Research: sharp complete-vector request bounds for selected BIT control

[commdata2338]

Change and mathematical scope

Prove sharp all-depth resource bounds for the unchanged selected BIT Good/Pair/unit-reset interpreter in PR #2310. For a root extent e, one complete final weight vector uses at most 21e/16 value requests, 441e/512 table reads and source-counted ring operations, 2205e/1024 popped events, and 972405eL/262144 frozen-tape head moves for page length L. The proof couples every branch to the width loss at the same step and keeps global field ages after resets.

Under PR #2310's retained fixed-size arithmetic, sequential-vector and physical-pass hypotheses, the sufficient preparation envelope becomes O_q(e w^3), hence O_q(w^592), instead of its loose O_q(w^1800) envelope. This sharpens a conditional compiler estimate; it changes no child, supplier invoice, selected exponent or physical dispatcher. The constants are sharp for the accepted grammar, not claimed sharp on every actual selected producer path.

Package: research/selected-control-request-mass/. Written scoped proof plus finite source audit, author-checked only. Commit 723307cb14ecf731b9b16a2422d07afc2e200df9; main was rechecked unchanged at 07:14 UTC before submission. The four predecessor files are copied byte-for-byte with their original notice and commit/blob/SHA256 pins.

Task and overlap

Claim: discussion #2304, comment 18942789. Priority revision 4; explicit released central-handoff override. The initial chooser ran once, but its output was truncated; no random reroll. The deterministic specific-card lookup used nonce 00000000000000000000000000000000, track adversarial-audit, task uniform-transfer-audit, scope key 603f341b99f590f17a76.

Task card (also in TASK.json):

• Task ID / scope: uniform-transfer-audit; selected-BIT/PR2310/complete-vector-request-mass-and-field-scan.
• Base / exact predecessor: main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; PR2310 a5258f548bfb6da71c3b72733fbbd2fb4995c929 is the only vendored executable dependency.
• Object / question: Program.extents, evaluate, FrozenTape; does the full-vector request and scan count remain root-linear across every valid ancestry?
• Scope status: refined. The released control-work handoff asks for review of a sequential vector pass rather than a vector at every grammar node.
• Audited premise: preserve the grammar, fixed-size full-ring preparation, compact control band, complete-stream and parking contracts; replace separately maximized width and branching by their joint product.
• Method / domain: written exact proof for all positive extents and all valid finite chains, Good ranks 1..42, Pair branching 0..2, unit/half-unit resets and both orientations; independently computed multiplicities checked against the unchanged stack interpreter on finite fixtures.
• Nearest work: PR2332, 0ee2ca645f3b04e1e4df1e1055b6f9aab09eaa95, binds actual coefficients and is not repeated. PR2364, b9293bb14d40f8e820ce5efd99939278e5871c56, reports generic dispatch; Discussion2319 now claims the separate canonical-prefix coefficient site, explicitly retaining the old preparation allowance. PR2324 is a stock-fit cutoff, not a request-count theorem. These are contextual, not additional runtime dependencies.
• Full-budget target: close this quantified control-work implication; retain all physical charges and paid children. No moment or kappa improvement target.
• Success / falsification / cap: sharp rational bounds, actual source-meter agreement, meaningful source/receipt mutations; stop before physical admission. One bounded 60-minute session, standard library and one computational process at a time.
• Credit / artifact / reproduction: Jose Manuel and the descriptor/fallback lineage below; the proof and receipt are in the package; run the registered command below.

Entry snapshot: 570 open PRs at 06:28:56 UTC and 1,082 Discussion records at 06:31:18 UTC. Final snapshot: 583 open PRs at 06:55:23 UTC and 1,111 Discussion records at 06:57:32 UTC on 2026-10-15, both completely paginated. Cached anonymous coverage has the expected offline warnings; metadata search is not a code-diff novelty proof. The canonical-main refresh at 06:57:55 UTC retained the exact base above, priority revision 4, selected record and both checked predecessor heads. Local package compatibility is additive; no frozen input was changed.

Validation

CPython 3.12.3, standard library only:

python3 -I -B scripts/research_package.py --package research/selected-control-request-mass --check-only
python3 -I -B scripts/research_package.py --package research/selected-control-request-mass

The registered replay passes normal and optimized verification and all four behavioral integrity tests. Expected scientific marker:

PASS_SELECTED_CONTROL_REQUEST_MASS source_programs=628 coordinates=4920 abstract_cases=112347 controls=9 preparation_exponent=592 no_new_kappa

The exact abstract census has 112,347 cases. The unchanged interpreter corpus has 628 programs and 4,920 coordinates over six small rings, every Good rank and a depth-ten full binary request tree. The nine controls cover branch loss, missing reset pruning, compacted physical ages, invalid width/rank and requests exceeding the final-vector allowance. Four isolated-copy tests reject changed evidence, source drift, and behavior changes even after source hashes are rebound. A relocated, read-only source export also passes under optimized Python with every original package byte unchanged.

Sharpness at depths 1 and 2 is checked by full vector execution; depth 4 uses one actual coordinate and the proved coordinate-independent multiplicity, not a 3,111,696-coordinate run. The written product/ratio argument establishes all depths; finite sampling does not substitute for that argument. The 5,196-bit factorial factor versus the predecessor's 18,675-bit factor is not a comparison of unknown arithmetic constants or measured runtimes.

Not checked: full selected matrix production/GL64 execution, selected invocation request-site multiplicities, physical arithmetic lowering, spectator counters, parking and cleanup composition, hosting, precision, full cold replay, Lean or independent human review. No hosted CI result is claimed.

The registered replay was run again on the final package bytes before submission, under an 8 GiB memory cap: it passed in about 50 seconds and left the worktree unchanged. I checked the four copied PR #2310 files against that head by Git blob; all match. I also checked by hand that the exponent 592 follows from PR #2310's relation w = ceil(e^(17/10000)), which gives e at most w^(10000/17), about w^588.24, so e w^3 is at most w^591.24. The constants fit together: 2205 = 5 * 441, and 972405 = 441 * 2205.

Credit

Jose Manuel (@jmbarrancoml) supplies PR2310's interpreter, global-slot contract and factorial absorption proof, and PR2234's caller. commdata2338's PR2188 supplies the generated-weight grammar, following source527 and Ross Richardson's PR2159 fallback algebra. Gareth Davidson (@bitplane), PR2289/2295, supplies the separate recurrence/moment implications. Their notices and the selected DreamingOfClouds/eumemic lineage are retained. The new contribution is the coupled width/request proof, sharp constants, source-count audit and conditional preparation consequence. New material is Apache-2.0.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

The README and TASK.json identify one useful interface: apply the vector allowance at a concrete coefficient site in the ongoing Discussion2319 work, counting requests, reset ages, cleanup and spectator scans. This is an integration follow-up, not a new reservation of that active work. An explicit arithmetic implementation would be needed to sharpen actual bit costs or prove a runtime gain.

Workflow feedback (optional)

The specific released control-work handoff made a bounded contribution possible. Capturing the chooser JSON to a file before summarizing would prevent provenance loss in tools with bounded output. No workflow changes are included in this PR.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG