Research: save 6,934 R420 XORs with a restored helper basis

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

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+name: R420 compensation basis exact checks
+
+on:
+  pull_request:
+    paths:
+      - 'research/r420-compensation-basis/**'
+      - '.github/workflows/r420-compensation-basis.yml'
+  push:
+    paths:
+      - 'research/r420-compensation-basis/**'
+      - '.github/workflows/r420-compensation-basis.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  exact-native-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 }}
+      - name: Ensure Boost headers are available
+        run: |
+          if ! test -f /usr/include/boost/multiprecision/cpp_int.hpp; then
+            sudo apt-get update
+            sudo apt-get install -y libboost-dev
+          fi
+      - name: Exact Python and unchanged C++ checks
+        run: |
+          python3 -I -O -B research/r420-compensation-basis/verify.py --native
+          git diff --exit-code

research/r420-compensation-basis/CERTIFICATE.json

@@ -0,0 +1,126 @@
+{
+  "after": {
+    "D_binary_additions": 12988,
+    "D_grouped_gates": 522,
+    "binary_additions": 19982,
+    "exported_records": 22940,
+    "forward_and_reverse": [
+      {
+        "columns": 660,
+        "copies": 9
+      },
+      {
+        "columns": 660,
+        "copies": 9
+      }
+    ],
+    "forward_prefix": 202699,
+    "frame_paths_sha256": "ef52add0118de86406ed3c58d6ff53b06b127c05238895b475181e55b98021ca",
+    "paid_histogram": {
+      "1": 1320,
+      "2": 1440,
+      "4": 60,
+      "5": 120,
+      "8": 9
+    },
+    "payload_prefix_bits": 102,
+    "payload_prefix_upper": "3191004937361206117331766365184",
+    "rank_mass": 5112,
+    "record_sha256": "17cf0f3edef8899ed34c180c89f9eb9d49d03dcb6d0e1a4a9ae5ea7973df9e46",
+    "reverse_prefix": 2446788,
+    "scalar_stream_sha256": "06007a8cad184bf9bea1941a5b0a19ce6273992836f8e0250d1173eff7e05c91",
+    "semantic_word_sha256": "02a652417125bef15a2c01946a642d45dae8bba11a09a1ac13f3b7d2057be3dc"
+  },
+  "all_other_legacy_interface_checks_pass": true,
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "before": {
+    "D_binary_additions": 19922,
+    "D_grouped_gates": 120,
+    "binary_additions": 26916,
+    "exported_records": 29874,
+    "forward_and_reverse": [
+      {
+        "columns": 660,
+        "copies": 9
+      },
+      {
+        "columns": 660,
+        "copies": 9
+      }
+    ],
+    "forward_prefix": 144651,
+    "frame_paths_sha256": "ef52add0118de86406ed3c58d6ff53b06b127c05238895b475181e55b98021ca",
+    "paid_histogram": {
+      "1": 1320,
+      "2": 1440,
+      "4": 60,
+      "5": 120,
+      "8": 9
+    },
+    "payload_prefix_bits": 100,
+    "payload_prefix_upper": "998206739997057013039187410944",
+    "rank_mass": 5112,
+    "record_sha256": "f7e6cceaceb04d7bd70918981405dcead988a890cfca03b51e80d935f00a960f",
+    "reverse_prefix": 2270064,
+    "scalar_stream_sha256": "95be862aadd3cd5dc9a8ba76e1ede1cc367d51f26fc24af3f56795b4807ba6f0",
+    "semantic_word_sha256": "e597e3885c0a8daa262afa5985ee2930443329126aece76d33159d81882bdcc2"
+  },
+  "binary_additions_saved": 6934,
+  "controls": [
+    {
+      "name": "missing compute",
+      "rejected_by": "D endpoint differs on an independent input column"
+    },
+    {
+      "name": "missing helper restoration",
+      "rejected_by": "D endpoint differs on an independent input column"
+    },
+    {
+      "name": "missing recoded target read",
+      "rejected_by": "D endpoint differs on an independent input column"
+    },
+    {
+      "name": "cancelled compute",
+      "rejected_by": "D endpoint differs on an independent input column"
+    },
+    {
+      "name": "nonzero prefix frame",
+      "rejected_by": "D is not at the zero frame"
+    },
+    {
+      "name": "F2-neutral target-fed helper outside the contract",
+      "rejected_by": "D reads a source or target"
+    },
+    {
+      "name": "unrelated A change",
+      "rejected_by": "change outside D"
+    },
+    {
+      "accepted_endpoint": true,
+      "extra_binary_additions": 2,
+      "name": "neutral pair still charged"
+    }
+  ],
+  "labels": {
+    "frames": 672,
+    "gram_det": 1,
+    "labels": 120,
+    "lattice_rank": 8
+  },
+  "legacy_H2_accepts_changed_syntax": false,
+  "legacy_raw_D_column_extraction_accepts_changed_syntax": false,
+  "matching_pairs": 201,
+  "schema": "r420-compensation-basis/1",
+  "scope": "Finite circuit improvement; semantic D-prefix substitution is proved separately. No new kappa or hosted-supplier invoice.",
+  "seed": 12,
+  "semantic_prefix_contract": {
+    "all_columns": 660,
+    "all_helpers_restored_before_A": true,
+    "dirty_helper_columns": 420,
+    "target_response_sha256": "98e46ceb6f4dc645e07c02417ac8782cc2de48406f793d5441ca7ce2f3acb7b2"
+  },
+  "source_pr": 543,
+  "source_pr_head": "2065fe4f72a914d907f1046603f5a36f17018535",
+  "status": "PASS_R420_COMPENSATION_BASIS",
+  "touched_helpers": 402
+}

