Research: save 3,150 R420 XORs with a restored target basis

.github/workflows/r420-target-basis.yml

@@ -0,0 +1,42 @@
+name: r420-target-basis
+
+on:
+  push:
+    paths:
+      - 'research/r420-target-basis/**'
+      - '.github/workflows/r420-target-basis.yml'
+  pull_request:
+    paths:
+      - 'research/r420-target-basis/**'
+      - '.github/workflows/r420-target-basis.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  verify:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 8
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.11', '3.13']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7
+        with:
+          python-version: ${{ matrix.python-version }}
+      - run: python -B research/r420-target-basis/verify.py
+      - run: python -B -m unittest discover -s research/r420-target-basis -p 'test_*.py'
+      - name: Install Boost for unchanged C++ checkers
+        if: matrix.python-version == '3.13'
+        run: |
+          sudo apt-get update -qq
+          sudo apt-get install -y --no-install-recommends libboost-dev
+      - name: Fresh C++ legality and multistage columns
+        if: matrix.python-version == '3.13'
+        run: CXX=g++ python -B research/r420-target-basis/native.py
+      - run: git diff --exit-code

research/r420-target-basis/CERTIFICATE.json

@@ -0,0 +1,68 @@
+{
+  "D_ADDs": [
+    19922,
+    16772
+  ],
+  "after": {
+    "ADDs": 23766,
+    "forward_prefix": 144651,
+    "histogram": {
+      "1": 1320,
+      "2": 1440,
+      "4": 60,
+      "5": 120,
+      "8": 9
+    },
+    "payload_bits": 102,
+    "payload_prefix_upper": "2657306775507971405724759110400",
+    "rank_mass": 5112,
+    "record_sha256": "6ca2f063e4e160d613bb638edf6b0306de0f98a21c9d34d4c491f1e4af5b3dc7",
+    "records": 26724,
+    "reverse_prefix": 3703810
+  },
+  "assignment_seed": 5,
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "before": {
+    "ADDs": 26916,
+    "forward_prefix": 144651,
+    "histogram": {
+      "1": 1320,
+      "2": 1440,
+      "4": 60,
+      "5": 120,
+      "8": 9
+    },
+    "payload_bits": 100,
+    "payload_prefix_upper": "998206739997057013039187410944",
+    "rank_mass": 5112,
+    "record_sha256": "f7e6cceaceb04d7bd70918981405dcead988a890cfca03b51e80d935f00a960f",
+    "records": 29874,
+    "reverse_prefix": 2270064
+  },
+  "candidate_word_canonical_sha256": "091a62fa54f0aeb3a46c7e3ebefbbbc2e0b00b85be9d90521b9077456e650e09",
+  "columns_in_each_direction": 660,
+  "labels": {
+    "frames": 672,
+    "gram_det": 1,
+    "labels": 120,
+    "lattice_rank": 8
+  },
+  "legacy_H2_and_literal_K_accept": false,
+  "oriented_pairs_scored": 14280,
+  "pair_count": 57,
+  "positive_control": "F2-neutral target pair preserves operator and costs two ADDs",
+  "rejection_controls": [
+    "missing final target restoration",
+    "missing initial target shear",
+    "wrong transformed helper row",
+    "nonzero D frame",
+    "source accessed at frame zero",
+    "unrelated cleanup modification",
+    "omitted exported ERASE",
+    "omitted exported target shear"
+  ],
+  "saved_ADDs": 3150,
+  "scope": "finite native bit circuit; no new kappa",
+  "source_pr543": "2065fe4f72a914d907f1046603f5a36f17018535",
+  "status": "PASS_R420_TARGET_BASIS"
+}

research/r420-target-basis/CLAIM.json

@@ -0,0 +1,51 @@
+{
+  "track": "Bit supplier",
+  "assignment_seed": 5,
+  "randomness": "secrets.randbelow(100), OS randomness, 2026-10-13 04:23:56 UTC",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "object": "PR543 R420 frame-zero D correction: conjugation by disjoint target transvections, with arbitrary target inputs restored",
+  "method": "score all 14280 oriented pairs of 120 targets; greedy disjoint positive-gain matching with Random(5) tie breaking; no helper basis changes",
+  "candidates": [
+    {
+      "task": "phase-B block 5 resynthesis",
+      "disposition": "already completed by PR674 and composed by PR688"
+    },
+    {
+      "task": "phase-A quad 5 resynthesis",
+      "disposition": "possible but near concurrent PR691 quad13 mechanism"
+    },
+    {
+      "task": "frame-zero target-basis conjugation",
+      "disposition": "chosen: changes target rows, unlike helper-column factoring in PR686/694"
+    }
+  ],
+  "overlap_checked_through_pr": 709,
+  "coordination": "No pinned issue exists; local claim",
+  "expected_deliverable": "finite exact circuit, complete native dirty-input/frame replay, charged restoration/prefix costs, rejection controls; no kappa claim",
+  "expected_finish_utc": "2026-10-13 04:49:00 UTC",
+  "status": "completed",
+  "optimistic_complete_cost": {
+    "baseline_D_ADDs": 19922,
+    "transformed_row_reads": 16658,
+    "preparation_ADDs": 57,
+    "restoration_ADDs": 57,
+    "total_D_ADDs": 16772,
+    "new_helpers": 0,
+    "new_COPYs": 0,
+    "new_frame_moves": 0,
+    "recursive_profile": "unchanged",
+    "no_kappa_reason": "selected composition is complex-limited; local scalar count changes finite overhead only"
+  },
+  "result": {
+    "saved_native_ADDs": 3150,
+    "target_pairs": 57,
+    "new_local_payload_bits": 102,
+    "native_stage_counts": [
+      5,
+      9,
+      11
+    ],
+    "kappa": "unchanged",
+    "url": "https://github.com/swbiggart/integer-mult-bounds/tree/research/seed5-target-basis/research/r420-target-basis"
+  }
+}

research/r420-target-basis/NATIVE-CERTIFICATE.json

@@ -0,0 +1,52 @@
+{
+  "source_pins": "cecb7cb56f36434b5ddca4be7aa2eef4b39841337b874effb90f1355348d5b09",
+  "status": "PASS_R420_TARGET_BASIS_NATIVE",
+  "words": {
+    "after": {
+      "legality": "PASS",
+      "stages": [
+        {
+          "bridge_controls": 6,
+          "formal_columns": 900,
+          "missing_D_end_rejected": true,
+          "stages": 5
+        },
+        {
+          "bridge_controls": 18,
+          "formal_columns": 1380,
+          "missing_D_end_rejected": true,
+          "stages": 9
+        },
+        {
+          "bridge_controls": 24,
+          "formal_columns": 1620,
+          "missing_D_end_rejected": true,
+          "stages": 11
+        }
+      ]
+    },
+    "before": {
+      "legality": "PASS",
+      "stages": [
+        {
+          "bridge_controls": 6,
+          "formal_columns": 900,
+          "missing_D_end_rejected": true,
+          "stages": 5
+        },
+        {
+          "bridge_controls": 18,
+          "formal_columns": 1380,
+          "missing_D_end_rejected": true,
+          "stages": 9
+        },
+        {
+          "bridge_controls": 24,
+          "formal_columns": 1620,
+          "missing_D_end_rejected": true,
+          "stages": 11
+        }
+      ]
+    }
+  }
+}