Specialize the encoded BIT coefficient evaluator to every fixed dimension and bound its retained continuation backing

research/fixed-dimension-bit-coefficients/CHECKPOINT.md

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+# Local recovery trail and author verification checkpoint
+
+Base: e54523517d0f03e58352e647c403a5af3e525a57.
+Branch: research/continuous-20261110-bit-history.
+Package: research/fixed-dimension-bit-coefficients.
+Initial WIP commit: aaca699b. It was explicitly unverified and not offered for
+publication. The later author checkpoint below supersedes its draft status;
+no selected result is updated, and independent review is a separate gate.
+
+Implemented: 17 authenticated specialization sites over the four #6903
+encoded numerical modules; one exclusive four-tape continuation Workspace;
+explicit source-arena/record historical bounds; separate small-block modular
+oracle and pre-guard demand observer.
+
+Executed coverage before this checkpoint:
+
+* N=2,w=1,depth 0: exact coefficient 2; residue/index pending 28/11.
+* N=3,w=2,descriptor GUPG: coefficient 8; pending 59/18.
+* N=65,w=2,depth 0: coefficient 8; all 4,225 field digits read; pending 16,912/11.
+* N=130,w=1,depth 0: coefficient 2; target row 129 crosses the historical
+  multiplier cap; all 16,900 field digits read; pending 67,612/11.
+* Earlier exploratory controls rejected insufficient capacity, a wrong global
+  field code and a truncated field. A GUPG call repeated four times used the
+  same four continuation Tape identities and retained erased backing.
+
+At the initial WIP checkpoint the proof was a draft. Missing then:
+the final registered verifier/receipt, full boundary-control suite, complete
+package metadata/attribution/overlap report and independent review. The
+selected source label generation, root-size map, literal table lowering and
+changing-precision physical bank are explicitly outside the proved seam.
+
+Reproduce one current positive fixture:
+
+    python3 -B research/fixed-dimension-bit-coefficients/check_consumer.py
+
+Next command after completing the verifier:
+
+    python3 -B scripts/research_package.py --package research/fixed-dimension-bit-coefficients
+
+The initial scaffold verify.py intentionally exited DRAFT. That scaffold is
+now replaced by the actual read-only verifier.
+
+## Author verification completed after the WIP
+
+The final registered normal/optimized replay passed fourteen positive cases,
+ten runtime controls and the isolated Git-free three-corruption suite. The
+typed mathematical receipt digest is
+`afd86ba5470b877b6cad58a86fe26a58d98bb7e81129be4f1db47fd1a285a39a`.
+Exact executed commands and limitations are in VALIDATION.md. Added tests
+include N=44/rank43, a halved Unit, a dead earlier global-code mismatch,
+full warm erased slots and normal exclusive Workspace reuse.
+
+The supported entry is Workspace.open. The untouched legacy selected_offset
+wrapper does not pass borrowed stack roles and is outside the contract.
+Review clarified the linear current-handle contract: closed/aborted callbacks
+cannot be reused after a later open, and no physical stale-generation service
+is claimed. This changes the stated scope only; numerical source and receipt
+are unchanged.
+Scientific proof and implementation are frozen for independent review; only
+explicitly reported review fixes should change them. Root coordinates review,
+publication and a separate durable recovery-branch snapshot. No push or PR
+creation is performed by this worker.
+
+Next action: integrate the independent review if it passes, rerun affected
+registered checks and the committed-byte preflight, then let the root publish
+the verified package. In parallel this worker cross-reviews the separate
+encoded-balanced-crt-entry package under the root's Wave-2 assignment.

