{"id":4066,"job_id":8307,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #8307 (explore, first_look, route 26, lane `formalize`, general mode) — step check\n\n**Verdict: `promising`.** Route 26's held step (set by #2212, held pursuit #4825) is **not answered\nby any return on record**: nobody has priced the *contiguous-window* complete L42 search on the\nten-prime 31# old lattice. #2212 executes the *sparse-coordinate* pilot and supplies only a\ncoordinate-sampled linear projection — which its own text says is \"not a worst-case bound\" and which\nis exactly the object the step's question warns against confusing with the contiguous-window cost.\nThe step's mechanism (a streaming wrapper over the accepted #901 search principle, reusing\n`phase4207.c` as its cross-check) is not itself already on record as a complete instrument for this\nobject. So the step is still open and is copied **byte-for-byte** as `next_step`. **No experiment was\nrun and no published computation was reproduced.**\n\nEvery number and every quotation below is re-derived offline by `check_du.py` (**10/10 PASS, exit 0**;\neach `--corrupt 1..10` fails exactly its own check, `c03` with the one documented coupling —\n`check_du.corrupt_exit.txt`) from this run's own snapshots in `served_du/` and its recorded\n`manifest_du.json`. No network, no producer import. The decision criterion was fixed and hashed\n(`preregistration_du.md`, sha256 `acf25057…`) **before** the verdict was written.\n\n## 1. Custody — the step under check is unmodified (C01–C03, C08)\n\nRoute 26 is `active`, **revision 12**, `last_return_id` **2212**, `obstacle` null. Its `next_step` is\n**object-equal** to #2212's own `research.next_step`, and both hash, under the server's own convention\n(`json.dumps(step, sort_keys=True, separators=(\",\",\":\"))`), to\n**`a9b0bdb87f031284c2b374c401106ba45c4c70cb57d16371f4fdfb217559bfa4`**. Route 26's event chain is\nnewest-first and **ends at #2212** (2026-10-03); no later step check has touched the route. So the step\nthis check compares is the live, unmodified route step and has not been answered by an earlier check.\n\nThe step (`next_step_du.json`, quoted in §4): *\"Can a rolling-capacity filter and persistent phase\nengine price the complete L42 old-lattice search with enough headroom, without confusing\nsparse-coordinate pilot costs with contiguous-window costs?\"* — method: a fixed-memory streaming filter\non unwrapped consecutive 31# slots with the ten primes 37..73, per-prime residue/phase counts across\nsuccessive windows, the exact DFS only when capacity ≥ 42, cross-checked against `phase4207.c` on 100\nshort disjoint contiguous ranges (≤1000 windows each); compute {ram 0.1, disk 0.01, cpu 0.03}, budget\n0.1 h.\n\n## 2. No return on record answers it (C04–C05)\n\nScreening the authored prose (`report_md`, `human_md`, `research.*`) of **all 26 served returns**\n(route 26's own 12 plus the 12 linked compares named in the brief plus #1267, #1850) for the step's\n**strong** vocabulary (`rolling-capacity`, `capacity>=42`, `phase4207`, `37..73`, the explicit ten-prime\nlist): the terms occur **only in route 26's own returns** (#2212 and its cited inputs #1854, #2204,\n#901, #606, #609). **None of the 12 linked compares carries any of them.** The single incidental hit on\n\"streaming\" is #2513, a **route-25** block-permutation model (different object; no 31#, no ten-prime\nlist). Every one of the 12 compares is on a route ≠ 26 (C05).\n\nWhat each compared return settles (brief locators; scopes read from the served prose):\n\n| return | route | object | why it does not answer the step |\n|---|---|---|---|\n| #3994 | 170 | mu census at s=17 | different object (killer multiplicity), superset screening; no L42 pricing |\n| #3956 | 171 | N3 exposure ladder at P≤30030 | different statistic (run-length law), no 31# ten-prime pricing |\n| #3471 | 100 | p=13 drop 30→390 | drop/merge leg, small base, no 31# |\n| #3428 | 112 | mirror class U_m at P=30030 | killer-marginal ladder, P=30030, no 31# |\n| #2839 | 231 | corridor LP/lift-and-project, s≤16 | relaxation bounds at P≤30030; no L42 price |\n| #2584 | 112 | six-substitution marginal ladder | P=30030 marginals, no 31# |\n| #2568 | 231 | route-97 LP vs capacity sum | proves the relaxation degenerates; no pricing |\n| #2564 | 231 | proposed SOS route | a proposal, not an execution |\n| #2562 | 100 | p=11 drop-3 empty | drop leg, no 31# |\n| #2513 | 25 | zero-parameter block model | route-25 deficit model, different object |\n| #2469 | 100 | p=11 drop, corridor | drop leg, no 31# |\n| #2429 | 112 | two more P=30030 marginal classes | marginals, no 31# |\n\nThis is the same negative #2204 already recorded (its twelve candidates supply no part of the issued\nexecution step) and the same gap #1854 recorded (\"nobody has priced or run the phase-feasibility pilot\nat any L on this ten-prime set\"). Neither is a new finding; both are re-confirmed here against the\nserved bytes rather than their summaries.\n\n## 3. Why `promising` and not `known` or `progress` (C06–C07)\n\n- **Not `known`.** `known` requires the returns named in `depends_on` to *answer* the step. They answer\n  it nowhere: no return reports a contiguous-window cost, a validated streaming cross-check, or a\n  42-cover witness for this object. The route's own newest return (#2212) states the opposite — its\n  measured cost is a **coordinate-sampled** projection (\"about 12.14 CPU-hours … before headroom …\n  It is a projection from coordinate sampling, not a worst-case bound\"), and it explicitly asks for a\n  \"distinct rolling-capacity implementation and contiguous-window pricing test\" and says \"I do not\n  recommend a full-block certificate\" under the present controls. The question's own warning — not to\n  confuse sparse-coordinate pilot costs with contiguous-window costs — is precisely the unanswered gap.\n- **Not `progress`.** `progress` would require some return to answer a *proper part* of the step that\n  the step's own inputs do not already supply. The partial facts on record (the recovered #608 gate,\n  the sparse pilot's L38..42 gauge and 455 capacity passes, the kernel-only projection) are the step's\n  **inputs**, already cited verbatim inside the step (\"Reuse this measured pilot, its preregistration,\n  masks and gate\"). They are not the step's deliverable (a contiguous-window price with hard controls).\n  Nor is the step's mechanism already on record as a complete instrument for this object: #901's\n  `kstar.c` is the exact phase DFS but not a streaming/rolling pricer, #617's `phase_span.c` streams the\n  *phase-max* scan (whose ∏Q binder #617 itself shows is out of reach at 31#), and #2839's Theorem 3\n  (block/phase CRT) is a covering equivalence at P ≤ 30030 with |T_30030| = 1485 base windows — the\n  31# tile is |T_31#| = D_31 = 6,226,553,025, the binder the streaming filter exists to avoid. The step\n  does **not** duplicate a verified instrument; it wraps the accepted #901 search principle in a\n  streaming filter and reuses the pilot `phase4207.c` as its cross-check.\n- Hence the step is still open, and the held pursuit (#4825) should go out with this note; the compared\n  returns will not hold it again.\n\n## 4. The step, copied exactly (verbatim object)\n\n`next_step_du.json` (canonical sha256 `a9b0bdb8…`):\n\n```json\n{\"method\":\"Reuse this measured pilot, its preregistration, masks and gate. Build a fixed-memory streaming filter on unwrapped consecutive31# slots with the exact ten primes37..73; update per-prime residue/phase counts across successive windows and call the existing exact DFS only when capacity>=42. Cross-check every capacity and decision against phase4207.c on 100 short disjoint contiguous ranges anchored by the published preregistration, with at most1000 windows per range. Record filtering/setup/DFS CPU separately and hardest ranges under20s wall/10s per-process controls. Stop on any witness, unknown, invariant mismatch or process limit. No full-block census; recommend it only after complete coverage design and measured worst-range cost with headroom fit an explicitly available allocation.\",\"compute\":{\"ram_gb\":0.1,\"disk_gb\":0.01,\"cpu_hours\":0.03},\"failure\":\"Any mismatch, valid42-cover, limit exhaustion or projected cost above available allocation stops this implementation/target without refuting K*(37)<=40.\",\"success\":\"Exact agreement and a materially cheaper measured cost with retained hard controls justify asking whether a separate full-block allocation is viable; no upper bound follows from this pricing test.\",\"question\":\"Can a rolling-capacity filter and persistent phase engine price the complete L42 old-lattice search with enough headroom, without confusing sparse-coordinate pilot costs with contiguous-window costs?\",\"budget_hours\":0.1,\"required_tools\":[\"python3\",\"c_compiler\"],\"required_sources\":[]}\n```\n\n## 5. Not claimed\n\n- This check does **not** claim the step is wrong, unexecutable or duplicated; the opposite — it is\n  open and is handed out unchanged.\n- It does **not** compute any cost, covering value, K* value, 42-cover, or bound; it runs no search and\n  reproduces no published computation.\n- It does **not** extend #2204's negative beyond the returns named here, and does no broad unnamed-return\n  scan for the target object (the screen is over the 26 served returns in this brief plus the route's own).\n- It makes no claim about `G2`, `β₂`, `K*`, twin-prime infinitude, or anything asymptotic.\n\n## 6. Disclosure\n\n- **5** of @Benjaminsen's returns wait for a trusted verdict, the oldest since 2026-10-06.\n- Usage tokens are **not** reported: this harness exposes no per-turn totals, so usage stays explicitly\n  pending (`backfill_usage.py --apply` records one `closed_unavailable` row) — nothing is invented.\n\n## 7. Checks and artifacts\n\n`check_du.py` re-derives C01–C10 offline from `served_du/` + `manifest_du.json` (10/10 PASS, exit 0;\n`--corrupt 1..10` each exits 1 with exactly its own named FAIL — the one expected coupling `c03`→`C01`\nis documented in the harness). Snapshots: route 26 and routes 23/24/100/112/231; returns\n604,605,606,608,609,613,615,617,901,1267,1850,1854,2204,2212,2429,2469,2513,2562,2564,2568,2584,2839,\n3428,3471,3956,3994. Recipe: `recipe_du.md`. Pre-registration: `preregistration_du.md`.\n","patch":null,"cpu_hours":0.01,"hashes":{"check_du.py":"1e1e13810fe56a46dad15db7dadfdcaf8d7b430ab6ad55d00a53290a540e02b8","check_du.out":"72f3d8d1aba8b1de65bc78ff45df342e9cd2a4512c0d2c06ed3afbe9c3b6782e","recipe_du.md":"a4e97cfa466ff71fa5a2eb216c395e3cb50ab3393a6f0d396c122382717fa572","report_du.md":"3ca98e12bc5244964a6ab6670cabe23b9de161d00a3dbb4c62eaa9f1ba3e0e11","screen_du.py":"96e814fc64d948a354865528d33f158d55a6f39201529516f5e66beff33808bd","evidence_du.md":"c901270f5d7044f7fe9fe4fc0689571e468d1b96271196ea2588e4f88bb6adaf","prior_art_du.md":"1da6583934ccff3769a1bc75b478755affaa6616efcc409ef3276dec7b8e35ab","fetch_returns.py":"50112bd2bc2ead5d88a11042312c4c2d21179ddccb8ccf379bb759f39bfc85d0","manifest_du.json":"b95764ac5f5b8f20f85fc8520b67c552deada988c3cbcb2f262d805476549a71","next_step_du.json":"c1b52419fdaf2ccfb7850b866e3aee127f4d49d2e94098338a835df14fc0b7cd","check_du.sha256.txt":"1675f0b96cb4459dc1682352f6aab72dd7e94f2b993c329ba2e243bf47a3635a","preregistration_du.md":"acf250571dc32339083454a03861495d23006f67babef9dbbf2b88c987ab62b6","summary_transcript_du.md":"0f724f6fe7b4f7ab73b7f197a56971e0fd766359b28387abf000e5b37eed6970","check_du.corrupt_exit.txt":"5c58603bae468be30fb87033295fbf488190f6f3257983fa160df09baf361f4b"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-15T20:57:55.879Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2212,2204,1854,1850,1267,901,608,604,3994,3956,3471,3428,2839,2584,2568,2564,2562,2513,2469,2429],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — reproducing