Certify fixed-basis R420 target matching and the eight-ADD gap

research/r420-optimal-composed-pairs/CERTIFICATE.json

@@ -0,0 +1,129 @@
+{
+  "status": "PASS_R420_OPTIMAL_COMPOSED_PAIRS",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "baseline": {
+    "semantic_word_sha256": "983aec23d244575ae6205c53ed8ccae2f4a2aa8171463eef71d64c6bfceafe40",
+    "scalar_stream_sha256": "6494f36ba4ce06ae142ab0f81c2178d91c6a1c0c812a57f40958e48635b1853c",
+    "binary_additions": 18378,
+    "D_binary_additions": 11562,
+    "D_grouped_gates": 634,
+    "forward_and_reverse": [
+      {
+        "copies": 9,
+        "columns": 660
+      },
+      {
+        "copies": 9,
+        "columns": 660
+      }
+    ],
+    "forward_prefix": 253149,
+    "reverse_prefix": 4334338,
+    "payload_prefix_upper": "19505369118995241654063407203584",
+    "payload_prefix_bits": 104,
+    "paid_histogram": {
+      "1": 1320,
+      "2": 1440,
+      "4": 60,
+      "5": 120,
+      "8": 9
+    },
+    "rank_mass": 5112,
+    "frame_paths_sha256": "ef52add0118de86406ed3c58d6ff53b06b127c05238895b475181e55b98021ca",
+    "exported_records": 21336,
+    "record_sha256": "df920f588352d4d1d165d034655480c55f2182ae7fe4cee620d1a2c395c05b6b"
+  },
+  "replacement": {
+    "semantic_word_sha256": "37e695efa7f5a941a63255a57fda688d28e84b38d9486f11ae47d64910f159f5",
+    "scalar_stream_sha256": "00db3567d098be8c5523191a75153fb053682d4bc5561b900e35509ae9b5c33c",
+    "binary_additions": 18362,
+    "D_binary_additions": 11546,
+    "D_grouped_gates": 638,
+    "forward_and_reverse": [
+      {
+        "copies": 9,
+        "columns": 660
+      },
+      {
+        "copies": 9,
+        "columns": 660
+      }
+    ],
+    "forward_prefix": 253149,
+    "reverse_prefix": 4334338,
+    "payload_prefix_upper": "19505369118995241654063407203584",
+    "payload_prefix_bits": 104,
+    "paid_histogram": {
+      "1": 1320,
+      "2": 1440,
+      "4": 60,
+      "5": 120,
+      "8": 9
+    },
+    "rank_mass": 5112,
+    "frame_paths_sha256": "ef52add0118de86406ed3c58d6ff53b06b127c05238895b475181e55b98021ca",
+    "exported_records": 21320,
+    "record_sha256": "61331871038292444b4d8a2289e33da6ac999048c049cd9f86ea5fffcabef095"
+  },
+  "saved_additions": 16,
+  "selected_ADDs": 26916,
+  "saved_from_selected": 8554,
+  "matching_optimum": {
+    "unordered_edges": 7140,
+    "oriented_edges": 14280,
+    "pairs": 58,
+    "saving": 1442,
+    "twice_dual_objective": 2884
+  },
+  "controls": [
+    "omit helper preparation",
+    "omit target preparation",
+    "omit target restoration",
+    "omit helper restoration",
+    "omit middle read",
+    "D leaves frame zero",
+    "zero vertex prices",
+    "overlapping target pairs",
+    "feasible but nontight dual",
+    "inflated pair saving",
+    "certificate on original K",
+    "missing cleanup",
+    "neutral endpoint accepted and two ADDs charged"
+  ],
+  "PR733_matching_on_PR681_body": {
+    "semantic_word_sha256": "2f283fa62cfda57ee233604958ab02fbe5832899e18f0d10cd04b2623bc0b267",
+    "scalar_stream_sha256": "c23e94d72ff4cc878ca34ef500b52118e834ec1ffe521ab0a8415aaa68a0bce7",
+    "binary_additions": 18370,
+    "D_binary_additions": 11554,
+    "D_grouped_gates": 636,
+    "forward_and_reverse": [
+      {
+        "copies": 9,
+        "columns": 660
+      },
+      {
+        "copies": 9,
+        "columns": 660
+      }
+    ],
+    "forward_prefix": 253149,
+    "reverse_prefix": 4334338,
+    "payload_prefix_upper": "19505369118995241654063407203584",
+    "payload_prefix_bits": 104,
+    "paid_histogram": {
+      "1": 1320,
+      "2": 1440,
+      "4": 60,
+      "5": 120,
+      "8": 9
+    },
+    "rank_mass": 5112,
+    "frame_paths_sha256": "ef52add0118de86406ed3c58d6ff53b06b127c05238895b475181e55b98021ca"
+  },
+  "saved_beyond_prior_matching_on_same_body": 8,
+  "inherited_PR733_ADDs": 18548,
+  "same_optimum_on_PR733_body_ADDs": 18540,
+  "literal_H2_claimed": false,
+  "semantic_D_columns": 660,
+  "no_new_kappa": true
+}