research/fixed-dimension-bit-coefficients/NOTICE.md

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+# Attribution and inherited scope
+
+New explicit dimension specialization, fixed continuation Workspace, scoped
+source-arena proof, exact checks and package: prepared for @CubeJerry with
+substantial OpenAI Codex assistance. New material is Apache-2.0. A source-aware
+AI cross-review is separate from the author checks; no independent human or
+formal-kernel acceptance is implied.
+
+Jose Manuel (@jmbarrancoml) supplied the binary word arithmetic, matrix
+preparation, records and Good/Pair/Unit evaluator retained through #2697/#2809
+and copied in #6903. This package authenticates and specializes those live
+canonical files, preserving their comments. The complete retained source
+notice is pinned at
+`research/delayed-cover-chronological-fields/numerical/NOTICE.md`; its parent
+NOTICE.md is also pinned. Their source527, commdata2338, Ross Richardson,
+Douglas Colkitt/OpenAI, and earlier word/hosting credits remain applicable.
+
+Ross Richardson's #2835 supplies the first-failed-allocation proof method and
+the credited primitive effects, following Nick Petalas's #2759/#2770/#2778/
+#2781 and Arham Tahir's #2796 lifetime results. No new sharp N=64 inventory is
+claimed. #5404 supplies the distinction between current live arrays and
+retained backing. #6896 proves a separate actual recursive N=64 numerical
+capacity theorem, and #6879 a source-specific ordinary helper space theorem.
+
+The chronological field producer is credited to #6903, Ali Romman's #5829
+whole-high geometry, thu-nmrc's #6719 physical recursion and David Arias's
+#2776 machine lineage. This package preserves the entire format and original
+source labels; it does not claim to have executed its new numerical consumer
+inside that producer's literal ready port. The completed current BIT base
+remains the query-thinned `.0034` lineage, with its actual source generation
+and five foundational assumptions retained.

research/fixed-dimension-bit-coefficients/OVERLAP.md

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+# Scope, overlap and source selection
+
+Scientific base: e54523517d0f03e58352e647c403a5af3e525a57. The orchestrator
+supplied the canonical selected state, live PR snapshots and nonoverlapping
+assignment. The first wave's stratified reserve theorem remains a separate
+package; this package does not import it as an established selected layout.
+
+| Predecessor | Established scope retained here | What this package adds |
+| --- | --- | --- |
+| #6903, delayed-cover-chronological-fields | Generic-N literal field producer; full chronological labels; N=64 numerical join only | Concrete arbitrary-fixed-N specialization of its retained numerical consumer and four-tape reentry contract |
+| #2835, selected-coefficient-capacity-prefix | N=64 closed coefficient pending-demand proof, including warm histories and first failed allocation | Source-site conservative N-parametric demand for the new specialization; no sharp old constant claimed |
+| #6896, recursive-physical-capacity-prefix | Fixed N=64 source numerical inventory across actual recursive cuts | No whole-recursion replacement; keeps actual varying-precision and all historical caller records outside the local theorem |
+| #6879, ordinary-bit-retained-space | Source-bound retained ordinary helper with its local domain | Addresses a concrete coefficient component it leaves open; does not identify that helper with the current `.0034` base |
+| #5404, continuation-retained-backing | Separate historical maxima and concrete continuation role obligations | Explicit actual Workspace reuses four tapes; exact full-prefix and stack bills for this specialization |
+| selected-binary-control and #2697 source lineage | Encoded arithmetic, matrices, Good/Pair/Unit semantics and index operations at N=64 | Seventeen finite-dimension/interface edits, including the separate 128 finite-multiplier guard |
+| #4440/#4470 query-thinned controller lineage | Completed conditional ordinary `.0034` BIT interface | No replacement construction; distinguishes its unspecified huge fixed dimension from the old 64-dimensional implementation |
+
+Source inspection specifically excludes re-publication of the generic peak
+versus history principle, local CLEAR semantics, the raw 54/43 lifetime census,
+whole-high V/L child geometry, and the existing N=64 capacity constants. Those
+results are credited and used only where their exact interfaces apply.
+
+The bounded live overlap lookup included PR searches for `"parametric"
+"Callback"` (the returned #5164 concerned setup rollback) and
+`"N-dimensional" "encoded"` (no matching PR returned). The root also supplied
+the current sprint/PR claims. Absence from these queries is not proof of
+novelty; the concrete comparison is with the source/domain statements above.
+Later merged work must be checked by the publication coordinator before a
+remote branch is offered for review.
+
+The first claim was narrowed from the full `.0034` historical per-tape B₀
+contract: that source-specific mapping is not currently supplied by the
+retained implementation. The accepted scope is the concrete dimensional
+consumer seam and its source-arena proof, with all label/dispatcher/physical
+bank obligations visible. This is partial assumption-directed progress and
+does not assert an unconditional multiplication theorem or a changed κ.

