Research: Fine expansion admission

research/fine-expansion-page-admission/CHECKPOINT.md

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+# Recoverable wave 9 checkpoint
+
+Worker: analytic_join. Track 50/75, approved narrow source-admission pivot.
+Canonical parent: `7c49fe32c55de02c2c873655c804b16e4c3fef0a`.
+Worktree: `/workspace/scratch/a365d332d434/worker-analytic-wave9`.
+Branch: `research/fine-expansion-page-admission-20261109`.
+Package: `research/fine-expansion-page-admission`.
+
+## Completed findings
+
+The source-relative proof admits the actual full-period explicit expansion
+page producer for its stated finite source/precision domain. It proves the
+original-coordinate halo and all multiplicities, coefficient positivity,
+near-unit upper-endpoint acceptance and header/precision guards. It spends
+the existing forward normalizer K_f with final J=K_f-D, reaches the public
+middle's half-disk from actual quarter-disk ingress, and gives the explicit
+component-l1 prefix allowance (12*2^-J+2)2^-q. Gaussian Gamma is unchanged;
+both S factors and outer recovery remain separate.
+
+The declared direct schedule retains all costs. Mandatory per-axis Tile
+writes are Omega(DTq), and the specified full-axis FieldMove route costs
+Omega(Tq log T). This is an admitted slow reference for future grouped-map
+comparison, not a fast production prefix or a general lower bound.
+
+The dimension-changing return adapter is implemented and runs the real
+native words and public codec. It borrows/copies an encoded T Count and
+pays the T-record clock, dummy native input, protected return and cleanup.
+Its prepared q/J format boundary is explicit. No complete expansion
+controller, Tile, coefficient producer or production Fourier was executed.
+
+## Executed verification
+
+- Metadata/source pins: `PASS_PACKAGE_METADATA_AND_PINS`.
+- Registered normal and optimized replay: both
+  `PASS_FINE_EXPANSION_PAGE_ADMISSION`; identical mathematical/native
+  receipts; complete registered run 7.865 seconds on Python 3.12.14.
+- Thirty canonical files, six exact public files, 22 source clauses and
+  21 altered-clause controls authenticated.
+- Exact independent finite evidence: 4,320 headers, 7,557 blocks, 68,013
+  quadratic identities, 288,036 residue multiplicities, 16 positive-lower
+  countermodels, 16 near-unit countermodels, 768 reciprocal/unit cases,
+  240 budgets, four axis layouts and 26 stage invoices.
+- Real native T16/S9 q12/J3 output matches the independent oracle, with
+  maximum component-l1 projection error 3/8192. Protected return, short/
+  long fields, old S record clock, native/count/work aliases, borrowed
+  origins, cleanup and real coarse-grid erasure controls pass.
+
+The first native attempt correctly failed because the fixture tried to
+initialize the marker already owned by a freshly constructed Tape. The
+fixture now erases that marker before initializing; all inherited guards
+and sources are unchanged. `evidence/attempt-1.json` preserves the failure.
+The first successful adapter receipt in `evidence/normal.json` predates
+the final sixth retained public proof; the final source-bound passes are
+in `evidence/registered.json` and `evidence/REPLAY.json`.
+
+## Reproduction and next action
+
+```sh
+python3 -B scripts/research_package.py --package research/fine-expansion-page-admission
+python3 -B scripts/check_research_commit.py --package research/fine-expansion-page-admission --check-modes
+```
+
+After the staged-tree/mode gate, freeze the commit and tree for lead source
+review and publication. The lead owns remote actions; this worker creates
+no upstream PR or external post. The tested base is preserved. Exact source
+dependency commits and hashes are in `SOURCES.json`/`DEPENDENCIES.json`.
+Any final commit identifier is supplied by the containing Git commit and
+the lead's durable recovery manifest, avoiding self-referential file hashes.
+
+Outstanding: independently admitted grouped Broad source/physical cost,
+production scalar/Fourier/native contracts, the opposite transform and
+complete CRT/integer recovery. No selected certificate, full bound or
+foundational assumption is changed. The temporary local worktree is not
+durable by itself; only the lead's verified remote branch will be durable.

