Research: exact asynchronous P104 carrier bound across 7,168 decoders

[aliromman]

The P104 decoder saves eight COPY ranks, but its nonzero endpoints still need a delivery word. This scoped negative result extends PR #1071 from one decoder and a common read order to all 7,168 mixed frame-pair decoders, with independent target orders, extra frame directions, and paid downward moves.

Review files: Proof and scope · Evidence · Source pins and credit.

Every decoder has the same cube support family. Exact antichains and chain covers give width 32, or 26 after any one term is removed. The written terminal-read theorem gives

L >= q + 2 max(0, width(F_K) - P_K).

Here P counts continuous fixed-term delivery paths, including the eight seeds; q counts terms whose survivor line is lost in a frame move; K contains the remaining terms; and L is excess frame-move rank. Thus P <= 26 forces at least two extra ranks. The path count is not peak memory, and the chain covers do not construct a legal schedule.

Two exact moment engines show that two extra ranks per call already exceed both the base PR #942/T37 and refreshed PR #1042/T16 budgets, even at price one per rank. This implication requires the remaining paid moment to retain or exceed the corresponding PR #968 P104 knob profile. The proof does not establish that cost premise for every new word. Term mixing, different COPY endpoints, larger path banks, and savings elsewhere remain open. No new kappa or physical supplier is claimed.

Only research/p104-asynchronous-carrier-bound/ is added. The exact base is abdc6a7002abdbcd9e21bfc5e1a795784deacfdf. Source hashes, the refreshed selected record, proof, nine exact certificates, failed attempts, and the execution receipt are included. The selected frontier and upstream/ are unchanged.

Validation:

python3 -I -B research/p104-asynchronous-carrier-bound/verify.py
python3 -I -B research/p104-asynchronous-carrier-bound/independent.py

Both pass. The separate checker constructs the roots and all 896 by eight dual partitions without importing the primary checker or PR #968. The primary check also proves that the reflection orbit equals the complete 2,025-frame set. Seven controls, an optimized relocated run, an actual changed-source rejection, and the base selected-record check pass. Full supplier replay, repository-wide regeneration, hosted CI, and Lean were not run.

Credit PR #717 and PR #968 for the decoder model and family, PR #1071 for the delivery question, PR #1077 for the distinct coefficient-field floor, and the PR #942, PR #1042 and bit supplier lineages. The final overlap scan covered open PRs through PR #1120; PR #1099 accelerates the earlier enumeration and does not duplicate this scheduling theorem. See NOTICE.md for attribution and SOURCES.json for pins. Prepared for Ali Romman (@aliromman) with substantial OpenAI Codex assistance. Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at 9f7c0679d64bab954b7161d8586dc626a59b92ee.

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

Reviewed scope: All 7,168 mixed P104 decoders share a support-poset obstruction; asynchronous path lower bound requires fixed-term carriers and the explicit retained-cost premise.

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.