Research: restored decoder stars save 128 R420 XORs (no new kappa)

research/r420-decoder-bundles/CERTIFICATE.json

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+{
+  "status": "PASS_R420_DECODER_BUNDLES",
+  "assignment_seed": 19,
+  "search": {
+    "operands": 80,
+    "oriented_edges_checked": 6320,
+    "positive_edges": 463,
+    "packings_tried": 1,
+    "star_savings": [
+      18,
+      17,
+      14,
+      4,
+      3,
+      2,
+      2,
+      1,
+      1,
+      1,
+      1
+    ],
+    "unselected_operands": 25,
+    "stopping_rule": "no positive edge remains among unused operands"
+  },
+  "stars": 11,
+  "edges": 44,
+  "columns": 660,
+  "decoder_additions_before": 321,
+  "decoder_additions_after": 257,
+  "native_additions_before": 26916,
+  "native_additions_after": 26788,
+  "saved_with_cleanup": 128,
+  "baseline_canonical_sha256": "e597e3885c0a8daa262afa5985ee2930443329126aece76d33159d81882bdcc2",
+  "candidate_canonical_sha256": "d914b4d213175249af4fcd0a98f3f2b5addef1aea702c0224945c79f4d614eef",
+  "original_H1_H5": true,
+  "independent": {
+    "status": "PASS",
+    "columns": 660,
+    "scope": "relative scalar-word rewrite; closed E8 frames and cohort hosting inherited",
+    "checks": {
+      "all_A_columns_equal": true,
+      "all_frame_paths_equal": true,
+      "scalar_invoice_equal": true,
+      "baseline_full_operator": true,
+      "baseline_inverse_operator": true,
+      "baseline_interface": true,
+      "candidate_full_operator": true,
+      "candidate_inverse_operator": true,
+      "candidate_interface": true
+    },
+    "different_A_output_registers": [],
+    "different_frame_path_registers": [],
+    "words": {
+      "baseline": {
+        "full_operator_is_target_add": true,
+        "inverse_operator_is_target_add": true,
+        "interface": {
+          "no_target_feeds_source_or_helper": true,
+          "D_targets_from_zero_frame_helpers": true,
+          "targets_and_helpers_start_at_zero": true,
+          "A_never_writes_target": true,
+          "C_literal_reverse": true,
+          "sources_and_helpers_finish_at_full": true
+        },
+        "gates": {
+          "D": 120,
+          "A": 2064,
+          "B": 837,
+          "C": 2661
+        },
+        "adds": {
+          "D": 19922,
+          "A": 2376,
+          "B": 1077,
+          "C": 2973
+        },
+        "scatter_adds": 568,
+        "positive_scalar_bounds": {
+          "forward": {
+            "maximum": 144651,
+            "bits": 18
+          },
+          "inverse": {
+            "maximum": 2270064,
+            "bits": 22
+          }
+        },
+        "scalar_invoice": {
+          "paid_histogram": {
+            "1": 1320,
+            "2": 1440,
+            "4": 60,
+            "5": 120,
+            "8": 9
+          },
+          "rank_mass": 5112,
+          "moves": 2940,
+          "copies": 9,
+          "scope": "scalar MOVE and scatter COPY invoice, before cohort hosting"
+        }
+      },
+      "candidate": {
+        "full_operator_is_target_add": true,
+        "inverse_operator_is_target_add": true,
+        "interface": {
+          "no_target_feeds_source_or_helper": true,
+          "D_targets_from_zero_frame_helpers": true,
+          "targets_and_helpers_start_at_zero": true,
+          "A_never_writes_target": true,
+          "C_literal_reverse": true,
+          "sources_and_helpers_finish_at_full": true
+        },
+        "gates": {
+          "D": 120,
+          "A": 2086,
+          "B": 837,
+          "C": 2683
+        },
+        "adds": {
+          "D": 19922,
+          "A": 2312,
+          "B": 1077,
+          "C": 2909
+        },
+        "scatter_adds": 568,
+        "positive_scalar_bounds": {
+          "forward": {
+            "maximum": 235233,
+            "bits": 18
+          },
+          "inverse": {
+            "maximum": 3088728,
+            "bits": 22
+          }
+        },
+        "scalar_invoice": {
+          "paid_histogram": {
+            "1": 1320,
+            "2": 1440,
+            "4": 60,
+            "5": 120,
+            "8": 9
+          },
+          "rank_mass": 5112,
+          "moves": 2940,
+          "copies": 9,
+          "scope": "scalar MOVE and scatter COPY invoice, before cohort hosting"
+        }
+      }
+    },
+    "scalar_ADD_saving_including_C": 128
+  },
+  "negative_controls": [
+    "missing star restoration",
+    "uncancelled decoder operand",
+    "scalar-valid nonliteral cleanup",
+    "unpaid frame-zero preparation",
+    "retained register used as hub",
+    "overlapping stars",
+    "missing dirty compensation",
+    "changed source word"
+  ],
+  "three_register_separation": {
+    "group": [
+      515,
+      489,
+      347
+    ],
+    "all_oriented_edge_weights": [
+      [
+        515,
+        489,
+        2
+      ],
+      [
+        515,
+        347,
+        2
+      ],
+      [
+        489,
+        515,
+        1
+      ],
+      [
+        489,
+        347,
+        1
+      ],
+      [
+        347,
+        515,
+        1
+      ],
+      [
+        347,
+        489,
+        1
+      ]
+    ],
+    "star_saving": 4,
+    "disjoint_pair_ceiling": 2
+  },
+  "kappa_claim": "none"
+}

