DONE: PR4100 CRT reservoir placement and coordinate descriptors

[kumagi]

DONE — PR4100 CRT reservoir placement and coordinate descriptors

Contribution: #4174, commit 5fec853f0c048871de3b8098d1e30d4ee19cda23, based on canonical main 12fa8c5c844be21bfefb38a19503fbd867a11244 under priority revision 7.

The scoped proof supplies the placement premise for CRT.md §3 with the actual dense left-child dependencies: nonroot opposite halves, root inactive quarters, mixed ell/ell−1 widths, the integer floor bound, at most 25,600 batches per synchronized switch layer, three mutually disjoint placements and their inverses, and at most d+12 fragments for reconstructing split axes. Arbitrary dirty values restore conditionally on the completed repaired switch's all-address contract. Six width-H exchanges per batch remain charged.

Evidence (Python 3.12.13): ordinary and optimized registered replay passed on 104,864 production descriptor plans / 524,288 active-axis visits; a separate reduced root-axis caller passed all 4,096 dirty addresses, 28,672 single-layer conjugations, 86,016 borrowed-field toggles, forward/inverse composition and six semantic controls. Source pins and commit/source-history preflight passed. A deterministic source export passed integrity checking and Git-free optimized replay without modifying exported bytes; corrupt predecessor bytes were rejected.

Limits: the large run is descriptor verification, not payload execution. The finite fixture is a single root-axis projection with ideal completed-switch endpoints, not a raw compact-word replay. No complete fixed-tape control evaluator, ordinary-callee implementation, tail branch, sorting tariff, precision theorem, full CRT/multiplication theorem or new κ is claimed. No selected record changed; no PR was merged or another contributor's work closed.

Next question: bind these descriptors to the actual E(p,ell) evaluator and itemize reconstruction, scans, ordinary exchanges, head returns and erasure before accepting the complete cost. Inspect live handoffs before claiming that separate scope.

Credit: Cinna Davis's PR4100 supplies the audited construction. Vlado Vojdanovski's PR1673 and Jose Manuel's physical support router supply the generic exchange/recoloring predecessors, with the retained compact/routing lineage credited in the package. PR4169's repair audit is complementary context and not an imported dependency. Prepared by Hiroki KUMAZAKI (@kumagi), with substantial OpenAI Codex assistance; new work Apache-2.0. This is not independent human review or formal proof-assistant verification.

Pre-submission refresh: canonical main remained 12fa8c5c844be21bfefb38a19503fbd867a11244. Complete pagination covered 295 open PRs (08:59 UTC) and 2,695 Discussion records (09:04 UTC), with no newly competing placement scope found. This is an overlap search, not proof of novelty.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "uniform-transfer-audit",
  "scope": "PR4100 CRT reservoir allocation, dense dependency omission and coordinate descriptor reconstruction",
  "base": "12fa8c5c844be21bfefb38a19503fbd867a11244",
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/4174"
}

[ToikY]

DONE / RELEASED — conditional CRT last-K sequential lowering, following PR4174’s open tail obligation.

PR: #4187
Exact head: 45fc075
Base: 12fa8c5; priority7 / uniform-transfer-audit.

Scope: an explicit fixed-tape two-slice lowering of CRT.md §4. Given the uniform numerical evaluator, omitted complete H-bit suffix and paid width-one interchange, each target uses exactly M/2^(H+1) preparations; at most K targets cost O(VK). The 13V coefficient covers middle-stage payload actions only. Evaluator/counters/markers, ordinary exchanges and owned-intermediate cleanup are separately charged; full visited space includes the V-bit streams and callee workspace.

Evidence: six normal/optimized registered commands passed locally and from exact committed Git-free bytes. Primary:4,328 Boolean/layout cases over252,060 dirty endpoints. Retained-source control projection:4,096 dirty addresses/seven layers; it is suffix-only transport, not full production three-reservoir placement. Separate oracle:2,164 cases/1,209,888 address columns. One-bit payload control:15,016 cases/119,440 records. Semantic/admission/tariff controls detect their intended faults. Exact source history and all18 committed input/package byte bindings passed; all15 remote PR blobs match frozen bytes. Hosted run39419635034 passed on this exact head; decoded logs confirm all six commands, and the unchanged-input step passed.

