Research: Cached chirp/cyclic join

research/cached-chirp-cyclic-join/CHECKPOINT.md

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+# Wave 8 recoverable checkpoint
+
+Worker: analytic_join. Track 50/75. Local branch:
+research/cached-chirp-cyclic-join-20261109. Canonical parent:
+7c49fe32c55de02c2c873655c804b16e4c3fef0a.
+
+Root owns publication; this worker has neither pushed nor submitted a PR.
+The package is independent of all earlier frozen worktrees. The one approved
+pivot moved from already-covered generic expansion error to #6906's exact
+open convolution/grid interface; broad Core is excluded.
+
+The first genuine T8 physical attempt completed inside its 120-second bound
+and emitted PASS_CACHED_CHIRP_CYCLIC_JOIN. Exact output hash:
+2e1c1b26ba13815c4baa8dcf46169b27152fe2f035475a4ee99c1bf96a32a548.
+The actual over-radius failure occurs before any new cached call; cleanup
+and borrowed-source origins are checked. The dense comparison is only the
+specified q2 finite-provider witness, not production GL64/O73 admission.
+
+An earlier source-opening probe failed the existing cold-module guard:
+our initially chosen local helper name source.py collided with a native
+module named source. No guard was disabled and no failed probe is reported
+as a completed physical replay. Renaming our helper to join_sources.py
+resolved the collision; all inherited sources and checks stayed unchanged.
+
+Public caller dependency was updated from its identical local tested tree
+to root-verified commit 96211247643059ae48af4c7d9dc960034798935d.
+The source-specific universal proof, original-period conventions, grid
+allocation and complete cost invoice are in PROOF.md. Direct normal and optimized replays passed in 62.094 and 63.201 seconds.
+The first registered pair also passed. Final registered replay additionally
+strengthens the omitted-grid control by retaining the actual unprojected
+f-grid oracle words: those values differ and overflow the q carrier. This
+check does not substitute a production provider. Final review and commit
+gates are recorded below after freezing.
+No full transform, removed foundational assumption or new kappa is claimed.
+
+Final registered normal/optimized replay passed (133.551 seconds combined,
+120-second per-command caps), with identical receipts. Metadata/pins passed.
+The full registered output is retained in evidence/registered.json; the
+compact parsed receipt and original direct runs are in evidence/REPLAY.json.