research/r420-compensation-basis/CLAIM.json

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+{
+  "track": "Bit supplier",
+  "assignment_seed": 12,
+  "random_source": "Python secrets.randbelow(100), operating-system randomness",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "started_at_utc": "2026-10-13T03:52:32.749133+00:00",
+  "claim_recorded_at_utc": "2026-10-13T03:59:21.808995+00:00",
+  "expected_finish_at_utc": "2026-10-13T04:37:00+00:00",
+  "coordination": "No pinned sprint issue; narrow scope recorded locally.",
+  "candidate_tasks": [
+    {
+      "task": "Single R420 block-node resynthesis",
+      "disposition": "Not selected: PR670 and PR674 already simplify individual phase-B blocks."
+    },
+    {
+      "task": "Fixed-order R420 phase-B frame tuning",
+      "disposition": "Not selected: PR661 establishes a scoped simultaneous-frame bound for that word."
+    },
+    {
+      "task": "Reversible helper-basis compression of the frame-zero D compensation",
+      "disposition": "Selected: factor only the 120 by 420 dirty-response matrix, restore all helper inputs before A, and price every compute/uncompute XOR."
+    }
+  ],
+  "object": "The 19,922 binary additions in the D section of the accepted PR543 R420 bit word.",
+  "method": "Score every unordered pair of 420 helper columns in both orientations; a deterministic seed-12 tie order chooses a greedy disjoint positive-gain matching. Insert compute, re-encoded target reads, and inverse compute at frame zero.",
+  "domain": {
+    "unordered_helper_pairs": 87990,
+    "orientations_per_pair": 2,
+    "stopping_rule": "One complete pair-score enumeration and one greedy matching; no iterative search or optimality claim."
+  },
+  "expected_deliverable": "One finite circuit improvement with exact arbitrary-dirt endpoint, unchanged frame/paid profile checks, a semantic D-prefix contract and complete prefix accounting. No new kappa claimed.",
+  "overlap_snapshot": {
+    "open_prs": 500,
+    "through_pr": 680,
+    "related_work": "PR259 and the response-kernel lineage change entrances; this scope restores its entire zero-frame basis before the unchanged A/scatter/B/C word."
+  },
+  "status": "completed_local_contribution",
+  "completed_local_at_utc": "2026-10-13T04:18:40.934986+00:00",
+  "result": {
+    "D_additions_before": 19922,
+    "D_additions_after": 12988,
+    "complete_word_before": 26916,
+    "complete_word_after": 19982,
+    "saved": 6934,
+    "disjoint_pairs": 201,
+    "helper_count": 420,
+    "paid_rank_mass": 5112,
+    "prefix_bits_before": 100,
+    "prefix_bits_after": 102,
+    "new_kappa_claim": false
+  },
+  "concurrent_overlap": {
+    "pr": 686,
+    "head": "23dcb610c2b156b76b9d599ea296c3cbde224b2d",
+    "author": "Mikhail R. Gadelha",
+    "shared_scope": "The same restored frame-zero pair mechanism and semantic H2 contract; helpers 552/521 also occur here.",
+    "additional_contribution": "A simultaneous disjoint matching of 201 pairs, saving 6934 XORs including restoration, with a fully recomputed 102-bit prefix budget. No priority claim for the pair mechanism."
+  },
+  "presubmission": {
+    "open_prs": 510,
+    "through_pr": 690,
+    "no_pinned_coordination_issue": true,
+    "native_Cpp": "Pending dedicated Linux CI; local standard-library exact/record checks passed."
+  }
+}

research/r420-compensation-basis/NOTICE.md

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+# Attribution and license
+
+Prepared by **Greer Guthrie (g-guthrie)** with substantial **OpenAI Codex**
+assistance in research, implementation, verification and writing. New
+material is under the repository's Apache-2.0 license.
+
+- **eumemic**: #543 R420 bit circuit, source data, interleaved-interface
+  proof, exact labels/frames and arbitrary-dirty-input checker; #493 lineage.
+- **Dylan Crow / DreamingOfClouds**: the literal record exporter, E8
+  adaptations and preceding bit-circuit work.
+- **DaysSky**: the generalized bridged-stage column checker and its controls.
+- **Zhihao Chen, Chafik Boukhalfa, icekylinx, Rohan Arun** and all authors
+  credited in the retained #543/#493 notices: mutable-source realization,
+  compilation, hosting, exact arithmetic and finite accounting.
+- **Mikhail R. Gadelha (@mikhailramalho), concurrent #686**: the same
+  restored frame-zero helper-pair mechanism and semantic prefix contract,
+  published for helpers 552/521 while this experiment was underway. That
+  pair is included here. This contribution adds the 201-pair simultaneous
+  matching and its full cost/prefix evidence, without a priority claim for
+  the one-pair idea. No #686 source code is imported.
+- **yongjae321, x0hu and Ali Romman**, #670/#674/#688: distinct concurrent
+  phase-B block simplifications and their integration; not imported here.
+
+The elementary binary basis-change identity is standard linear algebra.
+The response-kernel/entrance lineage, including #259, is related prior
+work; this construction restores its helper basis before the unchanged A.
+All original files and their assistance disclosures remain unchanged.