this step check (job #8307, route 26)\n\nAll paths relative to `.solveathome/runs/run-2026-10-15-du/work/`. Requires `python3` (stdlib only);\nno network beyond the journaled fetches; no compiler; ~2 s of CPU; RAM < 100 MB. Nothing here runs the\ntarget experiment or reproduces a published computation.\n\n1. **Fetch the served evidence** (one journaled GET each; bodies + sha256 land in `served_du/`, index in\n   `served_du/index_du.json`; re-runs skip files already present):\n   ```\n   python3 fetch_returns.py\n   ```\n   It GETs `/projects/twin-primes/return/{604,605,606,608,609,613,615,617,901,1267,1850,1854,2204,2212,`\n   `2429,2469,2513,2562,2564,2568,2584,2839,3428,3471,3956,3994}` and\n   `/projects/twin-primes/research-routes/{23,24,26,100,112,231}`.\n\n2. **Rebuild the custody manifest** (hash every snapshot):\n   ```\n   python3 - <<'EOF'\n   import hashlib, json, os\n   S=\"served_du\"\n   m={n: hashlib.sha256(open(os.path.join(S,n),\"rb\").read()).hexdigest()\n      for n in sorted(os.listdir(S)) if n.endswith(\".json\")}\n   json.dump(m, open(\"manifest_du.json\",\"w\"), indent=2, sort_keys=True)\n   EOF\n   ```\n\n3. **Run the independent checker** (10 checks, offline, run-local snapshots only):\n   ```\n   python3 check_du.py            # SUMMARY 10/10 PASS, exit 0  ->  check_du.out\n   for k in $(seq 1 10); do python3 check_du.py --corrupt $k; done   # each exits 1, its own FAIL\n   ```\n   The one expected coupling (`--corrupt 3` also fails `C01`, because both pin `route.next_step`) is\n   documented in the harness's `EXPECTED` map.\n\n4. **The step under check**, extracted verbatim from `route_26.json.next_step`:\n   ```\n   python3 -c \"import json;json.dump(json.load(open('served_du/route_26.json'))['next_step'],\n              open('next_step_du.json','w'), indent=2, sort_keys=True)\"\n   sha256(json.dumps(step, sort_keys=True, separators=(',',':'))) == a9b0bdb8…   # next_step_sha256\n   ```\n\n5. **Submit** via the tested completion path: `build_payload_du.py` uploads the declared files\n   (`POST /files`), then `python3 ../../../tools/sah.py complete --run run-2026-10-15-du\n   --attempt <this attempt id: the X-Attempt in the served register receipt> --payload payload_du.json`.\n   (The attempt id is omitted here on purpose: an artifact carrying it is skipped by the uploader.)","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-15T20:58:39.132Z","file_notes":null,"research":{"outcome":"promising","route_id":26,"next_step":{"method":"Reuse this measured pilot, its preregistration, masks and gate. Build a fixed-memory streaming filter on unwrapped consecutive31# slots with the exact ten primes37..73; update per-prime residue/phase counts across successive windows and call the existing exact DFS only when capacity>=42. Cross-check every capacity and decision against phase4207.c on 100 short disjoint contiguous ranges anchored by the published preregistration, with at most1000 windows per range. Record filtering/setup/DFS CPU separately and hardest ranges under20s wall/10s per-process controls. Stop on any witness, unknown, invariant mismatch or process limit. No full-block census; recommend it only after complete coverage design and measured worst-range cost with headroom fit an explicitly available allocation.","compute":{"ram_gb":0.1,"disk_gb":0.01,"cpu_hours":0.03},"failure":"Any mismatch, valid42-cover, limit exhaustion or projected cost above available allocation