Research construction: R439 phase-B blocks 506/523 to 24/39 ADDs + certified single-write class boundaries (no new kappa)

research/r439-bsection-survey/CLAIM.md

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+# Sprint scope claim (recorded locally)
+
+No pinned sprint coordination issue exists (checked 2026-10-13; the only open
+issue is #650, unrelated), so the scope claim is recorded here, per the sprint
+protocol.
+
+- Track and seed: **bit supplier (00-19), OS random seed 8**.
+- Base commit: `f567884aeb8851b6e794af1184119a3bfbe1e631` (origin/main at
+  sprint start; selected PR799/PR589, conditional kappa
+  0.001661634653669567).
+- Object: the phase-B block schedule of PR589's tuned punctured R439 word
+  (`research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz`), section B
+  runs at frames 506-509 and 519-524.
+- Method: whole-block single-write class (PR #873's formulation) searched by
+  a realized-subset dynamic program with meet-in-the-middle donor sums;
+  class-infeasibility by two independent exhaustive recursions plus
+  order-independent per-row donor-supply certificates.
+- Parameter range: all ten phase-B blocks of the word; constructions spliced
+  only for frames 506 and 523.
+- Expected deliverable: one verified research package
+  (`research/r439-bsection-survey/`) with two block shortenings (24,305 ->
+  24,289 local ADDs), certified class minima for the feasible blocks, and
+  scoped infeasibility certificates for the rest; no new kappa.
+- Overlap check at claim time (2026-10-13): open PRs #873 (block 508),
+  #843 (block 509), #844 (block 520), #857 (block 523) cover four claimed
+  blocks with other mechanisms; #728/#792 cover phase-A mini-nodes. No open
+  PR changes frames 506/507/519/521/522/524. Blocks 508/509/520/523 appear
+  here only as cross-checks (and frame 523 as a strictly shorter independent
+  witness than #857's published 40-gate program).
+- Overlap refreshed before submission (2026-10-13): PR #880 (frame 507,
+  fixed-factor class, 35 -> 30) and PR #884 (frame 521, factorization class,
+  47 -> 31) landed on two surveyed blocks after the search completed; both
+  use mechanisms outside the single-write class and are disclosed as
+  complementary evidence in README.md. Frames 506 and 523 remain uncovered
+  by any open PR except #857's weaker 523 witness.
+- Status: completed in session; submitted as
+  https://github.com/CrocSwap/integer-mult-bounds/pull/891 (branch
+  `research/agent-04-bit-seed08`, commit `bdff756c`). See README.md and
+  VALIDATION.md.

research/r439-bsection-survey/EXPECTED.json

@@ -0,0 +1,327 @@
+{
+ "bill_after": {
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+  "copies": 9,
+  "erasures": 9,
+  "forward_positive_bound": 49347,
+  "payload_bits": 93,
+  "record_sha256": "ebc8fd69144216f36df9311c7b2af1e1fb163db59ce43bda9887ce99e514550e",
+  "records": 27218,
+  "reverse_positive_bound": 1090494
+ },
+ "bill_before": {
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+  "erasures": 9,
+  "forward_positive_bound": 49347,
+  "payload_bits": 93,
+  "record_sha256": "ea44aa047a2a9cf034de8b56b2166c49cf2dbdf9cd9ed6a20299a4f2b05ef09a",
+  "records": 27234,
+  "reverse_positive_bound": 1113070
+ },
+ "spliced_frames": [
+  506,
+  523
+ ],
+ "survey": {
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+    "minimum": 24,
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+    "states": 1024
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+   "minimum": 24,
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+   "registers": [
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+   ],
+   "reverse_entrywise_dominated": true,
+   "reverse_larger_entries": 0,
+   "reverse_strictly_smaller_entries": 5
+  },
+  "507": {
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+    "recomputed_supply": 1,
+    "row": 3,
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+   }
+  },
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+    "states": 2048
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+  },
+  "509": {
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+   "registers": [
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+   "supply_witness": null
+  },
+  "519": {
+   "backward_optimality": {
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+    "states": 4096
+   },
+   "original_gates": 42,
+   "registers": [
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+   ],
+   "supply_witness": {
+    "col": 8,
+    "demand": 2,
+    "recomputed_demand": 2,
+    "recomputed_supply": 1,
+    "row": 2,
+    "supply": 1
+   }
+  },
+  "520": {
+   "backward_optimality": {
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+    "feasible_edges": 5584,
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+    "states": 4096
+   },
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+   "registers": [
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+    "recomputed_supply": 0,
+    "row": 9,
+    "supply": 0
+   }
+  },
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+    "states": 4096
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+  },
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+   "registers": [
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+    "row": 5,
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+   "reverse_larger_entries": 13,
+   "reverse_strictly_smaller_entries": 16
+  },
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+   "registers": [
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+   }
+  }
+ },
+ "survey_frames": [
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+  507,
+  508,
+  509,
+  519,
+  520,
+  521,
+  522,
+  523,
+  524
+ ]
+}