Finite construction: R439 frame 519 saves 20 complete local ADDs (no new kappa)

research/r439-frame519-seed02/CERTIFICATE.json

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+{
+  "after": {
+    "adds": 24285,
+    "copies": 9,
+    "erasures": 9,
+    "moves": 2911,
+    "payload": "8176146235754724278798992128",
+    "payload_bits": 93,
+    "positive_bounds": [
+      49347,
+      1031082
+    ],
+    "profile": {
+      "1": 1323,
+      "2": 1342,
+      "3": 79,
+      "4": 44,
+      "5": 102,
+      "6": 11,
+      "7": 19
+    },
+    "rank_mass": 5129,
+    "record_sha256": "1d4e22ec19384f3b93d6a6bd357fd76b1bfa73d27992c10aa0a7a46746be7c50",
+    "records": 27214
+  },
+  "assignment_seed": 2,
+  "base_commit": "f567884aeb8851b6e794af1184119a3bfbe1e631",
+  "before": {
+    "adds": 24305,
+    "copies": 9,
+    "erasures": 9,
+    "moves": 2911,
+    "payload": "9528119495320518471870892800",
+    "payload_bits": 93,
+    "positive_bounds": [
+      49347,
+      1113070
+    ],
+    "profile": {
+      "1": 1323,
+      "2": 1342,
+      "3": 79,
+      "4": 44,
+      "5": 102,
+      "6": 11,
+      "7": 19
+    },
+    "rank_mass": 5129,
+    "record_sha256": "ea44aa047a2a9cf034de8b56b2166c49cf2dbdf9cd9ed6a20299a4f2b05ef09a",
+    "records": 27234
+  },
+  "boolean_local_inputs": 4096,
+  "candidate_sha256": "dbc98e37719ff3a034c164a44a141346146ddd70f0276766e5ee7554ff515821",
+  "conclusion": {
+    "C_is_U_inverse": true,
+    "J_identity": true,
+    "K_equals_D": true,
+    "U_block_form": true
+  },
+  "controls_rejected": [
+    "delete_add",
+    "wrong_donor",
+    "self_add",
+    "frame_zero",
+    "unclaimed_helper",
+    "factor_swap",
+    "duplicate_donor",
+    "stale_source",
+    "wrong_minimum",
+    "wrong_matrix",
+    "stale_cleanup_H4"
+  ],
+  "copy_ranks": [
+    7,
+    7,
+    7,
+    7,
+    7,
+    7,
+    7,
+    7,
+    7
+  ],
+  "finite_columns": 661,
+  "frame_paths": 661,
+  "hypotheses": {
+    "H1_no_target_feeds_z": true,
+    "H2_D_frame0_targets_from_helpers": true,
+    "H3_A_z_only_scatter_targets_B_split": true,
+    "H4_C_literal_reverse_at_full": true,
+    "H5_V_identity": true
+  },
+  "kappa": "not_recomputed; no_new_kappa",
+  "minima": [
+    {
+      "feasible_edges": 20352,
+      "minimum": 16,
+      "state_destination_pairs": 24576,
+      "states": 4096
+    },
+    {
+      "feasible_edges": 19456,
+      "minimum": 16,
+      "state_destination_pairs": 24576,
+      "states": 4096
+    }
+  ],
+  "reverse_positive_strict_entries": 22,
+  "schema": "r439-frame519-verification/1",
+  "variant_content_sha256": "be3a8f25c5fb0bee8c13e6f979d7654d3f463a5f3e90a25eb556306eb8a352fc"
+}

research/r439-frame519-seed02/CLAIM.md

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+# Bit supplier claim, seed 02
+
+Claimed by Ross Richardson (@RossRichardson), with substantial OpenAI Codex
+assistance, on 2026-10-13 at 11:29 UTC (22:29 Melbourne).
+
+- Assignment: OS randomness, `python3 -c 'import secrets; print(secrets.randbelow(100))'`
+  returned **2**, bit-supplier track.
+- Exact base: `f567884aeb8851b6e794af1184119a3bfbe1e631`.
+- Selected certificate: PR799/PR589, conditional kappa
+  `1661634653669567/10^18`; no new kappa is proposed.
+- Object: PR589's tuned R439 phase-B block index 2, frame 519,
+  `B[163:205]`, on twelve existing source registers.
+- Method: split at `B[182]`, preserving the two exact integer-linear factors;
+  exhaust destination-once positive-addition schedules for each factor.
+  Verify the full dirty-input F2 map, literal reverse cleanup, frame paths,
+  native ADD counts and positive prefix bounds.
+- Deliverable: a checked shorter finite circuit or a scoped negative result,
+  reproducible search, exact certificate and mutation controls.
+- Finish target: 2026-10-13 12:09 UTC (23:09 Melbourne), reserving the final
+  quarter for verification and handoff.
+
+Three narrow candidates considered:
+
+1. Frame 519 two-factor scheduling (chosen by seed 02 as block index 2).
+   No specific construction claim found. PR891's whole-block single-write
+   obstruction does not cover this two-factor search.
+2. Frame 522 fixed-factor scheduling: another unclaimed block, but not chosen
+   because the seed selects block 2.
+3. Historical R480 quad 2: distinct from PR823's quad 1, but farther from the
+   selected source than the chosen object.
+
+Overlap: inspected open PRs 891, 873, 848 and 844 and refreshed the full open
+PR inventory. Neighboring frame constructions 506/507/508/509/520/521/523 and
+phase-A mini-nodes are distinct objects. Related methods and independent
+evidence will be credited. No pending implementation is imported.
+
+GitHub returned no pinned issues; the only open issue was #650 (Discussions).
+Therefore the claim is recorded here rather than in a new reservation issue.
+
+## Result update
+
+Completed: [the checked frame-519 circuit](README.md) saves twenty complete
+local ADDs (42 to 32 forward block gates, plus literal reverse cleanup),
+with exact fixed-factor class minima 16+16. The reverse positive bound drops
+to 1,031,082, the payload stays 93 bits, and the paid profile stays unchanged.
+All local and native checks and controls pass; no new kappa is claimed.
+See the [exact certificate](CERTIFICATE.json),
+[native certificate](NATIVE-CERTIFICATE.json) and [executed validation](VALIDATION.md).
+Final refresh found PR904's one-ADD `B[200:204]` replacement inside this
+block. Our ten-ADD whole-block replacement and exact 16+16 class minima add
+distinct coverage and evidence; [the overlap and attribution](README.md)
+are recorded explicitly. No combined saving is claimed.