Remaining: actual uniform E evaluator and complete tariff, paid ordinary callee/owned output, production placement and exceptional-target classification, compact repair integration, precision and complete CRT/multiplication theorem. A useful next step is a literal fixed-inventory control-array scan bound; the present callbacks do not certify it.

Credit: Cinna Davis’s PR4100 (337d049) supplies the original exchange, transformed control and suffix amortization. Hiroki KUMAZAKI (@kumagi), PR4174 (5fec853), supplies placement/split-coordinate context; PR4169 (835c356) is complementary repair. Complete retained NOTICE lineage preserved.

Current-main and live overlap refreshed before submission; 308 current open/draft PR bodies (including the newly posted, distinct F3 connector PR4189) plus current handoffs/focused last-K Discussion search, broader coverage partial. No new κ, merge, frontier change or closure of others’ work. Maintainer edits disabled. ToikY with substantial OpenAI Codex assistance; separate-agent review is not human/formal-kernel acceptance.

[ToikY]

DONE / RELEASED — uniform sequential-arena Beneš compiler/query component.

PR: #4192
Exact head: 519d811
Canonical base/current main:12fa8c5c844be21bfefb38a19503fbd867a11244; priority7 / uniform-transfer-audit.

Established: for a canonically encoded N=2^h permutation,1<=h<=p, a fixed-inventory flattened arena program returns the exact retained source tables and an owned queried bit, preserving source/output and clearing private work. The written lowering proves O(N³(p+2)^7) time and O(N(p+2)^3) visited space, with exact record count N(h²+3h+1) and access count N²+2Nh²+(37Nh−35N)/2. Every logical get/put makes a full scan and head return. Output roles are reused after consuming/clearing the previous owned result.

Evidence: primary49cases/284endpoints/1,260queries;15,984logicalaccesses and3,583,480record scans. Batched contiguous tape macros agree with expanded one-cell execution. A separate preimplementation FIFO oracle passes40,394permutations/324,452endpoint columns/1,630,756controls; a hash-pinned direct comparison passes37cases/848queries. Six registered normal/optimized checks pass locally and from exact committed Git-free exports. All21 package/input bytes and source ancestry pass; all18 remote PR blobs match frozen bytes. Hosted run39424181200 passes on this exact head; decoded logs confirm all six registered commands and the unchanged-input step passed. The exact review helper referenced by the cost receipt is retained; its optimized replay passed. The original17 proof/algorithm/test/metadata files are byte-identical to the first publication.

Scope boundary: executed tape traffic is arena/key/input/output evidence. Canonical header decoding and bounded scalar/index/compare microcode are paid by the written construction, not an emitted complete transition table. Finite action totals are model invoices, not billions of individually executed microinstructions or measured cost constants.

Remaining: permutation construction, full CRT reconstruction/modular inverses, transported descriptors, macro inverse keys, complete E evaluator, production placement, ordinary callee, precision/native/outer theorem. The current finite global inverse table is not a cost certificate. Next useful task is an actual caller composition with explicitly shared mixed-width rows and correct endpoint-only padding validity, before claiming full E.

Credit: Cinna Davis PR4100 (337d049) original compiler/full-scan proposal; Hiroki KUMAZAKI PR4174 context, Douglas Colkitt/OpenAI framework, complete retained NOTICE lineage. This adds an explicit component lowering/audit, not a new Beneš mechanism.

Main and overlap refreshed before submission:309 open/draft PR bodies, current hub/4173 and focused evaluator Discussion search; broader coverage partial. No new κ, selected-frontier change, merge or closure of others’ work. Maintainer edits disabled. ToikY with substantial OpenAI Codex assistance; separate-agent review is not human/formal-kernel acceptance.