research/r420-optimal-composed-pairs/CLAIM.json

@@ -0,0 +1,71 @@
+{
+  "assignment_seed": 11,
+  "randomness": "One secrets.randbelow(100) draw, recorded before inspection",
+  "track": "bit supplier",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "started_utc": "2026-10-13T05:29:14Z",
+  "claimed_utc": "2026-10-13T05:37:00Z",
+  "expected_finish_utc": "2026-10-13T06:20:00Z",
+  "object": "Exact disjoint target-pair optimum after the frozen PR694 helper basis, applied to PR681 composed body",
+  "method": "All 7140 unordered pair inequalities; integer vertex-price dual and exact finite circuit replay. Assignment seed 11 chooses target-pair optimality after inspecting three candidates.",
+  "deliverable": "One scoped optimum certificate and fully charged composed word, compared to selected PR543 and pending PR681/733; no new kappa.",
+  "candidates": [
+    {
+      "task": "Certify target-pair optimum on KQ and apply to PR681",
+      "decision": "Selected. PR733 and PR681 use greedy matching, while PR716 certifies only the different original K matrix."
+    },
+    {
+      "task": "Optimize the helper matching in PR694",
+      "decision": "Not selected. One probe improves helper-only gain from 6934 to 7002, but the simple vertex dual has a 146.5 gap and no exact optimum is claimed."
+    },
+    {
+      "task": "Four-wire exact synthesis of R420 cleanup",
+      "decision": "Not selected. PR754 already exhausts the original disjoint-window class."
+    }
+  ],
+  "coordination": "No pinned sprint issue. GitHub search found one open issue, #650 about Discussions, so claim is local.",
+  "overlap": {
+    "open_PRs": 598,
+    "through_PR": 779,
+    "relevant": [
+      681,
+      694,
+      708,
+      713,
+      716,
+      733,
+      754,
+      759,
+      774
+    ]
+  },
+  "publication_status": "Complete local result; awaiting independent validation clearance",
+  "final_overlap": {
+    "through_PR": 799,
+    "new_relevant": {
+      "794": "6be7364e0245c5a1c931cb1c43b3da991b755850",
+      "789": "d1634f3b316f2c3a1bb5f93a6117c8ebab9ab011",
+      "790": "08b4a039ba4938dd4f4c89a69759f49ed21923ef"
+    },
+    "PR681_and_PR733_heads_unchanged": true,
+    "main_unchanged": true
+  },
+  "result": {
+    "local_ADDs": [
+      18378,
+      18362
+    ],
+    "fixed_helper_pair_optimum": 1442,
+    "native": "fresh 5/9/11-stage passed",
+    "hosted": "fresh parent/whole-owner/invoice passed",
+    "precision": "196 charged at 256; 432 charged at 512; unchanged from PR681",
+    "no_new_kappa": true,
+    "PR733_matching_on_same_PR681_body": 18370,
+    "new_ADD_saving_beyond_prior_matching": 8,
+    "emitted_local_invocation_events": [
+      6144768,
+      6140160
+    ],
+    "counter_scope": "288 expanded local streams; unchanged 69120 bridge ADDs and schedule/hosting work charged separately"
+  }
+}

