Verify five rank-four BIT terminals and their fixed-controller cost bound

[RossRichardson]

Summary

• Construct an exact BIT word with 433 width-eight and five width-four dirty helpers. The twenty removed query ranks also remove twenty helper-progress ranks, so the local reduction does not create free global capacity.
• Prove that this word cannot reach b >= 0.002 under its inherited controller, for every odd arity and recursion depth, even with fractional owners, extra full-progress helper stock and free omitted costs.
• Add one isolated package, bit-five-rank4-terminals, containing the word, exact terminal charts, proofs and bounded replay.

Scope and limits

Finite exact checks cover all 660 persistent input columns, both inverse orders, decoded integer source/helper restoration, the public Boolean shear and private cleanup. Physical helpers retain their stated residual frame operations. The all-input stream and all-odd-stage cost conclusions are written proofs, not formal-kernel certificates.

The original exponent target is ruled out only for this fixed histogram, chronology and full-progress auxiliary-stock contract. Coordinate counts are not native payload/tape costs. Changed controllers, partial-progress stock, native hosting, rounded-child cleanup, physical storage/tape costs and joint outer assembly remain open. No new kappa, universal BIT lower bound, selected-frontier change or full multiplication theorem is claimed.

Test plan

Evidence is bound to publication head c01f97ecfc7fa64847f6abd8f7b231e1df8c7b70 unless explicitly historical.

• python3.12 scripts/research_package.py --package research/bit-five-rank4-terminals — fresh registered normal and optimized replay; exact word/charts, rational moment enclosures and separate integer-power controls.
• python3.12 -B scripts/check_research_commit.py --package research/bit-five-rank4-terminals --check-source-history — committed bytes and available source history.
• Authenticated earlier Git-free export replay; reused evidence for unchanged mathematical files, with a fresh registered replay after the attribution edit.
• Separate AI mathematical and overlap review; no independent human or formal-kernel review claimed. Public independent checker and review are included under moment/independent/.
• Automatic Registered research packages CI passed at this exact head, including registered replay and unchanged committed inputs.

Python 3.12 and the standard library suffice. No private checker or external local path is required by the replay.

Sources and credit

Scientific base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90; exact inputs and provenance are in SOURCES.json, LOCAL-PROVENANCE.json and the preserved source manifests. This PR is the canonical public record for this contribution.

Retain Ali Romman's R438/#1043, Sagar Thakrar's transported/hosting lineage, cheesegrader's #540 framework, #589 hosting, and the earlier #1256 retirement and #1194/#1311 semantic-prefix work. Sagar Thakrar's #3948 at its pinned head already gives the generic idle-window formula, rank-42 nine-stage cap and no-fusion observation. Those facts are credited prior work; the added result is this five-terminal construction and its candidate-specific cost obstruction.

Apache-2.0. Substantial OpenAI Codex assistance, including separate AI mathematical review.