[ToikY]

DONE / RELEASED — explicit declared-width CRT shared-row caller.

PR: #4195
Exact head: 19cf7a0
Canonical base/current main:12fa8c5c844be21bfefb38a19503fbd867a11244; priority7 / uniform-transfer-audit, refined scope4600c179be2d8ba14466.

Established: an explicit global/local row map for h_i∈{ell−1,ell}, including two genuine short-axis idles with no target or table query, and a whole balanced-tree caller on every padded tuple. Declared widths remain explicit; only unchanged left-child offsets are frozen, current target values remain live. The written argument quantifies the endpoint and inverse: reverse tree levels and global rows using the same positive-offset tables. Existing all-active-target omission, compact inverse and placement are predecessor results, not newly claimed here.

A genuine caller (7,3), widths(3,2), input(1,1) visits invalid intermediate target3 and ends(1,2). Gating microscopic switches on current target validity instead gives(1,3). This is a control against an incorrect lowering, not a predecessor bug. The finite helper’s minimal-width API boundary and globally-invalid-but-moving tuples are documented separately.

Evidence: primary16,480 padded states/229,984 forward row checks/426,400 target toggles/32,960 literal idle checks. Separate preimplementation FIFO/brute scaled-CRT oracle exhausts16,448 padded tuples. Pinned crosscheck covers166 states/3,064 rows/510 decoder comparisons/648 idle specifications, including supplied ell=4 all-short and singleton identity. Six normal/optimized registered checks pass locally and from exact committed Git-free exports; all24 package/input byte bindings and declared source history pass. All21 remote PR blobs match frozen bytes, and19 review/helper hash references close.

Hosted run39427965417 passes on this exact head; decoded replay-job118646757850 logs confirm all six commands and the unchanged-input step passed.

Remaining: full uniform E evaluator and complete CRT arithmetic/descriptor tariff; production reservoir/exception integration, actual compact repair/ordinary callee, precision/native/outer theorem and human/formal-kernel acceptance. Canonical logical caller only; no tape cost or physical macro execution. A complementary bounded task is the separate ordered dense-guard mask scanner; check live overlap before claiming it.

Credit: Cinna Davis’s PR4100 (337d049) CRT/network construction; Hiroki KUMAZAKI (@kumagi) PR4169 (835c356) and PR4174 (5fec853) existing omission/inverse/placement; Douglas Colkitt/OpenAI and complete retained NOTICE lineage. Substantial OpenAI Codex assistance, including separate-agent oracle/proof reviews, not independent human review.

Main and overlap refreshed before submission:312 open/draft PR bodies plus current hub/4173 and focused CRT Discussion search; broader coverage partial. No new κ, frontier change, merge or closure of others’ work. Maintainer edits disabled.

[ToikY]

DONE / RELEASED — literal admitted-stencil CRT dense-guard scanner.

PR: #4201
Exact head: 4f49743
Base/current main:12fa8c5c844be21bfefb38a19503fbd867a11244; priority7 / uniform-transfer-audit, refined scope0593fcf1b94f3cd8f1be.

From an admitted ordered fixed-alphabet stencil of L cells, the marker-driven three-role program enumerates every M=2^L address, emits the owned BAD mask, preserves input, blanks private counter data/right marker and returns all heads. The written proof gives exactly8ML+15M+13L+18 cell/head actions andM+2L+6 visited cells. Finite-control/finite-alphabet bit-machine lowering adds a parameter-independent constant factor. O(ML)=O(V) requires the source’s L=Theta(p),R=Theta(p),V=MR premises.

The geometry/threshold/stencil producer and admission path are explicitly UNPRICED host adapters. No E callback is part of classification. This is the supplied-stencil detector, not a complete production caller. Predicate projections are not full reservoir execution; parity, inactive digits and spectators remain arbitrary.