research/r420-decoder-bundles/CLAIM.md

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+# Local sprint claim
+
+- Track: bit supplier. Assignment seed 19, drawn with Node crypto.randomInt(100), backed by operating-system randomness.
+- Base: `66849e1475c930fd7732b1a0067ffee7e1e95f60`.
+- Started: 2026-10-13 04:49 UTC. Expected finish: 05:30 UTC. Final verification begins no later than 05:20 UTC.
+- Object: the nine FULL-frame phase-A decoder totals of eumemic's PR543 R420 bit word.
+- Hypothesis: restored bundles of at least three non-retained operand registers can improve on the disjoint-pair mechanism in PR708, after paying preparation, restoration and literal reverse cleanup.
+- Method: exact enumeration of small bundles, followed by one bounded disjoint selection. Preserve every frame path and arbitrary dirty inputs; recompute positive scalar growth. Seed 19 fixes tie ordering.
+- Deliverable: one frozen circuit and exact verifier, or a scoped negative result if the paid budget fails. No new kappa claim.
+- Three candidates considered: phase-B block resynthesis, phase-A quad synthesis, and decoder bundles. PR670/674/688 cover block rewrites and PR691 covers quad synthesis. Bundles change the search class beyond PR708's pair matching.
+- Coordination check: GitHub pinnedIssues returned an empty list; no separate issue opened. Open PR metadata inspected through PR720. PR708 is the direct predecessor and will be credited and pinned; PR686/694 cover frame-zero compensation, a different circuit.
+- Contributor: Sagar Thakrar (@thakrarsagar), with substantial OpenAI Codex assistance. Apache-2.0.
+
+## Completed result, 2026-10-13 05:07 UTC
+
+[PR753](https://github.com/CrocSwap/integer-mult-bounds/pull/753) contains one
+finite bit-circuit construction. Eleven restored stars save 128 native ADDs,
+including every preparation/restoration and literal cleanup, preserving the
+complete A operator and D. The nine-stage C++ replay passes 1,380 columns and
+18/18 omitted-bridge controls for both words; payload grows from 100 to 103 bits,
+below 104. No new kappa or complete hosted invoice is claimed.
+
+The initial optimistic three-operand screen was replaced by exact partial-row
+accounting, giving additive star-edge costs. The single accepted nomination
+covers all 6,320 oriented edges on 80 operands, then one seed-19 greedy star
+packing; its frozen coverage and stopping rule are checked. A three-register
+witness separates stars from disjoint pairs on the same registers.
+
+Final overlap refresh through #751 found no duplicate fixed-A decoder-star
+contribution. PR708's head remained `2ec522a466ec448f148d4355dc43b51c0ef1e0b5`.
+PR748 at `0ccc0b425d2b9667108d3a0918a5cfa0aa7a5861` has larger savings via a
+changed dirt map and recomputed D; it is credited rather than superseded.
+PR733/742 change D bases. Their savings are not added here. Main remained at
+the exact base above and the pinned-issue query was still empty.
+
+Implementation and nomination were frozen before the final review and handoff.
+Final verification included a relocated minimal archive, eight built-in controls,
+an altered-coverage rejection, selected-record integrity, and staged whitespace.
+The separate AI review's metadata-binding and proof-wording findings were fixed.
+Full hosted/outer assembly, repository-wide verification, remote CI and full
+theorem formalization remain outside this contribution.