Tooling: 3.58× faster joint-frame product with identical receipts

certificates/rank-product-core.json

@@ -6052,7 +6052,7 @@
   "source_sha256": {
     "certificates/paired-network.json": "3b28a213059130bf683c3c70c57e083d90d2ffb0a401b8a50332b98b9ebb303f",
     "docs/research/rank-product-core.md": "1028abd145b367f94960264a874b847cdbeb3b4d84dd6d3a890fe4203922bd41",
-    "scripts/audit_joint_frames.py": "3df8061392ce0ba42bbde8c02f2a30c8141145e70e9a48c18da73d3aafb14423",
+    "scripts/audit_joint_frames.py": "818e86b4152b4eeb853f173c9aa795510caa593ec0e25b05a246f1df52575466",
     "scripts/audit_rank_product_core.py": "1471f17e86d6c02d5c288116cc3a53544c881ded47a3500f70dac97b366e46a7",
     "scripts/audit_stage_pair.py": "f4823525abb553f76ea33adf61ed51e88ec38dd6c346dbcac86f69ffa8fb0375",
     "scripts/experiments/rank_product_core.py": "7a91c1188c5d42e864a5d2e42397b09c435b526ae4f4210c44bf615de488708e",

research/joint-frames-cleared-product/NOTICE.md

@@ -0,0 +1,19 @@
+# Notice
+
+This package accelerates Douglas R. Colkitt's exact rational matrix product in
+`scripts/audit_joint_frames.py` while preserving the positive-side and
+rank-product historical checkers.
+
+Predecessor credit:
+
+- Douglas R. Colkitt — joint-frame helpers, positive-side compiler, rank-product
+  core recovery and the historical certificates.
+- Closest tooling priors on *different* objects: CrocSwap/integer-mult-bounds
+  PRs #756 (balanced-Fano packed replay), #1793 (inplace-side prefix), #1861
+  (parity-side basis/contains), #1217 (ternary frame-pair memoization), and the
+  local modular-rank adapter in `research/joint-frame-modular-screen/`.
+
+Prepared by Wentao Li with substantial AI assistance under Apache-2.0.
+No product or model names are claimed as co-authors. This is not
+independent human peer review and is not a formal proof of the multiplication
+theorem.

