigation tests pass. The base controls cover cap-one, corrupt source, duplicate key and forged independent source. Hosted checks are pending. No changed supplier, tape or all-size multiplier replay ran.

Credit and next question

Credit Clear1nsight #7244/#7161, Rohan Arun #7113, #7243/#7245, the canonical Clifford authors and the directed price and deadline work in #7111. OpenAI Codex and subagents materially assisted. Apache-2.0.

A new paid child on multiple independent inputs, changed scalar chronology or an arm count growing with multiplicity changes the contract. Price the complete compatible stock and actual routing, ownership, restoration, precision and tape costs before a prototype.