research/cached-chirp-cyclic-join/DEPENDENCIES.json

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+{
+  "schema_version": 1,
+  "files": [
+    {
+      "path": "research/cached-chirp-cyclic-join/retained/cached/NOTICE.md",
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+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "3c0443b2aa721ce692199ff31abc18e8d917596a",
+      "source_path": "research/physical-cached-chirp-payload/NOTICE.md"
+    },
+    {
+      "path": "research/cached-chirp-cyclic-join/retained/cached/PROOF.md",
+      "git_blob": "a75f9a771c679dc53bb8150724bf95cf46719418",
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+      "commit": "3c0443b2aa721ce692199ff31abc18e8d917596a",
+      "source_path": "research/physical-cached-chirp-payload/PROOF.md"
+    },
+    {
+      "path": "research/cached-chirp-cyclic-join/retained/cached/README.md",
+      "git_blob": "1e95863471783f5c87745c0eed63d755e0dfab4d",
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+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "3c0443b2aa721ce692199ff31abc18e8d917596a",
+      "source_path": "research/physical-cached-chirp-payload/README.md"
+    },
+    {
+      "path": "research/cached-chirp-cyclic-join/retained/cached/SOURCE.md",
+      "git_blob": "8433a71fdee13f8437a2cb4a04bbd53422a8789b",
+      "sha256": "c79144c0fb335903db21d26016455908d5b5662584f77e5312f7b24a7ff711c7",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "3c0443b2aa721ce692199ff31abc18e8d917596a",
+      "source_path": "research/physical-cached-chirp-payload/SOURCE.md"
+    },
+    {
+      "path": "research/cached-chirp-cyclic-join/retained/cached/chirp_consumer.py",
+      "git_blob": "19c77f56be7347406cc8ee689c999b7afd74dbed",
+      "sha256": "47b91b4b9773453b24064604d174dc1fb5304b76d1477c39f414f4517ecb51a1",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "3c0443b2aa721ce692199ff31abc18e8d917596a",
+      "source_path": "research/physical-cached-chirp-payload/chirp_consumer.py"
+    },
+    {
+      "path": "research/cached-chirp-cyclic-join/retained/cached/chirp_tables.py",
+      "git_blob": "9302c067210f5e1e7d2a0280c40186590bdbaadc",
+      "sha256": "221077b7660dc991d997d62065aec336d49b108d0307c1140b3e95ab4b9b8925",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "3c0443b2aa721ce692199ff31abc18e8d917596a",
+      "source_path": "research/physical-cached-chirp-payload/chirp_tables.py"
+    },
+    {
+      "path": "research/cached-chirp-cyclic-join/retained/cached/chirp_tapes.py",
+      "git_blob": "03916e432685d65f34c48fe6b125b64ca3c65db3",
+      "sha256": "cc257f302317fcfe332725a070fd9f90f20aa6b53bf0a70a9a3e0de20baa792b",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "3c0443b2aa721ce692199ff31abc18e8d917596a",
+      "source_path": "research/physical-cached-chirp-payload/chirp_tapes.py"
+    },
+    {
+      "path": "research/cached-chirp-cyclic-join/retained/boundary_codec.py",
+      "git_blob": "5fdbd993cc4d9087e509fec2d9fb6e34912fa232",
+      "sha256": "e28149c32d9a53fbbe9b93c67bc0b85f1587747f74fa0452b6ff26618972eace",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "73d5adaba2b7dc662e86eb901e81369a3f73be9f",
+      "source_path": "research/core-halo-source-bridge/boundary_codec.py"
+    },
+    {
+      "path": "research/cached-chirp-cyclic-join/retained/halo_tapes.py",
+      "git_blob": "b3dfa43ba0d08c6393731ac3cd2857a92e4c8aa2",
+      "sha256": "80b246fafae0adf53af7561e1be59f4374e6294d66bb7a12ef9524b9ef4f2a78",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "73d5adaba2b7dc662e86eb901e81369a3f73be9f",
+      "source_path": "research/core-halo-source-bridge/retained/halo/sparse-halo-tape-transaction/tapes.py"
+    },
+    {
+      "path": "research/cached-chirp-cyclic-join/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"
+    },
+    {
+      "path": "research/cached-chirp-cyclic-join/retained/caller-PROOF.md",
+      "git_blob": "08a808b09c4a888d27f468f236ba6ca1d7881ac4",
+      "sha256": "0dde51f56eee2c711afa3b5c1e4f783ad0b057b7c206aa931b260c407236dfdd",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "96211247643059ae48af4c7d9dc960034798935d",
+      "source_path": "research/fine-recovery-catalogue-obstruction/PROOF.md"
+    }
+  ]
+}

