Independent verification: ten optimal tests for R420 compensation faults

research/r420-adjoint-compensation/CLAIM.md

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+# R420 adjoint compensation claim
+
+- Track: independent verification, OS-random assignment seed 81.
+- Base: `66849e1475c930fd7732b1a0067ffee7e1e95f60`.
+- Selected context: PR626 with PR543, conditional kappa
+  `51110230636731/31250000000000000`. No new bound is proposed.
+- Object: the 120 by 420 dirty-helper compensation matrix in the selected
+  PR543 R420 native word. Check the raw A/scatter/B target map and equality
+  with D by reverse covector propagation, independently of the supplier's
+  forward all-column checker.
+- Deliverable: a standalone standard-library verifier, exact matrix/cut
+  certificate, rank and kernel information, rejecting controls, and proof note.
+- Time budget: approximately 30 minutes from 2026-10-13 04:50 UTC. Finish by
+  05:20 UTC, with the final 7.5 minutes reserved for verification and handoff.
+- Coordination: GitHub returned no pinned issues. This is the local claim.
+  Open PR titles and relevant bodies were inspected before claiming.
+
+Three candidates considered were the R420 compensation identity, selected
+complex cold-wrapper phases, and selected supplier moment bounds. PR702/712
+cover the phase route and PR678/706 cover the moments. Seed 81 selects the bit
+object and backward scalar method. PR612 checks typed R420 boundaries and
+B-XOR target translation, but explicitly leaves D parity/compensation equality
+open. The supplier's existing `xcheck.py` already checks that equality by a
+forward symbolic replay. This work independently corroborates it with backward
+covectors and an explicit matrix certificate; it does not claim that the
+identity itself is new or that a Python check completes the Lean obligation.
+
+Scope excludes frame legality, COPY/ERASE realization, hosting, costs, moments,
+all-size compilation and the multiplication theorem. No existing supplier,
+selected certificate, or `upstream/` file will change. Acceptance requires
+exact equality for every target and every original input coordinate, source
+binding, deterministic evidence, and controls that reject altered compensation
+and incorrect transpose semantics.
+
+Prepared for Sagar Thakrar (@thakrarsagar) with substantial OpenAI Codex
+assistance. Apache-2.0; independent implementation is not independent human
+peer review.
+
+## Completed result and one scope pivot
+
+Submitted [PR762](https://github.com/CrocSwap/integer-mult-bounds/pull/762).
+The result is ten optimal nonadaptive dirty-input tests for compensation-row
+errors of weight at most three, with an executable four-error blind witness.
+The primary command passes 129 rejection controls. The separate support-set
+and Boolean checker confirms the fixed baseline, all ten probes and malformed
+suite rejection. See README.md and VALIDATION.md for exact scope and checks.
+
+The initial queue scan ended at PR725. A later refresh discovered Joshua
+Snider's PR731 at `cf5ff54a358b400a7e69abe941d1d0ad0944b25e`, which had
+submitted the same adjoint/rank work with additional kernel evidence. The
+planned rank certificate was removed and the scope pivoted once to the
+optimal ten-test suite. This credits PR731 and adds a distinct result on the
+test matrix, not another claim about its compensation kernel.
+
+The pre-submission refresh covered 578 open PRs through PR759. No pinned
+coordination issue existed, so this is the single local completion update.
+No pending code was imported. Only this seven-file package was added.

