Independent verification: complete U8 terminal-cone census (no new kappa)

[ToikY]

The fixed compensated U8 prefix has no helper with a smaller terminal frame under monotone equal-common-frame invertible ADD/nonzero SCALE cleanup on the same arbitrary dirty registers. This adds one isolated research directory, independently certifying all 504 exact endpoint cones, including the 126 existing low-ended helpers. It is an independent finite verification / scoped negative result, with no new kappa.

For each helper q the certificate joins its end-B frame, exact inverse-row support frames and dirty-column support frames. Every joined subspace equals its current endpoint. The row/monotonicity test alone closes 496; the dirty-column condition closes the remaining dimension for helpers 347,349,359,361,370,371,372,373. Current and necessary widths remain {4:80,5:32,7:54,8:122,9:216}.

The two implementations use chronological Fraction rows versus right-composed integer/dyadic columns and exhaustive 512-vector GF2 subspaces. Both reconstruct compensation, the 12913-gate prefix, all 728 arbitrary-input endpoint columns and exact inverse identity; every support/frame record agrees. The written growing-high-frame-subsystem invariant states the precise cleanup hypotheses.

Reproduce with Python >=3.10:

python3 -I -B research/u8-terminal-cone-census/verify.py

Expected: PASS_EXACT_INDEPENDENT_U8_TERMINAL_CONE_CENSUS.

Validation: independent census and static review; all 504 valid endpoints and 4186 proper basis-deletion rejections; eight actual row-only false admissions; four reproducible semantic properties plus six separately executed semantic mutation rejections; actual corrupted-input/output-preservation/source-closure/false-certificate controls; normal and optimized interpreters; committed minimal-directory archive replay in an empty location; all 24 Git blobs and own-fork tree matched; selected-record check at the pinned base; whitespace check. Full make verify and cold selected replay were not rerun for this isolated research addition.

COST.md replaces the provisional single-final-climb screen with the actual split suffix and a favorable all-728 one-jump relaxation, returned-width idle accounting and complete recurrence obligations. It does not certify a numerical no-gain bound. Cheaper tails at unchanged endpoints, changed prefixes/end-B frames, additional storage or a different cleanup/compiler interface remain open. No native construction, global optimality, runtime gain, human peer approval or full multiplication theorem is claimed.

Source base: 0076643. Public head: 9892e3e. Exact tree: 795b44f84b44e57671ed4200440debfba3b6e15a. U8 raw payload: 090fd574747fbf9628e70cb9beb792732914cfa52e1df147579fe4dbccc68c5a. Historical refreshed main bbc600d selects merged #942 at the already known tied kappa; retained U8 inputs match. Sprint seed 51, recursive interfaces, complete 504-helper domain and deterministic stopping rule. Bounded overlap refresh includes #974, with explicit source/coverage limits.

Credit the inherited PR591/604/635 criterion, icekylinx, Jeremy Kothe's #869/#870 U8, @navinor's #864 unbundled FULL-only X4 cone test, and the #890/#942 lineage. This is an independently certified U8 extension, not a new cone method or first X4 obstruction. Adjacent #974 optimistic deletion/headroom pricing is credited and distinct from the complete endpoint census/returned-width recurrence.

Apache-2.0. Substantial OpenAI Codex assistance, including independent agent implementation/review; no independent human review claimed. Public receipt derivatives replace local filesystem/machine metadata with portable markers and preserve hashes of the full private originals.