research/fine-expansion-page-admission/CLAUSES.json

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+{
+  "schema_version": 1,
+  "scope": "AST source binding only; no projected execution or formal semantic acceptance.",
+  "clauses": [
+    {
+      "path": "research/physical-gaussian-expansion/expansion_geometry.py",
+      "names": [
+        "ProductionBlock",
+        "__init__"
+      ],
+      "sha256": "bc060d1d52efb44004016b7a5390552f9057f492d38304857e50f54f085523d2"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_geometry.py",
+      "names": [
+        "BlockGeometry",
+        "__init__"
+      ],
+      "sha256": "1ea95794efa09125cc12bff37d617ee0590ec7dd718da227a33ca93694e7e9ff"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_geometry.py",
+      "names": [
+        "BlockGeometry",
+        "prepare_quadratics"
+      ],
+      "sha256": "ec7f9e782818eb1dabee90e87a278a778529f696e655bb7e11e236d81e8a4225"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_geometry.py",
+      "names": [
+        "BlockGeometry",
+        "exponent"
+      ],
+      "sha256": "05877b418f6bcfc482d0f8864679cebf4573f0891653293478009e99612443f7"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_records.py",
+      "names": [
+        "compile_frame"
+      ],
+      "sha256": "55bd55077a8e80dac157c347d897ea1e87d7b390ab65e209916f78515de33536"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_tile_geometry.py",
+      "names": [
+        "stencil_bounds"
+      ],
+      "sha256": "6d658a8850f036dbb54ebb48c3838154a9a2f153b156931804aee3bb76cfa284"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_tile_geometry.py",
+      "names": [
+        "compile_tile"
+      ],
+      "sha256": "345fb7d48359c49c9812bea144195987a8f8eb37bd87158a1608237948b3ca4b"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_tile_geometry.py",
+      "names": [
+        "TileGeometry",
+        "__init__"
+      ],
+      "sha256": "81984c23f7c8b129f5a16d7922b153c469311bab5e672a0132ece0222cee4566"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_tile_geometry.py",
+      "names": [
+        "ProductionTile",
+        "__init__"
+      ],
+      "sha256": "36202b5dd3e2519ace31daa4d8476f94140be9f586c058cb66eb4db392f1cb82"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_prepare.py",
+      "names": [
+        "prepare_page"
+      ],
+      "sha256": "85d5305cbab581630de99fe35b7dcb5a2d180aa05c266136f012f0b4e9836a44"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_tile_prepare.py",
+      "names": [
+        "TilePreparation",
+        "run_explicit"
+      ],
+      "sha256": "5650bb2cf73c7599eb2145a60f2f9fa1fac165d414d1e3bc371f17f8bfa416f6"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_tile_prepare.py",
+      "names": [
+        "TilePreparation",
+        "run_production"
+      ],
+      "sha256": "4c0633aedfe97e444882d862edc06684e54a2f2a8c42e0b363a9f9d5994280cf"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_tile.py",
+      "names": [
+        "Tile",
+        "run"
+      ],
+      "sha256": "8f467f2d3bc7a1eb5be0ccd09a0dfd41dfadb9eb893ebd5b99da160095c890c5"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_block.py",
+      "names": [
+        "Block",
+        "scalar"
+      ],
+      "sha256": "20eec59f19402fa84ce02b4d8881e0a619c57f8ea4b7b844f22860a39297afef"
+    },
+    {
+      "path": "research/physical-gaussian-expansion/expansion_block.py",
+      "names": [
+        "Block",
+        "run"
+      ],
+      "sha256": "ef6d60b4132c152b40cd9fc71592d1fc596da335fcbf082866606f200dfd536a"
+    },
+    {
+      "path": "research/physical-gaussian-core/gaussian_exponentials.py",
+      "names": [
+        "Exponentials",
+        "positive_interval"
+      ],
+      "sha256": "fd81d34e25b14fc62ff416d578cfbe916eadc96f292a80fae33c5c7646cfef13"
+    },
+    {
+      "path": "research/physical-gaussian-core/gaussian_exponentials.py",
+      "names": [
+        "Exponentials",
+        "grid_interval"
+      ],
+      "sha256": "2ecc3f807dc07dc2f7394cd87a35ecfffed11ae57af47965959108f1dd8a81d6"
+    },
+    {
+      "path": "research/physical-gaussian-tensor/tensor_moves.py",
+      "names": [
+        "FieldMove",
+        "run"
+      ],
+      "sha256": "c05401dfbfe30d7c5d9798bdf9d88c611f48330a0b16092142f031025d873601"
+    },
+    {
+      "path": "research/physical-gaussian-tensor/tensor_moves.py",
+      "names": [
+        "FieldMove",
+        "stage"
+      ],
+      "sha256": "4f8e859cd7c86f3660e8441af1e5b9aab47102e762a905572f4b8f45b5d6d6e3"
+    },
+    {
+      "path": "research/physical-tensor-crt-sandwich-recovery/sandwich.py",
+      "names": [
+        "Sandwich",
+        "ingress"
+      ],
+      "sha256": "032f585adc3c96ba803a7995a6aaac32670700c1c37ad8d411066ee2c9dc8841"
+    },
+    {
+      "path": "research/fine-expansion-page-admission/retained/boundary_codec.py",
+      "names": [
+        "Codec",
+        "prepare_return"
+      ],
+      "sha256": "f19cc2b50aa92efbf0179f5d547078e1ebfd55cf8ce650d03dc4382e793bdb22"
+    },
+    {
+      "path": "research/fine-expansion-page-admission/retained/boundary_codec.py",
+      "names": [
+        "Codec",
+        "return_component"
+      ],
+      "sha256": "7ead0c8ad320b7782c0fc351242b19490811d4e3003c15b60f02fdac6acfb1d4"
+    }
+  ]
+}