research/fixed-dimension-bit-coefficients/PR-DESCRIPTION.md

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+## Why this is needed
+
+The selected #7000 application reaches a completed `.0034` BIT interface whose
+compiler dimension is large and fixed. The chronological whole-high producer
+in #6903 already handles arbitrary fixed N, but its actual numerical join is
+explicitly N=64. The existing #2835/#6896 capacity theorems also pin that old
+dimension. A generic claim that preparation is finite-dimensional does not
+supply the matching encoded consumer or its retained physical roles.
+
+## Exact contribution
+
+This package authenticates and specializes the four retained encoded
+Callback/Fields/Matrices/words modules with 17 explicit edits for each fixed
+N≥2. Runtime values remain binary words; all N² high digits and original
+global source labels are preserved. One Workspace supplies the same four
+continuation tapes on each closed reentry.
+Only the current live callback handle is valid; closed/aborted handles are
+retired permanently. No stale-handle generation service is claimed.
+
+The written proof establishes exact Good/Pair/Unit and coefficient semantics,
+pending demand of at most `16N²+128` residue and `128` index Words over **all**
+entry residents before the first capacity guard, and explicit full-prefix and
+separate historical-tape bounds. Every admitted descriptor contracts by at
+least `(N−1)/N`. The full local consumer bill is polynomial in w and its actual root
+size; absorption by `q^(ceil(e^.004)-1)` is conditional on a proved `root_size≤e`
+coupling and the actual number of calls per fibre.
+
+Base: `e54523517d0f03e58352e647c403a5af3e525a57`. Exact live-source SHA256 and Git
+blob pins are in SOURCES.json. No predecessor source or selected record changes.
+
+## Novelty and credit
+
+#6903 supplies the generic-N field producer and predecessor module bytes;
+#2835 supplies the noncircular prefix method; #5404 supplies the historical
+backing distinction. #6879/#6896 remain separate source-specific helper and
+recursive results. The new result is the implemented dimensional consumer
+and its precise per-call/fixed-arena history contract, not those earlier
+general principles or an increased N=64 constant.
+
+Prepared for @CubeJerry with substantial OpenAI Codex assistance. Credit Jose
+Manuel (@jmbarrancoml) for the retained numerical source lineage, Ross
+Richardson for #2835, Nick Petalas and Arham Tahir for its lifetime inputs,
+and #5829/#6719/#6903's authors for the chronological whole-high interface.
+NOTICE.md retains the broader source attribution.
+
+## Reproduction and failure detection
+
+```sh
+python3 -B scripts/research_package.py --package research/fixed-dimension-bit-coefficients
+```
+
+Normal and optimized modes compare the complete typed receipt. The exact
+oracle uses signed-permutation determinants/cofactors on dense N=2/3 fields
+and a closed block formula for the larger dimensions. Cases cover widths
+1/2/3, mixed Good/Pair/Unit histories, reversed Pair, inverse offset, leaf
+calls, a halved Unit, erased warm backing and repeated reuse of the same Tape
+identities. N=44/rank43 crosses the old rank guard; N=65 tests all 4,225 field
+digits; N=130 tests all 16,900 and target row 129.
+
+Controls reject wrong chronological labels, truncated fields, actual capacity
+exhaustion, the old 64² reader and rank-42 guard, the separate old 128 multiplier
+guard and fresh continuation tape creation. An isolated Git-free mirror rejects source-byte,
+typed-receipt and pending-budget corruption. Finite examples corroborate the
+written universal proof; they do not exhaust the selected source catalogue.
+
+## Limitations and κ status
+
+**No new κ.** All five foundational assumptions and the selected bound remain
+conditional. The actual `.0034` catalogue/label generator and root map,
+literal finite-table join, arbitrary changing-R/I physical bank and complete
+caller stock/history composition remain open. Entry allocated history and
+all live residents are charged explicitly. This theorem does not turn one
+fixed arena's slot bound into a varying-precision physical bank or erase
+other retained ancestor/producer/payload owners from the full source bill.
+
+The package is a narrowly scoped compiler/ownership enabling lemma. It claims
+no formal-kernel or independent human proof, selected cold replay, complete
+multiplier implementation, or unconditional asymptotic improvement.
+
+## Separate review
+
+A separate worker independently derived semantic and capacity obligations
+using rank-two I-J/3 and permutation projectors,14 exact generated-weight,
+coefficient and offset calls, and original17-bit labels. Normal and optimized
+checks pass10 finite-dimension boundaries, three actual larger constructors,
+816 footprint comparisons and12 controls. The four actual continuation tapes
+retain complete histories across reentry. The review detects the absence of
+stale-handle generation guards and admits only the clarified current-callback
+linear-use contract. See independent-review/REVIEW.md for source/proof pins,
+independent derivations and limits. No human or proof-kernel acceptance is claimed.

research/fixed-dimension-bit-coefficients/PR-TITLE.txt

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+Specialize the encoded BIT coefficient evaluator to every fixed dimension and bound its retained continuation backing