research/cached-chirp-cyclic-join/NOTICE.md

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+# Attribution and source integrity
+
+Prepared for **@CubeJerry** with substantial OpenAI assistance in source
+audit, mathematical proof, implementation, bounded independent oracles and
+packaging. Lead source/proof review is recorded separately. This is not
+independent human acceptance or formal proof-kernel verification.
+
+The repository Apache-2.0 license applies. Original notices in retained
+files remain unchanged. `DEPENDENCIES.json` records exact public commits,
+paths, Git blobs and SHA256 hashes; `SOURCES.json` records the canonical base.
+
+- CrocSwap/integer-mult-bounds#6906 supplies the unchanged certified cached
+  phase source, physical payload consumer, source preparation and their
+  proofs. Its public head is 3c0443b2aa721ce692199ff31abc18e8d917596a.
+  This package closes that report's stated convolution/grid interface.
+- CrocSwap/integer-mult-bounds#4325 and #5987 supply the cached suffix error
+  and table-travel results. Those lemmas are inherited, not reclaimed.
+- CrocSwap/integer-mult-bounds#3763 supplies the unchanged complete Cyclic
+  program, chirp identity, numerical contracts and full Fourier invoice.
+  Its original source credits Chafik Boukhalfa (#479) and Ross Richardson
+  (#948); those notices and the nested arithmetic authorship remain intact.
+- CrocSwap/integer-mult-bounds#3787, #3851 and the authenticated nested ring
+  and Fourier packages supply the actual arithmetic cohort and binder.
+  No new scalar multiplier or native Fourier theorem is claimed.
+- The public Core/halo source bridge at
+  73d5adaba2b7dc662e86eb901e81369a3f73be9f supplies the retained common-grid
+  codec and external tape model.
+- The public Reference/ideal compression join at
+  4509310a9a58d4c41c74029f899cbf36be1af9a1 and recovery-catalogue audit at
+  96211247643059ae48af4c7d9dc960034798935d supply the exact successor boundary.
+- CrocSwap/integer-mult-bounds#5295/#5325 and #4100 already establish other
+  expansion/analytic error components; no complete theorem from them is
+  silently admitted. Mason Hale's unchanged interval implementation is
+  used in source preparation and retains its original authorship.
+
+The independently written fixture oracle uses exact integers, isqrt and
+Fractions. It imports no predecessor numerical checker. Its finite q2
+physical provider and exact metadata specialization remain explicit.
+The selected kappa and five inherited assumptions are unchanged.

research/cached-chirp-cyclic-join/OVERLAP.md

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+# Bounded overlap audit and precise novelty
+
+Canonical main: 7c49fe32c55de02c2c873655c804b16e4c3fef0a. This is a bounded
+source audit, not a claim of exhaustive archive coverage.
+
+| Predecessor | Already established | Distinct work here |
+| --- | --- | --- |
+| #6906, head 3c0443b2aa721ce692199ff31abc18e8d917596a | Certified inward cached phases, real scalar payload passes, travel/error/source bill | Actual same-bank kernel and two endpoints around canonical Cyclic, carrier/common-grid conversion and joined radius/error |
+| #3763, canonical physical-chirp-middle | Actual cyclic program, old independently generated chirps, normalization and complete 3 T_F bill | Bind #6906's fresh rounded suffix kernel A at all three occurrences and fund f versus external q |
+| #4325/#5987 | Cached suffix mechanism and improved table travel | Reused without claiming new suffix/travel theorem |
+| #5295/#5325 | Old expansion and restored-error telescopes | Reused only as context; no generic expansion theorem is reclaimed |
+| #3851/#3935 | Different original Gaussian/source08 production plan and chirp path | Current exact cached tables and common-grid compression entrance; old catalogue admission is not waived |
+| Public caller audit 96211247643059ae48af4c7d9dc960034798935d | Unchanged old Tensor recovery port is incompatible with the fine-family guards | Explicit one middle term in its missing prefix equation; no full caller replacement |
+| Concurrent broad Core work | Another active session's source/implementation responsibility | Excluded; no modification, duplicate publication or claim of their execution |
+
+The initial expansion-prefix scope would repeat established generic bounds.
+The one approved pivot was therefore the exact open question stated in
+#6906 README: complete chirp convolution and payload-grid conversion. The
+actual canonical `tensor_sources.bind_chirp` already supplies the correct
+cohort join; it is reused unchanged, with no new binder claim. The new
+runtime glues existing children while the proof binds their actual rounded
+kernel, radius and grid semantics. No Fourier identity, cached stability or
+complete multiplication exponent is claimed as new.