Evidence:49,408 complete source addresses and6,525,207 literal actions, plus all-SKIP smallest counters. Separate preimplementation oracle:49,152addresses/196,608 parity and spectator toggles/12 boundaries. Pinned crosscheck:all49,408 masks plus181 generic stencils/1,300addresses. Separate machine-cost checker:14cases/2,058addresses, with an underbilled READ fault that preserves semantics/ownership but fails the invoice. Actual controls detect wrong threshold strictness/significance, unadjusted whole-K guards, skipped counter bit and omitted owned-output return. Eight normal/optimized registered checks pass locally and from exact committed Git-free bytes; all24 package/input byte bindings and declared source history pass, all21 remote blobs match frozen bytes and21 review/helper hash references close. Both reviewers independently checked the required README heading-only addendum; primary scientific code, proof and RESULT.json remained unchanged.

Hosted run39433438366 passes on this exact head. Decoded replay-job118665637413 logs confirm all eight registered commands; the unchanged-input step passed.

Remaining: uniform charged stencil production/admission at transported descriptors, complete E/arithmetic/table work, exception extraction/keys/sorting/reinsertion, payload routing/repair, ordinary callees, precision/native/outer composition and independent human/formal acceptance. Smallest next step: implement one actual encoded stencil producer and bind its mask consumer, pricing every read, transfer, return and erasure.

Credit: Cinna Davis PR4100 supplies the original predicate and ordered-scan proposal; Hiroki KUMAZAKI (@kumagi), PR4169 at835c3563ee7ede8ceaf329ede7372e50f7823136 and PR4174 at5fec853f0c048871de3b8098d1e30d4ee19cda23, supplies repair/placement/descriptor context with tape tariffs open. Douglas Colkitt/OpenAI and complete retained NOTICE lineage preserved. Substantial OpenAI Codex assistance, with separate-agent semantic and cost reviews, not independent human or formal-kernel review.

Final pre-submission refresh covered316 current open/draft PR bodies, current hub/4173 and focused dense-guard Discussion search; broader coverage partial. Frozen task metadata retains its315-body checkpoint; the added BIT COPY PR4200 is distinct, as are4197 forests and4198 Stein generators. No new κ, merge, selected-frontier change or closure of others’ work. Maintainer edits disabled.

[ToikY]

CLAIM — unary one-target CRT geometry → paid stencil → retained mask consumer (expires 2026-10-20 16:03 UTC).

Taking PR4201’s explicit encoded-producer handoff at head 4f49743a9df0cf7501cdc62bd5707a122fa071e9. Canonical main 12fa8c5c844be21bfefb38a19503fbd867a11244, priority7, uniform-transfer-audit refined to one actual encoded r=1 boundary. Six protected unary fields G,H,K,Y,J,B, with G≥1,H≥G,K≥G+4,Y≥J+K,J,B≥0; produce the ordered stencil for target J, then consume it with the unchanged literal scanner. The finite-alphabet fixed-role program must pay admission, arithmetic, threshold construction, transfers, returns and private erasure; input encoding from binary/global transported descriptors remains open.

Success: a written uniform bound plus independent finite source-predicate/oracle/traffic checks and actual semantic/ownership/tariff controls. Stop at this producer/consumer component; no complete E/CRT/outer theorem or new κ. Complete obligation ledger: supplied-stencil scan predecessor-proved; this unary setup under construction; binary/global descriptor production, many-target composition, extraction/keys/sorting/reinsertion, payload repair, ordinary callee, precision and complete native/outer admission UNKNOWN. Narrow continuation is justified because it replaces an explicitly unpriced input adapter with actual charged tape actions; no downstream construction campaign follows from it.

Overlap checked:322 open/draft PR bodies at15:09:22UTC, fresh #1166 and this canonical thread; no matching active producer claim found. Broader closed/code/Discussion coverage partial. Credit Cinna Davis PR4100 for predicate/ordered scan, Hiroki KUMAZAKI PR4169/4174 for repair/placement context, and retained scanner lineage. ToikY with substantial OpenAI Codex assistance; separate agents do not imply human/formal acceptance. Maintainer edits disabled; no merge/frontier change.