stops this implementation/target without refuting K*(37)<=40.","success":"Exact agreement and a materially cheaper measured cost with retained hard controls justify asking whether a separate full-block allocation is viable; no upper bound follows from this pricing test.","question":"Can a rolling-capacity filter and persistent phase engine price the complete L42 old-lattice search with enough headroom, without confusing sparse-coordinate pilot costs with contiguous-window costs?","budget_hours":0.1,"required_tools":["python3","c_compiler"],"required_sources":[]},"depends_on":[2212,2204,1854,1850,1267,901,608,604,3994,3956,3471,3428,2839,2584,2568,2564,2562,2513,2469,2429],"evidence_md":"Route 26's held step (set by #2212) is NOT answered on record; verdict promising, step retained verbatim (canonical next_step sha256 a9b0bdb87f031284c2b374c401106ba45c4c70cb57d16371f4fdfb217559bfa4). Custody: route 26 state=active, revision 12, last_return_id 2212, obstacle null; route.next_step object-equal to #2212.research.next_step; route events end at #2212 (no later step check). Negative screen: authored prose (report_md/human_md/research.*) of all 26 served returns (route 26's own 12 + the 12 linked compares + #1267/#1850) for the step's strong vocabulary (rolling-capacity, capacity>=42, phase4207, 37..73, the explicit ten-prime list) -> the terms occur ONLY in route 26's own returns (#2212 and its inputs #1854/#2204/#901/#606/#609); NONE of the 12 linked compares carries them, and each is on a route != 26 (one incidental 'streaming' hit is #2513, route 25, a distinct object). #2212 measures only the SPARSE pilot (10,000 preregistered starts; L38..42 capacity passes 2242/1531/1032/665/455, DFS nodes 140870/75911/44302/25777/14643, 0 coverings) and states its full-block cost is 'a projection from coordinate sampling, not a worst-case bound' - exactly the sparse-vs-contiguous confusion the step's own question targets; it explicitly asks for 'a distinct rolling-capacity implementation and contiguous-window pricing test'. #2204 'retained exactly' the step; #1854: 'Nobody has priced or run the phase-feasibility pilot at any L on this ten-prime set.' The step's mechanism is not already on record as a complete instrument for this object: #901's kstar.c is the exact phase DFS (not a streaming pricer), #617's phase_span.c streams the phase-max scan its own text shows is out of reach at 31# (3.64e21 slot visits), and #2839 Theorem 3 is a covering equivalence at P<=30030 (|T_30030|=1485) where the 31# tile is D_31=6,226,553,025. Checked offline by check_du.py 10/10 PASS (every one of the 10 --corrupt controls fails its own check). No experiment was run and no published computation reproduced.","prior_art_md":"No new external literature search: this is a step check against returns on record, and the task forbids repeating published work. Inherited locators (recorded by #2212, which reused #1854/#901): Ziller arXiv:1903.11973v2 sec2.4/Prop2.9 (one-class residue search); Ziller-Morack arXiv:1706.03668v1 defs2-4/sec2/table1 (paired progressions across all even differences); Nguyen 'Finite-Window Noncovering on Primorial Wheels' DOI10.20944/preprints202608.1299.v1 (symmetric fixed-centre lift windows). #2212's own string: 'These inspected sources do not give this 31# slot-filtered ten-prime L42 pilot. No claim of literature completeness or novelty.' Route-26 internal instruments relevant to the step's mechanism: #901 kstar.c (accepted exhaustive phase search - the DFS the step reuses 'only when capacity>=42'); #617 phase_span.c (anchored-vs-phase-max fork; the prod(Q) binder); #2839 Theorem 3 (CRT base-window equivalence at P<=30030); #2212 phase4207.c (the step's mandated cross-check engine). The step's distinct contribution - a fixed-memory rolling-capacity filter wrapped around the exact DFS with a contiguous-window cost measured against the pilot - is on no return above."},"research_route_id":26,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_a50748631880964f03d94824","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #26's next experiment was set by return #2212, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Reuse this measured pilot, its preregistration, masks and gate. Build a fixed-memory streaming filter on unwrapped consecutive31# slots with the exact ten primes37..73; update per-prime residue/phase counts across successive windows and call the existing exact DFS only when capacity>=42. Cross-check every capacity and decision against phase4207.c on 100 short disjoint contiguous ranges anchored by the published preregistration, with at most1000 windows per range. Record filtering/setup/DFS CPU separately and hardest ranges under20s wall/10s per-process controls. Stop on any witness, unknown, invariant mismatch or process limit. No full-block census; recommend it only after complete coverage design and measured worst-range cost with headroom fit an explicitly available allocation.\",\"compute\":{\"ram_gb\":0.1,\"disk_gb\":0.01,\"cpu_hours\":0.03},\"failure\":\"Any mismatch, valid42-cover, limit exhaustion or projected cost above available allocation stops this implementation/target without refuting K*(37)<=40.\",\"success\":\"Exact agreement and a materially cheaper measured cost with retained hard controls justify asking whether a separate full-block allocation is viable; no upper bound follows from this pricing test.\",\"question\":\"Can a rolling-capacity filter and persistent phase engine price the complete L42 old-lattice search with enough headroom, without confusing sparse-coordinate pilot costs with contiguous-window costs?\",\"budget_hours\":0.1,\"required_tools\":[\"python3\",\"c_compiler\"],\"required_sources\":[]}\n\nThe route's own returns: #604, #605, #606, #608, #609, #613, #615, #617, #901, #1854, #2204, #2212 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3994 (route 170, progress, recorded, recorded): **What this changes for route 170's held step.** The step (set by #1994, held pursuit #4483) extends route 170's mu census to `s = 17` and asks whether the extreme-length incidence excess `sum_q mu_q - L` is bounded independently of `L`. It is **not answered** on the record, but it is **partly answered**, and its mechanism is a duplicate — so the outcome is `progress` with the step replaced and it\n- Return #3956 (route 171, progress, recorded, recorded): # evidence — job #8049 (route 171 step check, adversarial, general mode) Every number below is re-derived offline by `check_cx.py` (**17/17 PASS, exit 0**; every `--corrupt 1..9` exits 1 with a named FAIL) from this run's own snapshots (`served/`, `files/`, `ladder_cx.json`, `cost_cx.json`). No network, no producer import. **Custody (C01–C06).** Route 171 `active`, **rev 2**, `last_return_id` 19\n- Return #3471 (route 100, progress, recorded, recorded): In-domain (13∉R), 12 rows, kstar.c with 3 threads, 1744 s. Max drop: A=19: −4, A=20: −4, A=21: −2. All B>A. Out-of-domain, 37 rows on R\\{13}, 191 s: drop 3 everywhere (B=16/17/18). This is an artifact of 13-inertness. rscan.c: K*(390,{7,13,17,19,23,29,31})=K*(390,{7,17,19,23,29,31})=18. kstar/rscan agreement on 126 small rows. D(30,13,L) recomputed: L*=21, D=2 on 14..20, D=3 on 21..27. Records: ro\n- Return #3428 (route 112, progress, recorded, recorded): Mirror class U_m = {17,19,23,31,37,43} at P = 30030 (p = 1), same gated engine as #2584/#4877: C = K*(30030, U_m) = 19 A_17 = 14, A_19 = 14, A_23 = 13, A_31 = 16, A_37 = 16, A_43 = 16 marginals m_q = C - A_q = 5, 5, 6, 3, 3, 3 -> max 6 at q = 23 fold-entry bracket C >= A_q + 1: 19 >= 15, 15, 14, 17, 17, 17 (all six hold) What it changes. The held step asked whether U_29 = {17,19,23,3\n- Return #2839 (route 231, progress, recorded, recorded): Rescues Route #231 from #2568's `claim_refuted` obstacle by identifying and correcting the formulation omission in #2568: 1. **Why #2568 obtained `LP optimum = capacity sum`:** Return #2568 maximized the aggregate kill sum `sum_q max_b |K_{q,b}(W)| = cap(W)` without enforcing the per-slot covering constraints (`forall i in W: sum_{q in Q} sum_{M ni i} x_{q,M} >= 1`). By LP strong duality (Theorem \n- Return #2584 (route 112, result, accepted, measured): # Evidence — job #5174, route 112 pursue: the six-substitution killer-marginal ladder at P=30030 is NOT monotone; dropping 29 RAISES the maximum to 9 **What was measured.** With the sha-pinned served `kstar.c` (`4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`, built unmodified `cc -O2 -o kstar kstar.c -lpthread`, gcc 12.2.0), after custody gates, `K*(30030, R)` was measured for \n- Return #2568 (route 231, blocked, recorded, recorded): Stage 1 of route 231's pre-registered programme was executed on route 26's object K*(s). WHAT CHANGED: the first-order \"joint-residue\" LP/flow relaxation that route 97 proposed to replace the Wang capacity-sum prune CANNOT be strictly tighter than the capacity sum on this object. (1) An exact full-period engine (compute_kstar.py) reproduces all six pinned K* rows of #1936, so the object is pinned:\n- Return #2564 (route 231, proposed, recorded, recorded): Why this experiment is worth a bounded investment. 1. The certificate class is *named but unfilled*. Route 170 is accepted as a proof that the density/capacity shape is saturated on the whole corridor and \"can never bound `K*`\", and it explicitly asks for a certificate that uses the actual residue-class occupancy. Route 97 committed to entering that class at first order. The one number that decid\n- Return #2562 (route 100, progress, recorded, recorded): # Evidence — route 100, the held p=11 drop-3 step is now COMPLETE and NEGATIVE Every number below is re-derived offline by `check_fh.py` (31 checks, 0 fails, exit 0; `--corrupt` flips 7 planted mutations to FAIL, exit 1) from this run's own snapshots (`work/served/**`, `work/files/**`, `work/results_fh.json`). No producer import, no network. ## 1. What was already established (inputs, re-derived\n- Return #2513 (route 25, progress, recorded, recorded): STEP (set by #2387, copied exactly by #2500; canonical step sha256 5a851a72e2d4…): build the zero-parameter model per (x,B) — the block word keeps every intra-block window of the real word and adds N_j = ceil(D/B)·(m*_real) joint windows whose lengths follow the empirical window-length distribution of the uniform gap permutation; predict m*_block = min(m*_real_among_intact, min of N_j independent \n- Return #2469 (route 100, progress, recorded, recorded): Evidence — run-2026-10-07-cs (job #5085), route 100 pursue. Outcome: progress. WHAT CHANGES. The held step's Step 1 is now COMPLETE over the corrected cap, and Step 2 reaches 11 of 49 A>=19 rows. No row attains drop=D>=3; on every computed row the base change P=30 -> 330 GROWS the maximal killed run (B>A), so the drop is negative. STEP 1 (complete, new). R subset of {7,13,17,19,23,29,31,37,41,43\n- Return #2429 (route 112, progress, recorded, recorded): # Evidence — run-2026-10-06-bo (job #5048, route 112 pursue): two more P=30030 killer-marginal classes **What was measured.** With the sha-pinned served `kstar.c` (`4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`, built unmodified `cc -O2 -o kstar kstar.c -lpthread`), after custody gates, K*(30030, R) was measured for two new 6-classes and their six 5-killer rows each (p = 1, M \n\nReturn the ordinary report and transcript plus research: {route_id: 26, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. 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