Research: minimize balanced ternary dirty echo calls at fixed scratch

.github/workflows/ternary-dirty-composition.yml

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+name: Ternary dirty composition
+
+on:
+  pull_request:
+    paths:
+      - 'research/ternary-dirty-composition/**'
+      - '.github/workflows/ternary-dirty-composition.yml'
+  push:
+    paths:
+      - 'research/ternary-dirty-composition/**'
+      - '.github/workflows/ternary-dirty-composition.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  replay:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 10
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7
+        with:
+          python-version: '${{ matrix.python-version }}'
+      - run: python3 -I -O -B research/ternary-dirty-composition/verify.py
+      - run: git diff --exit-code

research/ternary-dirty-composition/CLAIM.json

@@ -0,0 +1,73 @@
+{
+  "track": "recursive interfaces",
+  "assignment_seed": 58,
+  "seed_source": "Python secrets.randbelow(100), operating-system randomness",
+  "seed_role": "arity = 2 + seed % 3 = 3; includes n=58 as generic diagnostic and n=63 as radix-64 factor count",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "start_eastern": "2026-10-12T23:21:34-04:00",
+  "claim_eastern": "2026-10-12T23:27:06.701824-04:00",
+  "expected_finish_eastern": "2026-10-13T02:15:00-04:00",
+  "hard_deadline_eastern": "2026-10-13T02:30:00-04:00",
+  "verification_reserve_starts_eastern": "2026-10-13T01:42:45-04:00",
+  "scope": "Minimize uniform leaf-call count among recursively balanced ternary PR673 dirty echoes at unchanged scratch; independently audit the pinned PR673 word with free nonlinear terms and noncommutative linear expressions; retain complete inherited precision/cost accounting. No selected supplier or kappa change.",
+  "method": "Place larger balanced blocks at twice-called ends; prove strict monotonicity and exchange optimality; check all balanced size placements through n=10000, 69 actual pinned PR673 words, and rounded unchanged PR628 leaves. No factor reordering.",
+  "expected_deliverable": "Standalone refinement and independent-verification package with an all-n proof, streaming dispatcher, deterministic certificate, source pins, attribution, reproduction command and one focused PR.",
+  "candidates": [
+    {
+      "task": "Encoded width-9 residual split across owners",
+      "decision": "Not selected: fresh PR665 already supplies exact spectral dilation and its unfavorable boundary bill."
+    },
+    {
+      "task": "Native bit ADDRESS fusion in a complete recursive call",
+      "decision": "Not selected: PR521 already covers the narrow local fusion; full integration exceeds this bounded scope."
+    },
+    {
+      "task": "Ternary product-of-shears schedule",
+      "decision": "Selected: PR628 has binary recursion; PR663 independently audits that fixed binary word and exact count, without changing it. This changes the schedule and prices extra scratch."
+    }
+  ],
+  "coordination": "No pinned issue; only open issue #650 asks for Discussions. Claim recorded locally, as instructed.",
+  "overlap_snapshot": {
+    "open_prs": 486,
+    "recent_highest_pr": 668,
+    "reviewed_related_prs": [
+      628,
+      663,
+      665,
+      666,
+      521,
+      448,
+      451,
+      522,
+      667,
+      668
+    ],
+    "no_matching_ternary_schedule_found": true
+  },
+  "status": "completed",
+  "deliverable_paths": [
+    "research/ternary-dirty-composition/",
+    ".github/workflows/ternary-dirty-composition.yml"
+  ],
+  "overlap_refresh": {
+    "open_prs": 497,
+    "recent_highest_pr": 677,
+    "concurrent_overlap": 673,
+    "pr673_commit": "0e35f56cab3cae1eb0a99447135569d687c5695a",
+    "evidence_driven_pivot": "PR673 supplies general multiway echoes, including ternary. Narrow the contribution to optimal balanced ternary placement and independent free-term/noncommutative verification of the pinned PR673 generator. At 15 factors this reduces 208 calls to 160, preserving 5 scratch arrays. No new echo identity or exponent is claimed."
+  },
+  "result": "Proved the balanced ternary uniform-call minimum and retained independent symbolic/rounded evidence. At 15 factors, calls fall from PR673's 208 to 160 with the same 5 scratch arrays; no new kappa.",
+  "result_url": "https://github.com/dillona/integer-mult-bounds/tree/research/seed58-ternary-dirty-composition/research/ternary-dirty-composition",
+  "final_overlap_snapshot": {
+    "at_utc": "2026-10-13T04:06:58.068676+00:00",
+    "open_prs": 506,
+    "recent_highest_pr": 686,
+    "pinned_coordination_issue": null,
+    "main_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+    "related_pr673_commit_unchanged": true,
+    "additional_related_prs_checked": [
+      679
+    ],
+    "distinct_contribution": "Balanced ternary placement minimum and independent free-function/noncommutative verification of the pinned generator, as described in README.md."
+  }
+}