research/cached-chirp-cyclic-join/PR-BODY.md

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+## Problem and exact result
+
+The public cached phase payload package (#6906) explicitly leaves complete
+chirp convolution and payload-grid conversion open. A compression-only
+precision ledger does not fund those operations or their actual intermediate
+radius. This package connects that exact public consumer to canonical
+`Cyclic.run` (#3763), retaining every original padded coordinate and the
+same immutable rounded phase bank at all three chirp occurrences.
+
+For D>=2, t_0=r>=4, t_i in {r/2,r}, odd original slopes, T=product t_i,
+M=T/r=2^A and an actual q-grid input of maximum modulus at most one half,
+the joined output satisfies
+
+`||yhat-Q_freq F_t x||_* < (8M+9D+18)2^-f + 2^(1-q)`.
+
+Here the norm is maximum component-l1 and F_t is normalized. Choosing
+`q>=chi+2` and
+`f=max(q,16,A+13,chi+1+ceil(log2(8M+9D+18)),ceil(log2(6D)))`
+gives strict error below `2^-chi`; `f=O(p0)` for the stated fine family.
+The reached output modulus is below .501. The exact q-to-f lift and final
+f-to-q projection introduce no normalizer or new Gaussian Gamma.
+
+## What changes and why it is useful
+
+- Execute kernel-on-ones, both conjugate payload passes and the actual
+  complete Cyclic child, consuming each protected return.
+- Check input radius with actual exact scalar products; join the different
+  native signed carrier widths and the public common-grid codec.
+- Reuse the unchanged canonical cohort binder, which authenticates and
+  compares every corrected ring export byte before enabling the APIs.
+- Prove the actual-input defect from the shared rounded kernel A, and state
+  the precise broad-expansion term remaining at the public compression
+  caller. Keep all three full Fourier calls, complete padded-field scans,
+  source setup, copying, cleanup and retained backing in the invoice.
+
+Cached phase stability/travel (#4325/#5987/#6906), the cyclic algorithm and
+Fourier identity (#3763), old expansion bounds (#5295/#5325), and the exact
+binder are predecessor results. The distinct contribution is this executable
+source/grid/convolution interface and its explicit joined precision/radius
+budget. `OVERLAP.md` records the bounded audit.
+
+## Pins and reproduction
+
+Canonical base: `7c49fe32c55de02c2c873655c804b16e4c3fef0a`.
+Cached public source: `3c0443b2aa721ce692199ff31abc18e8d917596a` (#6906).
+Public codec: `73d5adaba2b7dc662e86eb901e81369a3f73be9f`.
+Public Reference/ideal join: `4509310a9a58d4c41c74029f899cbf36be1af9a1`.
+Public caller audit: `96211247643059ae48af4c7d9dc960034798935d`.
+Exact file hashes are in SOURCES.json and DEPENDENCIES.json; public unmerged
+heads are explicitly retained dependencies.
+
+```sh
+python3 -B scripts/research_package.py --package research/cached-chirp-cyclic-join
+python3 -B scripts/check_research_commit.py --package research/cached-chirp-cyclic-join --check-modes
+```
+
+The registered normal and optimized runs emit
+`PASS_CACHED_CHIRP_CYCLIC_JOIN`. The genuine T8 fixture has q10/f16/W19,
+radices (4,2), slopes (3,1), 192 cached scalar products and 16 input-radius
+squares, in addition to the actual Cyclic arithmetic. A separately written
+integer oracle matches all output words; an exact dense Gaussian-rational
+sum gives maximum component-l1 error 11/8192 below the 45/16384 bound.
+Actual radius and pending-return failures plus conjugation, missing M and
+grid controls detect the critical seams. All 75 finite allocation cases
+pass; the proof, rather than that finite list, supplies the universal claim.
+
+## Limits, status and credit
+
+**No new kappa.** The complete multiplication bound and selected certificate
+are unchanged. The finite q2 native provider is not production GL64/O73.
+The proof retains the source, scalar and Fourier contracts; it does not
+establish their all-size acceptance by replay. Broad Gaussian expansion,
+its reached radius/error, fine-family backend admission, opposite transform
+and complete CRT/integer recovery remain separate obligations. The old
+Tensor catalogue is neither invoked nor waived. Another session's broad
+Core work is outside scope.
+
+Prepared for @CubeJerry with substantial OpenAI assistance in research,
+implementation, proof, independent exact oracles and packaging. Predecessor
+credit is in NOTICE.md, and retained notices remain intact. Separate
+model-assisted lead review is not human or proof-kernel acceptance.

research/cached-chirp-cyclic-join/PR-TITLE.txt

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+Join cached chirp payloads to actual cyclic convolution and common grid