research/r420-optimal-composed-pairs/HOSTED.json

@@ -0,0 +1,184 @@
+{
+  "baseline": {
+    "parent_mutations": [
+      "omit an idle child",
+      "omit a bridge",
+      "omit terminal exchange",
+      "remove a local invocation",
+      "understate live stock",
+      "omit a local paid move",
+      "wrong reflected copy charge",
+      "alter residual orthogonal basis",
+      "misstate replication count",
+      "misstate stage count",
+      "alias data across stages",
+      "delay an idle advance past its level",
+      "truncate the last idle advance",
+      "re-use a helper bank slot",
+      "wrong residual frame",
+      "alias data across replica groups",
+      "omit the fourth replica group"
+    ],
+    "hosted_audit": {
+      "status": "PASS_INDEPENDENT_REPLICATED_HOSTING_AUDIT",
+      "template_sha256": "6a8436c8c33b88e3868086a124af88635bcd7f82e086a87d3159a7d5549fae66",
+      "emitted_program_sha256": "6d2c87e697b5b1a17efa0a34e815ebe5838c01151f15191d8b8d2f93f83e7edd",
+      "emitted_events": 6144768,
+      "profile": {
+        "1": 380160,
+        "2": 426624,
+        "4": 32640,
+        "5": 34560,
+        "6": 15360,
+        "7": 23040,
+        "8": 2592,
+        "42": 3456
+      },
+      "live": 30720,
+      "physical": 30729,
+      "hosted_residuals": 120960,
+      "bank_assignments": 0,
+      "rank_mass": 1956096,
+      "deficit": 9984,
+      "maxchild": 42,
+      "mutations_rejected": [
+        "slot outside window",
+        "copy index outside family",
+        "negative slot offset",
+        "wrong residual width",
+        "duplicate helper",
+        "omitted helper",
+        "hosted owner in another replica or outside the data stock",
+        "hosted owner on a wrong data family",
+        "wrong call orientation",
+        "duplicate call",
+        "changed idle rank",
+        "understated live stock",
+        "missing remainder summary",
+        "stale stage count",
+        "hosted coordinate beyond the pending set",
+        "overlapping hosted coordinates"
+      ]
+    },
+    "bit_lower": "413456747036699736067/250000000000000000000000",
+    "bit_lower_decimal": "0.001653826988146798944268",
+    "invoice": {
+      "live": 30720,
+      "physical": 30729,
+      "maxchild": 42,
+      "rank_mass": 1956096,
+      "hosted_residuals": 120960,
+      "bank_assignments": 0,
+      "prefix_bits": 196,
+      "charged_prefix_bits": 256,
+      "coefficient_bits": 196,
+      "two_level_coefficient_bits": 432,
+      "charged_two_level_coefficient_bits": 512,
+      "row_coefficient": 18355,
+      "halving_depth": 2
+    },
+    "global_prefix_bound": "96186053138539774649262655619329340866394145487272925986816",
+    "bit_profile": {
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+      "2": 426624,
+      "4": 32640,
+      "5": 34560,
+      "6": 15360,
+      "7": 23040,
+      "8": 2592,
+      "42": 3456
+    },
+    "local_additions": 18378
+  },
+  "replacement": {
+    "parent_mutations": [
+      "omit an idle child",
+      "omit a bridge",
+      "omit terminal exchange",
+      "remove a local invocation",
+      "understate live stock",
+      "omit a local paid move",
+      "wrong reflected copy charge",
+      "alter residual orthogonal basis",
+      "misstate replication count",
+      "misstate stage count",
+      "alias data across stages",
+      "delay an idle advance past its level",
+      "truncate the last idle advance",
+      "re-use a helper bank slot",
+      "wrong residual frame",
+      "alias data across replica groups",
+      "omit the fourth replica group"
+    ],
+    "hosted_audit": {
+      "status": "PASS_INDEPENDENT_REPLICATED_HOSTING_AUDIT",
+      "template_sha256": "528176278c3719970f984e5df9a28c970f73b5d6ac2ea6ea543deb4a9e9360c9",
+      "emitted_program_sha256": "b78f8e2dcb79f9d690b18e58cc2ba86972258dea487e1fd8700d5a4a28fb2f97",
+      "emitted_events": 6140160,
+      "profile": {
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+        "4": 32640,
+        "5": 34560,
+        "6": 15360,
+        "7": 23040,
+        "8": 2592,
+        "42": 3456
+      },
+      "live": 30720,
+      "physical": 30729,
+      "hosted_residuals": 120960,
+      "bank_assignments": 0,
+      "rank_mass": 1956096,
+      "deficit": 9984,
+      "maxchild": 42,
+      "mutations_rejected": [
+        "slot outside window",
+        "copy index outside family",
+        "negative slot offset",
+        "wrong residual width",
+        "duplicate helper",
+        "omitted helper",
+        "hosted owner in another replica or outside the data stock",
+        "hosted owner on a wrong data family",
+        "wrong call orientation",
+        "duplicate call",
+        "changed idle rank",
+        "understated live stock",
+        "missing remainder summary",
+        "stale stage count",
+        "hosted coordinate beyond the pending set",
+        "overlapping hosted coordinates"
+      ]
+    },
+    "bit_lower": "413456747036699736067/250000000000000000000000",
+    "bit_lower_decimal": "0.001653826988146798944268",
+    "invoice": {
+      "live": 30720,
+      "physical": 30729,
+      "maxchild": 42,
+      "rank_mass": 1956096,
+      "hosted_residuals": 120960,
+      "bank_assignments": 0,
+      "prefix_bits": 196,
+      "charged_prefix_bits": 256,
+      "coefficient_bits": 196,
+      "two_level_coefficient_bits": 432,
+      "charged_two_level_coefficient_bits": 512,
+      "row_coefficient": 18355,
+      "halving_depth": 2
+    },
+    "global_prefix_bound": "96186053138539774649262655619329340866394145487272925986816",
+    "bit_profile": {
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+      "2": 426624,
+      "4": 32640,
+      "5": 34560,
+      "6": 15360,
+      "7": 23040,
+      "8": 2592,
+      "42": 3456
+    },
+    "local_additions": 18362
+  }
+}