research/joint-frames-cleared-product/README.md

@@ -0,0 +1,108 @@
+# Faster exact joint-frame product with identical receipts
+
+**Tooling improvement; no new kappa.** At base
+`0b1cccf86e2f5132ed286a26ef0a681a495740ea`, the historical positive-side audit
+(`scripts/audit_positive_side.py`) builds cancellation-free side DAGs and checks
+every physical frame transition for small signed label families. Profiling shows
+most time in `scripts/audit_joint_frames.py:product`, which previously formed
+each entry as a left-associated sum of `Fraction` multiplies (each multiply and
+add reducing by GCD).
+
+This change clears denominators once per factor, multiplies with Python
+integers, then rebuilds canonical `Fraction` entries. Empty left factors,
+integer matrices, projector squares and every Boolean/arithmetical API besides
+`product` are unchanged. Only the source pin for `scripts/audit_joint_frames.py`
+changes inside the one certificate that binds that file
+(`certificates/rank-product-core.json`). The positive-side certificate does not
+pin `audit_joint_frames.py`; its mathematical payload is unchanged.
+
+## Reproduce
+
+Python **3.12**, standard library only, from the repository root:
+
+```sh
+python3.12 -I -B research/joint-frames-cleared-product/verify.py
+python3.12 -I -O -B research/joint-frames-cleared-product/verify.py
+python3.12 -B scripts/research_package.py --package research/joint-frames-cleared-product
+python3.12 -I -B research/joint-frames-cleared-product/benchmark.py --rounds 5
+```
+
+Expected:
+
+```text
+PASS_JOINT_FRAMES_CLEARED_PRODUCT positive_side_cases=12 random_cases=2500 certs=1 no_new_kappa
+PASS_REGISTERED_RESEARCH_PACKAGE research/joint-frames-cleared-product outcome=completed
+PASS_IDENTICAL_POSITIVE_SIDE_RECEIPTS
+```
+
+Default verify is read-only. Use `--write-certificate` only after editing the
+production source. Full `make verify`, selected cold replay, Lean, and
+multiplication-theorem obligations were not rerun for this isolated
+historical-checker change.
+
+## Result
+
+On Linux / CPython 3.12.3 (Linux-6.12.94+-x86_64-with-glibc2.39), five alternating fresh-process pairs of the full
+positive-side experiment stream gave median wall time
+**26.143 → 7.302 seconds (3.58×)**. Timing is host-descriptive and is not a
+correctness gate; all samples and environment pins are in
+[RESULT.json](RESULT.json). Every experiment receipt matches the baseline
+checker fieldwise (`side_roles`, `additions`, `dag_sha256`, invocation and frame
+fields). Restoring the old `audit_joint_frames.py` pin recovers the base
+rank-product certificate byte-for-byte after that single substitution.
+
+## Equivalence
+
+Write matrices \(A=(a_{ij}/d_{ij})\) and \(B=(b_{jk}/e_{jk})\) over \(\mathbb{Q}\).
+Let \(D_A=\mathrm{lcm}(d_{ij})\) and \(D_B=\mathrm{lcm}(e_{jk})\). Form integer
+matrices \(A'=D_A A\) and \(B'=D_B B\). Then
+
+\[
+(AB)_{ik}=\frac{(A'B')_{ik}}{D_A D_B}.
+\]
+
+Canonical `Fraction` reduction of each right-hand entry matches the historical
+entrywise `sum(x*y for ...)` result, including when \(D_A=D_B=1\) (pure integer
+path). No modular or floating-point acceptance is used.
+
+## Open next questions
+
+1. **Question:** Can the same cleared-denominator pattern accelerate
+   `inverse` / `row_basis` on the joint-frame and ternary frame streams without
+   changing receipts?
+   **Why it matters:** Those helpers still allocate many intermediate
+   `Fraction`s on large ambient forms.
+   **First step:** Profile `verify_invocation_frames` for h=9 with the ternary
+   package’s baseline and time a cleared `inverse` prototype against receipt
+   equality.
+   **Blocked by:** Out of this session’s stop rule; `product` was the profiled
+   positive-side bottleneck.
+
+2. **Question:** Should rank-product and positive-side certificates both pin
+   `audit_joint_frames.py` going forward?
+   **Why it matters:** Only rank-product currently records that digest, so a
+   silent product drift would not bump the positive-side pin list.
+   **First step:** Add the pin in a dedicated provenance follow-up if maintainers
+   want symmetric coverage.
+   **Blocked by:** Provenance expansion is outside this tooling change.
+
+## Overlap and credit
+
+Closest priors (different objects):
+[CrocSwap/integer-mult-bounds#756](https://github.com/CrocSwap/integer-mult-bounds/pull/756)
+packed balanced-Fano replay;
+[CrocSwap/integer-mult-bounds#1793](https://github.com/CrocSwap/integer-mult-bounds/pull/1793)
+inplace-side prefix scan;
+[CrocSwap/integer-mult-bounds#1861](https://github.com/CrocSwap/integer-mult-bounds/pull/1861)
+parity-side basis/contains memoization;
+[CrocSwap/integer-mult-bounds#1217](https://github.com/CrocSwap/integer-mult-bounds/pull/1217)
+ternary frame-pair memoization;
+local `research/joint-frame-modular-screen/` (modular *rank* screen for the
+joint-frame certificate, not matrix product).
+No competing open PR on cleared-denominator `product` at refresh.
+
+Douglas R. Colkitt authored the joint-frame helpers and positive/rank-product
+side compilers. Prepared by Wentao Li
+([VictorLiwentao](https://github.com/VictorLiwentao),
+[@Is__Victor](https://x.com/Is__Victor)) with substantial AI assistance, under
+Apache-2.0.