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Bound selected BIT control work uniformly across root contexts - #2310
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…ontrol tables Takes the preparation/evaluator handoff in discussion #2304. PR #2310's iterative control evaluator was checked on independently prepared unit tables; this package joins it to PR #2234's actual full-ring selected producer without changing either. The adapter checks the selected request, the exact frozen-field specification and the actual low-class child before building a table, keeps original global slots after unit resets, and binds the fallback child's final original-row permutation and physical atom reversal. A written lemma proves value agreement for every admitted finite Good/Pair/unit-reset chain under the stated producer normal-form hypotheses, and shows that numerical high fields before the last reset need not be prepared. Twelve selected MOVE/COPY/IDLE representatives cover every paid rank 1-7 and 42; 87 fixtures over Z/9, Z/25 and Z/27 give 801 generated- weight comparisons and 12,642 equalities against an independent weighted-elimination oracle. Thirteen controls reject, among others, low-only coefficients, a discarded row permutation and an omitted atom reversal. No mismatch in the correctly bound predecessors; no supplier or kappa change. Adds research/selected-control-table-binding/ only, with the consumed PR #2234 and PR #2310 files copied unchanged under sources/ (credited to Jose Manuel, notices retained). Submitted by @commdata2338 with substantial AI assistance (OpenAI Codex research and implementation; packaged with Claude Code). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG
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Takes PR #2310's released control-work handoff in discussion #2304. For the unchanged selected BIT Good/Pair/unit-reset interpreter and 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; each constant is sharp for the accepted grammar. 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 hypotheses the sufficient preparation envelope becomes O_q(e w^3), hence O_q(w^592), in place of its O_q(w^1800). A conditional compiler estimate only; no child, supplier or kappa change. Adds research/selected-control-request-mass/ only, with four PR #2310 files copied unchanged under sources/ (credited to Jose Manuel). Submitted by @commdata2338 with substantial AI assistance (OpenAI Codex research and implementation; packaged with Claude Code). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG
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I give an explicit control compiler and a root-independent nonchild-work bound for the pending selected BIT caller. This addresses the physical-charge handoff from PR2289/2295. Under the retained complete-stream payload and parking contracts, I derive one
C_q V(n+w)bound across the allowed root contexts.For
w=ceil(e^(17/10000)), the shared Good/FallbackPair evaluator visits at most8e^2nodes per weight. Fixed-size matrix arithmetic and sequential access to local controls give a preparation allowanceO_q(w^1800). The all-integer boundw^1800/q^(w-1) <= 2^1800*1800!absorbs this allowance into both body and high-header fibres, including width one. The compiler keeps arbitrary spectator counters outside ancestry scans. It replaces flattened-prefix address decoding with separate active-source and spectator counters.The implementation uses an iterative stack and charged sequential reads of frozen preparation tables. After a unit reset it retains global field slots. Tests exercise Good→unit reset→Good/Pair, varying dead and live controls, complete small body fibres and stale binding/capture faults. The code tests prepared unit tables; it does not rerun the full selected matrix producers or dispatch the entire recursive payload.
The registered Python 3.12 normal and optimized replays check 82 generated coordinates, full binary request trees through depth10, 2,916 complete body records and 82,680 header fibres. The control model counts 8,775,744 bit reads and 34,737,024 head moves in its main evaluator cases; those counts are not Python timing or a full Turing-machine runtime measurement.
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PROOF.mdsections3–6 for the polynomial envelope, all-width absorption, spectator-counter restriction and parking boundary. I retain the complete physical caller and payload primitives as named dependencies. I claim no new recurrence, moment, exponent, Lean instantiation or full selected-machine verification. The next step is a joined full-ring-preparation/control/payload implementation.Coordination: Discussion2304. I started from canonical main
0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4, and refreshed it before submission. The final text search covered 526 open PRs, 1,019 Discussions and 1,538 local records with complete remote pagination and no warnings. I inspected the relevant formal handoff comments; arbitrary code diffs remain outside coverage.TASK.jsonrecords remaining questions, andSOURCES.jsonpins the referenced interfaces.Jose Manuel (
jmbarrancoml), with substantial OpenAI Codex assistance. I retain credit for commdata2338's descriptor grammar and parking boundary, Ross Richardson's fallback algebra, the selected supplier lineage, the existing stream constructions, and Gareth Davidson's formal results and handoff. I claim no independent human verification.