research/r420-adjoint-compensation/EXPECTED.json

@@ -0,0 +1,192 @@
+{
+  "assignment_seed": 81,
+  "domain": {
+    "helpers": 420,
+    "original_inputs": 660,
+    "targets": 120
+  },
+  "format": "r420-compensation-optimal-test-suite-v1",
+  "gate_counts": {
+    "A": 2064,
+    "B": 837,
+    "C": 2661,
+    "D": 120
+  },
+  "matrix_binary_sha256": "c833a715013f78e383ca95a684d26c000db5cba0dc848221bb05e5db6e63d4ed",
+  "negative_controls": [
+    "omit_D_operand_0",
+    "omit_D_operand_1",
+    "omit_D_operand_2",
+    "omit_D_operand_3",
+    "omit_D_operand_4",
+    "omit_D_operand_5",
+    "omit_D_operand_6",
+    "omit_D_operand_7",
+    "omit_D_operand_8",
+    "omit_D_operand_9",
+    "omit_D_operand_10",
+    "omit_D_operand_11",
+    "omit_D_operand_12",
+    "omit_D_operand_13",
+    "omit_D_operand_14",
+    "omit_D_operand_15",
+    "omit_D_operand_16",
+    "omit_D_operand_17",
+    "omit_D_operand_18",
+    "omit_D_operand_19",
+    "omit_D_operand_20",
+    "omit_D_operand_21",
+    "omit_D_operand_22",
+    "omit_D_operand_23",
+    "omit_D_operand_24",
+    "omit_D_operand_25",
+    "omit_D_operand_26",
+    "omit_D_operand_27",
+    "omit_D_operand_28",
+    "omit_D_operand_29",
+    "omit_D_operand_30",
+    "omit_D_operand_31",
+    "omit_D_operand_32",
+    "omit_D_operand_33",
+    "omit_D_operand_34",
+    "omit_D_operand_35",
+    "omit_D_operand_36",
+    "omit_D_operand_37",
+    "omit_D_operand_38",
+    "omit_D_operand_39",
+    "omit_D_operand_40",
+    "omit_D_operand_41",
+    "omit_D_operand_42",
+    "omit_D_operand_43",
+    "omit_D_operand_44",
+    "omit_D_operand_45",
+    "omit_D_operand_46",
+    "omit_D_operand_47",
+    "omit_D_operand_48",
+    "omit_D_operand_49",
+    "omit_D_operand_50",
+    "omit_D_operand_51",
+    "omit_D_operand_52",
+    "omit_D_operand_53",
+    "omit_D_operand_54",
+    "omit_D_operand_55",
+    "omit_D_operand_56",
+    "omit_D_operand_57",
+    "omit_D_operand_58",
+    "omit_D_operand_59",
+    "omit_D_operand_60",
+    "omit_D_operand_61",
+    "omit_D_operand_62",
+    "omit_D_operand_63",
+    "omit_D_operand_64",
+    "omit_D_operand_65",
+    "omit_D_operand_66",
+    "omit_D_operand_67",
+    "omit_D_operand_68",
+    "omit_D_operand_69",
+    "omit_D_operand_70",
+    "omit_D_operand_71",
+    "omit_D_operand_72",
+    "omit_D_operand_73",
+    "omit_D_operand_74",
+    "omit_D_operand_75",
+    "omit_D_operand_76",
+    "omit_D_operand_77",
+    "omit_D_operand_78",
+    "omit_D_operand_79",
+    "omit_D_operand_80",
+    "omit_D_operand_81",
+    "omit_D_operand_82",
+    "omit_D_operand_83",
+    "omit_D_operand_84",
+    "omit_D_operand_85",
+    "omit_D_operand_86",
+    "omit_D_operand_87",
+    "omit_D_operand_88",
+    "omit_D_operand_89",
+    "omit_D_operand_90",
+    "omit_D_operand_91",
+    "omit_D_operand_92",
+    "omit_D_operand_93",
+    "omit_D_operand_94",
+    "omit_D_operand_95",
+    "omit_D_operand_96",
+    "omit_D_operand_97",
+    "omit_D_operand_98",
+    "omit_D_operand_99",
+    "omit_D_operand_100",
+    "omit_D_operand_101",
+    "omit_D_operand_102",
+    "omit_D_operand_103",
+    "omit_D_operand_104",
+    "omit_D_operand_105",
+    "omit_D_operand_106",
+    "omit_D_operand_107",
+    "omit_D_operand_108",
+    "omit_D_operand_109",
+    "omit_D_operand_110",
+    "omit_D_operand_111",
+    "omit_D_operand_112",
+    "omit_D_operand_113",
+    "omit_D_operand_114",
+    "omit_D_operand_115",
+    "omit_D_operand_116",
+    "omit_D_operand_117",
+    "omit_D_operand_118",
+    "omit_D_operand_119",
+    "omit_D",
+    "duplicate_D_operand",
+    "swap_D_targets",
+    "wrong_A_order",
+    "wrong_B_order",
+    "wrong_scatter_helpers",
+    "omit_scatter_operand",
+    "D_reads_source",
+    "self_alias"
+  ],
+  "nonzero_entries": 19922,
+  "positive_controls": [
+    "duplicate_D_pair",
+    "two_gate_transpose",
+    "two_gate_wrong_order"
+  ],
+  "raw_sections": [
+    "A",
+    "scatter",
+    "B"
+  ],
+  "row_weight_range": [
+    121,
+    204
+  ],
+  "suite": {
+    "blind_four_support": [
+      240,
+      241,
+      242,
+      243
+    ],
+    "blind_target": 201,
+    "blind_witness_dirty_helper": 240,
+    "column_rule": "1 | (helper_relative_index << 1)",
+    "fault_radius_per_target": 3,
+    "optimality_bound": "420 <= 2^(q-1), hence q >= 10",
+    "pair_supports": 87990,
+    "pattern_hex": [
+      "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
+      "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc",
+      "0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0",
+      "0ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00",
+      "0ffff0000ffff0000ffff0000ffff0000ffff0000ffff0000ffff0000ffff0000ffff0000ffff0000ffff0000ffff0000ffff0000",
+      "f00000000ffffffff00000000ffffffff00000000ffffffff00000000ffffffff00000000ffffffff00000000ffffffff00000000",
+      "000000000ffffffffffffffff0000000000000000ffffffffffffffff0000000000000000ffffffffffffffff0000000000000000",
+      "fffffffff00000000000000000000000000000000ffffffffffffffffffffffffffffffff00000000000000000000000000000000",
+      "fffffffffffffffffffffffffffffffffffffffff0000000000000000000000000000000000000000000000000000000000000000"
+    ],
+    "single_supports": 420,
+    "test_count": 10,
+    "triple_supports": 12259940
+  },
+  "zero_columns": []
+}