[ToikY]

DONE / RELEASED — this claim is complete. Result: PR4208, exact head fb1f3c8. Canonical verified handoff, scope, evidence, remaining obligations and predecessor credit: #4173 (comment) . All eight local/committed Git-free/hosted checks pass. Unary one-target interface only; binary/transported/many-target/full E/outer work remains open. No new κ, merge or frontier change; maintainer edits disabled.

[ToikY]

DONE / HANDOFF — paid unary one-target CRT stencil producer.

PR: #4208
Exact head: fb1f3c84535f3e5138bd07e7ed2f211f08fc296d
Canonical main/base: 12fa8c5c844be21bfefb38a19503fbd867a11244, priority7 / uniform-transfer-audit refined to PR4201’s open producer boundary.

Established: an actual marker-driven finite-alphabet program takes six protected unary geometry words G,H,K,Y,J,B_back, implements syntax/inequality admission and threshold construction, and produces the exact one-target stencil consumed by the unchanged PR4201 scanner. For all admitted G≥1,H≥G,K≥G+4,Y≥J+K,J/B_back≥0, setup is exactly 33H+25K+38Y−6G−J+12B_back+335 <=63L+335, L=2H+Y+B_back. Complete producer+scan is at most 8ML+15M+76L+353, M=2^L, with seventeen fixed roles and at most M+7L+42 visited cells. All private data/END markers are blank and heads return; inputs remain protected. Stencil and BAD mask are owned outputs requiring consumption/clearing before role reuse. Exact coefficients are in the stated cell/head model; bit encoding adds a constant factor, not a supplied physical transition table.

Evidence: primary145 stencils/138,792 setup actions and four compositions/5,760 addresses; seven clean rejection cases, five actual program faults and two source-auth controls. Frozen pre-code oracle83geometries/433,280addresses plus360larger boundary/parity/spectator cases. Root composition executes all433,280 addresses through the unchanged scanner and both source predicates, with67,748 setup actions/51,658,145 scanner actions and three actual producer/consumer faults. Independent macro proof and14 primitive-instrumented cost cases; the underbilledREAD control has identical final cells/ownership but677 actual versus676 billed actions. Eight normal/strict-optimized commands pass locally and from exact committed Git-free exports; all26 package/input bytes unchanged. All23 public package blobs,21 review-snapshot bindings and declared source ancestry pass. Four minimal untouched predecessor exports reside in own public ancestor 5a41fea466cbeb7839bde864e563e191de47a0f7.

Hosted run39448005504 passed on this exact head; decoded replay-job118719083130 logs contain all eight registered checks and the unchanged-input step passed.

Remaining: this starts at six unary fields for one target. Producing those fields from actual binary/transported source descriptors, many-target ordering/admission, full E/arithmetic/tables, extraction/inverse keys/sort/repair/reinsertion, ordinary callees, precision, physical/native/outer composition and human/formal acceptance are open. It is a predicate projection, not a full production reservoir or CRT/multiplication theorem. Smallest useful next task: pin an actual binary/transported descriptor caller and price its conversion/admission, ownership, head returns and erasure before another family expansion.

Reproduce (CPython3.12 standard library, bounded seconds): python3.12 -B scripts/research_package.py --package research/crt-unary-stencil-producer; source-history/byte preflight: python3.12 -B scripts/check_research_commit.py --package research/crt-unary-stencil-producer --check-source-history.

Credit: Cinna Davis PR4100 original predicate/ordered scan; Hiroki KUMAZAKI (kumagi) PR4169/4174 repair/placement context; PR4201 at 4f49743a9df0cf7501cdc62bd5707a122fa071e9 scanner/atom/host-adapter/proof; Douglas Colkitt/OpenAI and complete retained NOTICE lineage. ToikY with substantial OpenAI Codex producer/proof, code-disjoint oracle and cost-review assistance; separate-agent review is not human/formal acceptance. Live submission refresh covered322 open/draft bodies, current1166/4173; broader closed/code/Discussion coverage partial. No new κ, merge, selected-frontier change or closure of others’ work. Maintainer edits disabled.