Integrate reviewed research PRs #780, #781, #782, #783, #784, #785, #786, #787, #788, #789, #791, #792, #793, #796, #798, #800, #802, #807, #808, #809

Preserve original author commits and pinned evidence. Scoped review and execution receipts: research/community-efficient100-audit. No selected frontier change.

Author: Mister-Meeseeks

certificates/cyclic-topology-audit.json

@@ -2237,7 +2237,7 @@
   "full_improved_frame_certificate_supplied": false,
   "source_sha256": {
     "docs/research/cyclic-topology-audit.md": "156f3bc880738b1a6d378fd5d1d97297fd1ae457eb71160690ccb1cc1f42fc4c",
-    "scripts/audit_cyclic_topology.py": "b20ece2cf1337e1808e35b602a0120c6aedaf602fa2315560726a149e9838c29",
+    "scripts/audit_cyclic_topology.py": "d8f91f6618adef8e080b2f4ee38531de972b1824590cd979c9ae9ce83a84f013",
     "scripts/finite_bit_contract.py": "3cff26a332cb6056f656b824e3a523fb8937d15206ddcc4118b911ac8df1b2a7"
   },
   "status": "GENERAL EXACT VERIFIER; ROUTING OBSTRUCTION; NO NEW KAPPA",

research/community-pr681-audit/README.md

@@ -0,0 +1,96 @@
+# Independent replay of PR #681's complex-factory resynthesis
+
+Audit of [#681](https://github.com/CrocSwap/integer-mult-bounds/pull/681) by
+Alluri (@alluri-ritual), pinned at head
+`e536f6fc8aad65adef8ac4682d13625598a5c3f9`. Credit for the construction belongs
+to #681. This audit covers its own contribution,
+`research/complex-factory5-resynthesis/`: one 34-gate exact replacement for the
+87-gate coordinate-total window in all fourteen blocks of the PR622 raw
+K-triangle constructor. The bundled #696 lowering was audited separately in
+[#783](https://github.com/CrocSwap/integer-mult-bounds/pull/783).
+
+Exact base: `66849e1475c930fd7732b1a0067ffee7e1e95f60` (current `main`, also the
+merge base of #681). Only `research/community-pr681-audit/` is added.
+
+**Verdict: the 1,484-operation saving is confirmed exactly, for the raw
+constructor word. It does not touch the selected providers and does not change
+κ.**
+
+## Reproduce
+
+From the repository root, Python 3.11+, standard library, offline, about 30 s:
+
+```sh
+python3 -B research/community-pr681-audit/replay.py
+```
+
+Expected last line:
+
+```text
+PASS_PR681_INDEPENDENT_REPLAY windows=14 scalar_saved=1484 fwd_primitives_old=170488->160296 fwd_primitives_pr696=128696->123768 kappa=51110230636731/31250000000000000
+```
+
+No #681 code is imported. The 87-gate template and 34-gate witness are
+transcribed (without frames) from #681's `CIRCUIT.json`, sha256
+`f64a9e88491af13fe564f0512e8455eb268d1732a978b1b4fe3b93e601b59f71`.
+Temporary files are removed.
+
+## What the replay checks
+
+1. Runs the unchanged constructor on `main` directly, not through #681's
+   tracing extractor.
+2. Scans the fresh `A` word for the 87-gate template under injective register
+   relabeling with a constant frame. It finds exactly 14 windows on pairwise
+   disjoint registers; `BLOCKS.json` is not used.
+3. Checks the template and witness give the same exact rational map, forward and
+   inverse.
+4. Splices the witness into each window with that window's frame. Before
+   rebuilding the cleanup, it confirms the old cleanup equals the literal
+   inverse rule.
+5. Compares exact sparse linear forms of all 716 registers after `A`, `A+B` and
+   `A+B+cleanup` for the old and new words. All other word fields are identical.
+6. Runs the inherited native audit, emitter and local auditor from `main` on
+   both words, then recounts the emitted programs.
+
+| Quantity | Before | After | Saved |
+| --- | ---: | ---: | ---: |
+| Raw scalar events (precondition+cut+A+B+cleanup) | 6,340 | 4,856 | **1,484** = 2·14·(87−34) |
+| Native scalar operations (incl. 10,632 compensation adds) | 16,972 | 15,488 | 1,484 |
+| Forward primitives, inherited Horner lowering | 170,488 | 160,296 | 10,192 (5.98%) |
+| Backward primitives, inherited Horner lowering | 170,536 | 160,344 | 10,192 (5.98%) |
+| Forward primitives, #696 lowering | 128,696 | 123,768 | **4,928 (3.83%)** |
+| Backward primitives, #696 lowering | 128,712 | 123,784 | **4,928 (3.83%)** |
+| Forward / backward prefix L1 bound | 86,491,024,246 / 2,028,759,644,357/2 | 68,417 / 1,649,462 | — |
+
+- **Beyond #696.** Once #696's lowering applies, #681 adds 4,928 primitives per
+  orientation on the raw word, not 10,192. The consolidation's 170,488 → 123,768
+  (27.40%) breaks down as 41,792 from #696 plus 4,928 from #681. It is
+  composed correctly, not added from headlines.
+- Paid profiles and phase/adapter/center events are unchanged. The 98 frame-climb
+  events within the windows are reordered because the new circuit touches
+  registers in a different order. Each register's climb path is unchanged, and
+  the inherited audit reports identical frames and edges.
+- A randomized replay of the emitted scalar programs with dirty inputs, including
+  the private register, gives identical final states.
+- Mutating one witness coefficient makes the replay fail.
+
+## κ
+
+#681 changes no existing file except a ledger note. In particular it leaves
+`certificates/selected-result.json` and the selected CK/JP8 provider words
+unchanged. Its README states that the edits are not transported through the
+selected provider recipes. The 1,484 operations are therefore raw-constructor
+operations, not selected-factory operations. As #783 showed, scalar primitives
+enter only the finite per-vertex invoice, not the κ assembly. The selected κ
+remains `51110230636731/31250000000000000`.
+
+## Limits
+
+The prefix bounds come from the inherited auditor and were not re-derived.
+`make verify`, `make frontier626-verify`, Lean and #681's hosted replay were not
+run. #681's local `verify.py` and the consolidation's local `verify.py` were run
+and pass. The other five consolidated packages (bit-supplier R420 work) were not
+audited. Transporting the edit into the selected providers remains open work.
+
+Rohan Guliani (@Rohansguliani), with substantial AI assistance. New files are
+under the repository's Apache-2.0 license.