Research: bind actual selected BIT matrix preparation to PR #2310's control tables

[commdata2338]

Change and mathematical scope

This takes the preparation/evaluator handoff in discussion #2304. PR #2310's iterative control evaluator was tested on independently prepared unit tables; this package joins it to PR #2234's actual full-ring selected producer, changing neither, and checks that the compiled tables give the producer's generated child weights.

• Adapter: before building a table it checks the selected request, the exact frozen-field specification and that the descent is one of the actual low-class children PR Close selected BIT recursion with an elementary interchange base #2234's residual_plan emits. It keeps original global slots after unit resets, and for a fallback (pair) child it uses all 128 entries of the full unweighted elimination's terminal diagonal with the final original-row permutation and the physical atom reversal: child(i) = d_j b(pi(j), t) / b(j, t), with t = i or f-1-i.
• Lemma (PROOF.md): compile_chain followed by the unmodified PR Bound selected BIT control work uniformly across root contexts #2310 evaluate returns the same unit weight as PR Close selected BIT recursion with an elementary interchange base #2234's generated expression for every valid final atom index, on every admitted finite Good/Pair/unit-reset chain, under the stated producer normal-form hypotheses. It reads only coefficient tables at their live global slots, never the current fresh matrix or unused stock, and restores the table head. Numerical high fields at and before the last reset need not be prepared.
• Finding: no mismatch between the correctly bound predecessors. Three binding requirements are necessary, each shown by a concrete modulo-9 failure: full-ring rather than low-only coefficients (8 versus 2), the final original-row permutation (8 versus 1) and the physical atom reversal (2 versus 8).
• Status: an author-checked conditional structural proof with a finite certificate. No child-count, moment or exponent change; no supplier or κ change.

Remaining obligations. The producer normal forms are hypotheses here, not proved. There is no exhaustive GL64 or high-lift census, no complete payload dispatcher or selected payload execution, no physical work, parking or cleanup implementation, no instantiation of PR #2310's runtime bound, no supplier cold replay, no formalization and no independent human review.

Task and overlap

• Task ID / scope key: uniform-transfer-audit (603f341b99f590f17a76), refined to selected-BIT/PR2234-full-ring-to-PR2310-table/actual-label-mixed-reset-binding. Chooser nonce 1666912cb72ea23ea7840a7d03438b89, track adversarial-audit, priority revision 4; the card was the chooser's third suggestion, taken for FINDING / HANDOFF: uniform control work for the selected BIT caller #2304's live, named handoff (passing over selected-stock-envelope, whose arithmetic and rank-42 descriptor cases are covered, and the less concrete supplier-boundary-audit). No reroll.
• Base and exact heads: base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, rechecked unchanged at 05:37 UTC; contribution 0ee2ca645f3b04e1e4df1e1055b6f9aab09eaa95. PR Close selected BIT recursion with an elementary interchange base #2234 d047ef86fbc5b1614d3d8e2b8d3441413beab73f and PR Bound selected BIT control work uniformly across root contexts #2310 a5258f548bfb6da71c3b72733fbbd2fb4995c929, both Jose Manuel's and both unchanged at submission. Their consumed files are copied byte for byte under sources/ with their notices; I checked all twelve against the two PR heads by Git blob. Main inputs are pinned in SOURCES.json.
• Scope status: refined: sampled unit tables are replaced by the actual producer's output, and the earlier descriptor identities are hypotheses, not new work.
• Nearest work: PR Bound selected BIT control work uniformly across root contexts #2310 owns the control grammar and uniform-control argument, PR Close selected BIT recursion with an elementary interchange base #2234 the producer and recursive closure; this checks the connection between them. This account's PRs Lower the selected BIT rank-42 residual to one contiguous weighted child #2160 and Selected BIT: generate a mixed good/fallback child-weight descriptor #2188 supply the earlier normal form and mixed descriptor. Gareth Davidson's PRs Formally audit the selected BIT stopped-recurrence implication #2289 and Discharge the selected BIT fractional-moment premise in Lean #2295 formalize the recurrence and moment premises. Jose Manuel's discussion #2319, opened a minute after this claim, covers joined physical dispatch with completed children on a generic two-dimensional caller; this package is limited to coefficient binding on the actual selected requests and leaves dispatch there.
• Claim and final check: the claim is in discussion #2304. A final overlap check of open PRs and Discussions (complete pagination), plus a live check of newer PRs, found no other competing work.

Validation

python3 -I -B scripts/research_package.py --package research/selected-control-table-binding --check-only
python3 -I -B scripts/research_package.py --package research/selected-control-table-binding
python3 -I -B research/selected-control-table-binding/verify.py

Linux x86_64, CPython 3.12.3, standard library. The registered replay (normal and optimized, plus three artifact-integrity test groups) was run again on the final package bytes before submission, under an 8 GiB memory cap: it passed in about 3 minutes and left the worktree unchanged.

PASS_SELECTED_CONTROL_TABLE_BINDING fixtures=87 coordinate_equalities=801 independent_equalities=12642 controls=13
PASS_REGISTERED_RESEARCH_PACKAGE research/selected-control-table-binding outcome=completed

• Twelve actual selected MOVE/COPY/IDLE representatives cover every paid rank 1-7 and 42. Eighty-seven fixtures over Z/9, Z/25 and Z/27, including mixed paths with resets and nonconstant parents and a width-one root, give 801 generated-weight comparisons. An independently written normalized-elimination oracle, which builds the raw-label projector without the producer's split basis, gives 12,642 local equalities across 39 dense cases. Catalogue decoding and incoming parent descriptors are reused and credited.
• Thirteen controls reject compacted reset slots, swapped field specifications, capture of the current fresh matrix, a wrong same-rank request, an orientation or reset absent from the macroplan, a pair event on a good class, access to unused stock and a nonunit good pivot, besides the three modulo-9 failures above. A dead high-field change leaves tables and values unchanged.
• The integrity tests reject corrupted sources or blobs and altered typed receipts before import. The fixtures are an explicit bounded family, not an exhaustive census, and no large payload is executed.

Credit

• Jose Manuel (@jmbarrancoml): PR Bound selected BIT control work uniformly across root contexts #2310's evaluator and handoff and PR Close selected BIT recursion with an elementary interchange base #2234's producer, whose files are reused unchanged. Ross Richardson (@RossRichardson, PR Certify the local-ring BIT fallback and common schedule #2159): the fallback algebra. This account's PRs Lower the selected BIT rank-42 residual to one contiguous weighted child #2160 and Selected BIT: generate a mixed good/fallback child-weight descriptor #2188: the normal form and mixed descriptor.
• Gareth Davidson (@bitplane, PRs Formally audit the selected BIT stopped-recurrence implication #2289 and Discharge the selected BIT fractional-moment premise in Lean #2295): the recurrence and moment formalizations behind the physical-charge handoff. The source527 and selected supplier lineage retained in NOTICE.md.

New work is Apache-2.0; retained notices are unchanged.

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

See the package README and TASK.json. The smallest useful follow-up, best done with #2319: connect this bound evaluator to one complete controlled-stream coefficient-preparation site, with the actual high-header spectators, inverse cleanup and local work lifetime. A separate formalization could prove the reset and extent induction on the explicit grammar.

Workflow feedback (optional)

• What helped: FINDING / HANDOFF: uniform control work for the selected BIT caller #2304 named the missing connection precisely.
• Friction: the producer and the evaluator represent field age after a reset differently, which took most of the binding work.
• Suggestion: a compiler handoff could link the exact producer function and consumer schema and state the reset-slot invariant.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG