Finite bit construction: R480 Q-node2 saves 18 ADDs (no new kappa)

research/r480-qnode-seed02/CLAIM.md

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+# Bit supplier claim — seed 2
+
+- Started 2026-10-13 08:55 PDT; planned finish by 09:55, final fifteen minutes reserved for verification and handoff. Finish sooner if complete.
+- Fresh OS randomness: `secrets.randbelow(100)` returned **2**, assigning the bit-supplier track.
+- Exact fetched base: `407d52ff15b2217b6e22bce44728b4c3907b6515`.
+- Selected record and actual construction/review read: PR942 U8/T37, conditional kappa `0.001661960547713947`, unchanged PR589/555 bit supplier. This investigation uses a historical R480 word deliberately.
+- Three candidates: (0) another R439 six-wire prefix pass (overlaps PR980); (1) an R480 six-wire quad (PR823 already supplies quad1 and the class has substantial precedent); (2) R480 twelve-source Q-node2. Seed `2 % 3` chooses the third; `2 % 10` chooses Q-node2.
+- Exact scope: historical PR503/510 word, phase A events `[2250:2302]`, frame484, twelve arbitrary source registers. Replace this one 52-XOR common-frame block, then regenerate and charge its literal reverse cleanup. No extra wire, source copy, frame transition or recursive child is proposed.
+- Method: bounded 1,000 seeded column-order Gauss-Jordan trajectories for the exact twelve-output F2 map; complete whole-word positive-prefix and native checks decide admission. This is a different twelve-source matrix from PR823's six-wire dirty-helper quad1, not a repeat with a different random seed. No unrestricted optimum claim.
+- Optimistic budget before packaging: a preliminary exact 43-XOR word would save nine in A and nine in C, or eighteen per complete local word; all other operations and paid recursive profile retained. Precision could invalidate it. No exponent improvement follows from this finite arithmetic saving.
+- Deliverable: one frozen exact recipe, executable bounded reproduction, independent full-column evidence, complete local/native bills and controls, proof/interface limits, source pins and attribution. If the candidate fails complete precision, record that failure distinctly and allow one bounded revision within this block.
+- Coordination: open issues650 and913 are unrelated; no pinned sprint issue found. Local claim used. Refreshed recent PRs through985 and all-state R480/Q-node queries immediately before claiming. PR823 is the relevant historical comparator, PR980 concerns R439, PR978 R420 compensation; none changes this Q-node. Review ledger records PR503/510 and PR691 as incorporated. No separate reservation issue.
+- Scope ownership: delegated work stays within this block; no edits to upstream, selected frontier, inherited generators or unrelated packages.
+- Prepared for ToikY with substantial OpenAI Codex assistance, Apache-2.0; full predecessor credit and exact pins will be included.
+
+## Completed result and claim update
+
+The candidate and search were frozen by approximately 09:03 PDT, followed by
+verification and packaging. Three preliminary orientation probes ran in order
+Q2, Q1, Q8, each with a fresh `random.Random(2)` and 1,000 trajectories. Their
+best lengths were 52 -> 43, 71 -> 41 and 62 -> 46. Only the seed-selected Q2
+was packaged and admitted; the other probes received no whole-word precision
+or native validation. Final Q2 coverage is exactly 1,000 trajectories; no
+further search or pivot was made. This disclosure avoids presenting the
+orientation probes as admitted additional results.
+
+Completed: Q2 uses 43 XORs and literal cleanup saves 18 complete local ADDs.
+Both independent Python implementations and retained native 5/9/11-stage
+checks pass; the paid histogram and frame paths are unchanged, and both
+complete payloads remain 102 bits within the 104-bit allowance. No new kappa,
+optimum or hosted-parent invoice is claimed. See VALIDATION.md for executed
+coverage and controls.
+
+Final overlap refresh through PR999 and all-state R480/Q-node searches found
+no duplicate of this matrix. Related PR823 is credited. New PR986 and PR989
+concern R439; main `f4a7051883bc76dad7861b3f0caf7361ce86fe90` preserves all
+21 consumed source blobs and the selected record. There is still no open
+sprint coordination issue. This is the one local claim update with the result:
+[reviewable contribution branch](https://github.com/ToikY/integer-mult-bounds/tree/codex/bit-supplier-seed02/research/r480-qnode-seed02).

research/r480-qnode-seed02/EXPECTED.json

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+{
+  "after": {
+    "adds": 33940,
+    "copies": 9,
+    "erasures": 9,
+    "formal_columns": 720,
+    "forward_positive_prefix": 176135,
+    "frame_paths_sha256": "2b384919c4b79258e608ceac2f71a9fa44d47d1b9e65c8fb55413de0388fd71a",
+    "inverse_positive_prefix": 3682548,
+    "payload_bits": 102,
+    "payload_upper": "4742570525118367822773353856000",
+    "scalar_stream_sha256": "f64831f5b9220db0d58e6b4aa9ba7ebb62d45d1bd414c7b791f908a6dca85b41",
+    "word_sha256": "29932aaf7435175372811fbd6d48902be00864cc07b313afa0cf2685db876ff8"
+  },
+  "assignment_seed": 2,
+  "base_commit": "407d52ff15b2217b6e22bce44728b4c3907b6515",
+  "before": {
+    "adds": 33958,
+    "copies": 9,
+    "erasures": 9,
+    "formal_columns": 720,
+    "forward_positive_prefix": 176135,
+    "frame_paths_sha256": "2b384919c4b79258e608ceac2f71a9fa44d47d1b9e65c8fb55413de0388fd71a",
+    "inverse_positive_prefix": 3751204,
+    "payload_bits": 102,
+    "payload_upper": "4921056267806722187755121024000",
+    "scalar_stream_sha256": "510dc7d43ccee1b463e92fa84141c0bcf4cfdd878d7326117fda0d2b1fee1367",
+    "word_sha256": "8639e22008c24a5690dd250eba702fe5fca85ddd036dcbec20baba77b7e213ba"
+  },
+  "controls": {
+    "deleted_candidate_gates_rejected": 43,
+    "identity_growth_rejected": true,
+    "stale_cleanup_endpoint_valid_adds": 33949,
+    "stale_cleanup_rejected_by_literal_contract": true,
+    "total": 45
+  },
+  "independent": {
+    "arbitrary_dirty_helpers": 480,
+    "arbitrary_targets": 120,
+    "columns_checked": 720,
+    "controls": [
+      "all_43_single_gate_deletions",
+      "swapped_output_rows",
+      "arbitrary_dirty_helper_assumed_zero",
+      "arbitrary_source_assumed_zero",
+      "arbitrary_target_assumed_zero",
+      "missing_dirt_compensation_ADD",
+      "missing_cleanup_ADD",
+      "wrong_local_frame",
+      "missing_private_ERASE"
+    ],
+    "frame_paths_sha256": "2b384919c4b79258e608ceac2f71a9fa44d47d1b9e65c8fb55413de0388fd71a",
+    "local_Boolean_assignments": 4096,
+    "local_rows": [
+      4095,
+      2390,
+      3835,
+      3831,
+      1625,
+      3935,
+      3951,
+      16,
+      207,
+      4,
+      1023,
+      1
+    ],
+    "local_word_xor_saving": 18,
+    "original": {
+      "endpoint_sha256": "900eeb83e7b68ae3474e74bdb5fa3cb64668877289fe540aa691450aac683bcf",
+      "five_stage_payload_below_2pow104": true,
+      "five_stage_payload_bits": 102,
+      "five_stage_payload_upper": "4921056267806722187755121024000",
+      "native_records": 36916,
+      "native_records_sha256": "a2f1946752268e8914e2790fc3d2d5e6d287f73132cbea6c1dee6f9f3a2b372a",
+      "positive_forward": {
+        "adds": 33958,
+        "bits": 18,
+        "copies": 9,
+        "max_row_l1_upper": "176135"
+      },
+      "positive_reverse": {
+        "adds": 33958,
+        "bits": 22,
+        "copies": 9,
+        "max_row_l1_upper": "3751204"
+      }
+    },
+    "register_frame_paths_checked": 720,
+    "replacement": {
+      "endpoint_sha256": "900eeb83e7b68ae3474e74bdb5fa3cb64668877289fe540aa691450aac683bcf",
+      "five_stage_payload_below_2pow104": true,
+      "five_stage_payload_bits": 102,
+      "five_stage_payload_upper": "4742570525118367822773353856000",
+      "native_records": 36898,
+      "native_records_sha256": "88aa5165b44687782bec4bf0cf88083754f3b6897aa0ead75f103737d82f038d",
+      "positive_forward": {
+        "adds": 33940,
+        "bits": 18,
+        "copies": 9,
+        "max_row_l1_upper": "176135"
+      },
+      "positive_reverse": {
+        "adds": 33940,
+        "bits": 22,
+        "copies": 9,
+        "max_row_l1_upper": "3682548"
+      }
+    },
+    "source_sha256": "92e399e9a486b55229b5624632ac54f800dd9e022f2aee97f1e5f264bbc0ef5c",
+    "status": "PASS_INDEPENDENT_R480_QNODE2"
+  },
+  "no_new_kappa": true,
+  "recipe_sha256": "cdbda3682cf215ed167418bfc1f53722ecac3e3421c546fbfd7d6abfa17f6d47",
+  "saved_adds": 18,
+  "status": "PASS_R480_QNODE_SEED02"
+}