research/fine-expansion-page-admission/DEPENDENCIES.json

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+{
+  "schema_version": 1,
+  "files": [
+    {
+      "path": "research/fine-expansion-page-admission/retained/middle-PROOF.md",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "8db3cc1e98ba295cec4d752478431515e159c34f",
+      "source_path": "research/cached-chirp-cyclic-join/PROOF.md",
+      "git_blob": "2f434e4b55550032656d95b558563c9f5c3df839",
+      "sha256": "1119909d64ed3af1637e039ea1c60ff5457ec987828c8f2a137a93a07155cc6d"
+    },
+    {
+      "path": "research/fine-expansion-page-admission/retained/ledger-PROOF.md",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "76a84e1c4bfa4035e5ee85410dbfc4541f0da168",
+      "source_path": "research/core-group-scale-ledger/PROOF.md",
+      "git_blob": "3e580dee35c9b597d9b66932282fefa4ef92306a",
+      "sha256": "59ee004f3d69e70abf8a7fd82f99312b31d4ad32fed3d6866d61e197177599a4"
+    },
+    {
+      "path": "research/fine-expansion-page-admission/retained/caller-PROOF.md",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "96211247643059ae48af4c7d9dc960034798935d",
+      "source_path": "research/fine-recovery-catalogue-obstruction/PROOF.md",
+      "git_blob": "08a808b09c4a888d27f468f236ba6ca1d7881ac4",
+      "sha256": "0dde51f56eee2c711afa3b5c1e4f783ad0b057b7c206aa931b260c407236dfdd"
+    },
+    {
+      "path": "research/fine-expansion-page-admission/retained/boundary_codec.py",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "73d5adaba2b7dc662e86eb901e81369a3f73be9f",
+      "source_path": "research/core-halo-source-bridge/boundary_codec.py",
+      "git_blob": "5fdbd993cc4d9087e509fec2d9fb6e34912fa232",
+      "sha256": "e28149c32d9a53fbbe9b93c67bc0b85f1587747f74fa0452b6ff26618972eace"
+    },
+    {
+      "path": "research/fine-expansion-page-admission/retained/halo_tapes.py",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "73d5adaba2b7dc662e86eb901e81369a3f73be9f",
+      "source_path": "research/core-halo-source-bridge/retained/halo/sparse-halo-tape-transaction/tapes.py",
+      "git_blob": "b3dfa43ba0d08c6393731ac3cd2857a92e4c8aa2",
+      "sha256": "80b246fafae0adf53af7561e1be59f4374e6294d66bb7a12ef9524b9ef4f2a78"
+    },
+    {
+      "path": "research/fine-expansion-page-admission/retained/reference-PROOF.md",
+      "git_blob": "cabc570bb170b8cf17a34ca457b7ffa6adb17c07",
+      "sha256": "24ce857bfef43e8e104110bde5c3a702a13f6b0f021f3b2bf3e85d6c026e89b3",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "4509310a9a58d4c41c74029f899cbf36be1af9a1",
+      "source_path": "research/reference-ideal-compression-join/PROOF.md"
+    }
+  ]
+}

research/fine-expansion-page-admission/NOTICE.md

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+# Credit, license and evidence status
+
+Prepared for **@CubeJerry** with substantial OpenAI assistance in source
+audit, mathematical proof, exact independent checks, code and packaging.
+Same-team lead review is recorded separately. No independent human or
+formal proof-kernel acceptance is claimed. The repository Apache-2.0
+license applies; all retained original notices remain unchanged.
+
+- Jose Manuel (@jmbarrancoml), CrocSwap/integer-mult-bounds#3878, supplies
+  the actual explicit expansion producer, Tile and original-coordinate
+  geometry. His #3851/#3935 and their nested native/ring/Gaussian sources
+  supply the unchanged cohort, encoded words and field movement.
+- JoyboyBrian, CrocSwap/integer-mult-bounds#5056, proves the actual signed
+  internal contraction; #6085 proves the encoded coefficient enclosure.
+  Those universal results and the nested Machin/interval work are retained
+  premises and are not claimed as new here.
+- Hiroki KUMAZAKI (@kumagi), CrocSwap/integer-mult-bounds#5295, supplies the
+  actual five-residual accuracy and axis telescope. Ali Romman (@aliromman),
+  CrocSwap/integer-mult-bounds#5325, supplies the different old Tensor error
+  composition and remains credited in the overlap boundary.
+- The above original packages retain Hanson Sun, Artus Krohn-Grimberghe,
+  Chafik Boukhalfa, Mason Hale, Dugongue, Vlado, RaD/hipotures, the inherited
+  FFT/Karatsuba/q-calculus authors, Harvey–van der Hoeven, the OpenAI
+  manuscript contributors and Douglas Colkitt, together with their nested
+  archive and license notices. Their complete canonical bytes are unchanged.
+- The public @CubeJerry packages at 73d5adaba2b7dc662e86eb901e81369a3f73be9f,
+  76a84e1c4bfa4035e5ee85410dbfc4541f0da168,
+  4509310a9a58d4c41c74029f899cbf36be1af9a1,
+  96211247643059ae48af4c7d9dc960034798935d and
+  8db3cc1e98ba295cec4d752478431515e159c34f supply the exact public codec,
+  normalizer, Reference, caller and middle boundaries. Their retained files
+  are byte-exact and pinned in `DEPENDENCIES.json`.
+
+The new checker uses independently written exact integer/Fraction reasoning
+for headers, halos, exponent identities, normalization and route counts.
+It imports no predecessor numerical checker. The native witness executes
+only the real dimension-changing return adapter under the original loader,
+not coefficient production, complete expansion or production Fourier.

research/fine-expansion-page-admission/OVERLAP.md

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+# Bounded overlap audit and scoped novelty
+
+Canonical base: 7c49fe32c55de02c2c873655c804b16e4c3fef0a. The lead refreshed
+canonical main and live PRs at the wave transition. This is a bounded exact
+source/PR audit, not an exhaustive absence-of-overlap claim.
+
+| Predecessor and exact head | Already established | Distinct boundary here |
+| --- | --- | --- |
+| #3878, 1a86a8fb73bb7a0982fff99852a031832c191902 | Actual explicit Tile, block geometry, coefficient factorization and local expansion, including fine theta | Complete original-period explicit-page/header and coefficient-acceptance admission; no claim to new local expansion |
+| #5056, fe624453057b7f0cb42870a594d314a148b9fb84 | Actual signed-stage inward norm and original-coordinate axis recurrence | Reused to establish the reached middle radius for the newly admitted full-period source |
+| #5295, 351975ee703ec5aa1b18f70f73700d434026199a | Five-residual local accuracy and actual-input telescope; matching producer/page admission left open | Bind all actual producer arguments and positivity/unit checks; spend the fine-family forward normalizer |
+| #6085, 9fc80f1db55d4939c7b53c0799e6840cce35fbf8 | Uniform encoded scalar enclosure and narrow-Axis argument admission | Reuse scalar theorem; independently bind expansion A/K/B families and the preparer's extra strict positivity/upper-unit checks |
+| #5325, bea42af24ee9850949a4b48d329a7dc85de72b11 | Old Tensor restored error telescope and normalization | Different fine-family Gaussian K_f/K_c policy and changing-volume common-grid return; no generic telescope novelty |
+| #3851, 7ab67b4a84d28cd562b9711aa315ca5b47822b37; #3935, f687fa171ef760fa98a4be1289717b47dd4ee0b3 | Physical Gaussian cohort and old paired production Tensor | Exact explicit expansion API only; none of the old paired guards is waived |
+| Public caller audit 96211247643059ae48af4c7d9dc960034798935d | Old catalogue cannot admit the fine family; complete integer recovery includes both S factors | Source-specific explicit-page replacement admission, not rehabilitation of the rejected old caller |
+| Public middle 8db3cc1e98ba295cec4d752478431515e159c34f | Actual cached/Cyclic/common-grid interface conditional on a half-disk supplied input | Supply a numerically admitted slow-reference prefix and pay its enlarged return; retain the middle's backend premises |
+| Public ledger 76a84e1c4bfa4035e5ee85410dbfc4541f0da168 and Reference join 4509310a9a58d4c41c74029f899cbf36be1af9a1 | Compression normalizer policy and exact H/N comparison | Preserve their existing K_c and the exact normalized compression term, without new restoration |
+| Concurrent broad Core work in another active session | Separate grouped source/implementation responsibility | Excluded; no edit, duplicate implementation or claim of its execution |
+
+The originally broad prefix question would repeat known generic error and
+norm proofs. The single approved pivot is the source-specific producer/page
+admission plus the preserved forward-normalizer and enlarged-return seam.
+The complete direct cost is checked before claiming usefulness: it fails
+the target fast bound. Its literal output/routing invoice is a scoped
+limitation, not a general Gaussian or multiplication lower bound. The
+admitted exact reference is useful for independently testing a future
+grouped source map; that future implementation needs its own proof.