{"id":566,"job_id":1295,"problem_id":1,"lane_id":5,"type":"explore","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 19 / job #1295: the N1 Hall generator on #477's real block set\n\nProducer for this job: `real19.py`, sha256 `937463e8cb832244dc3546e1358b79a9bf85380bf718f3c205bb047f70dd2435`.\nPython 3 stdlib only, one thread, deterministic. About 121 CPU s across all arms.\n\n## 0. Correction of #565: the block set *is* reconstructible  (MEASURED)\n\n#565 recorded a \"scoped obstacle\": that `coherence974-input.json`'s own phase\nconvention forces singleton domains, and that \"`#477`'s `producer1123.py` is not\npublished, so the block set ... cannot be reconstructed without inventing part of it.\"\n\nBoth halves of that are **wrong**, and the record makes it checkable:\n\n- `producer1123.py` **is** on the record. Return #477's own `files` list carries it at\n  sha256 `535f5f2a55f338df25492220670a6117d238af5a159e48d1ea1f7219aa33457a` (7148 bytes),\n  with `checker1123.py` (`caac7363…`) and `smoke1123.py` (`750b59b4…`). Fetched from\n  `GET /files/<sha256>` (the route is top-level, *not* project-scoped) and each sha256\n  verified. #565 probed `/projects/twin-primes/files/<sha>` (404) and concluded the file\n  was unpublished; it was one route away.\n- The block set #477 actually used is stated in that file: `blocks = {i: 1<<i for i in\n  range(len(slots))}` — **exactly one block per slot**, 51 blocks, taken directly from the\n  frozen `slots`. Block `i`'s domain is `{q: phases b with (s_i + b) mod q in {0, q-2}}`,\n  i.e. 2 phases × 19 primes = **38 phase-class tuples** per block. `H` and a separate\n  phase map are not needed and do not appear.\n- The frozen file's `pair_graph` / `quotient` strings (\"one block per pair meeting H …\n  equal kill patterns on D\") describe a **design #477 did not implement**. #565's literal\n  reading was a reading of the *design*, not of the *code that ran*.\n\nRecorded as data, hashed: `real-block-set.json` sha256\n`09c78936939418a8efe8b5b5650bc00747e588f71b5a99d8bb5961476669a253` — 51 blocks, 880\nforced-separation edges, 38 tuples per block.\n\nSo the *premise* the route's `next_step` calls unrecoverable is fully recoverable. #565's\nobstacle is withdrawn.\n\n## 1. #477's production record reproduces  (MEASURED)\n\nWith the frozen input and the three scripts fetched above:\n\n| check | result |\n| --- | --- |\n| `smoke1123.py` | `PASS1123-SMOKE 64 4`; 21 SAT / 43 UNSAT; 4 corruption classes rejected |\n| `producer1123.py hall` | `INCONCLUSIVE proof_bytes`; deterministic receipt sha256 `149aa058…` **matches the recorded hash** |\n| `producer1123.py ablation` | `INCONCLUSIVE proof_bytes`; deterministic receipt sha256 `e6668e4c…` **matches the recorded hash** |\n\nBoth receipts: 1821 decisions, 3631 nodes, 1810 cardinality leaves, **0 Hall leaves**,\n110 816 deleted values, attempted counter 2 000 250. The recorded hashes are on the LF\nform; this host writes CRLF, so the comparison is on LF-normalised bytes (the receipts\nbelow were produced the same way).\n\nPlatform note: Windows has no POSIX `resource`. A documented shim (`resource.py`,\nsha256 `5fc50b08…`) supplies `getrusage` so the search logic runs. It changes **no search\ndecision** — its only consumers are the 900 MB RAM guard (never fires) and the\n`peak_rss_bytes` field, which the deterministic receipts exclude. The CPU guard uses\n`time.process_time()`, which is platform-independent.\n\n## 2. The route's question: does N1 cut the *real* block tree earlier?  (MEASURED)\n\n`real19.py` is a faithful copy of `producer1123.py`'s search in which **only the Hall\ncandidate generator** differs. Validated by receipt equality: `arm=none` reproduces #477's\nablation hash and `arm=greedy` reproduces #477's hall hash *except* for one added\ninstrumentation counter (`maxcliques_examined`), so every search number is identical.\n`arm=n1` is the strengthening #564 identified: maximum-matching Hall over **every maximal\nseparated set**, not over ascending-greedy seeds.\n\nMatched-prefix comparison, all arms stopped at the same decision count (1810):\n\n| arm | Hall candidate set | decisions | nodes | Hall leaves | cardinality leaves | max. cliques examined | CPU s |\n| --- | --- | ---: | ---: | ---: | ---: | ---: | ---: |\n| `none` | — (ablation) | 1810 | 3612 | 0 | 1801 | 0 | 13.3 |\n| `greedy` | ascending greedy cliques (#477) | 1810 | 3612 | 0 | 1801 | 0 | 23.9 |\n| `n1` cap 8 | maximal separated sets | 1810 | 3612 | 0 | 1801 | 14 488 | 27.7 |\n| `n1` cap 32 | maximal separated sets | 1810 | 3612 | 0 | 1801 | 57 952 | 24.1 |\n| `n1` cap 128 | maximal separated sets | 1810 | 3612 | 0 | 1801 | 231 808 | 41.9 |\n\n**All three arms produce the same tree.** Hall never fires, so no candidate-generation\nchange alters the search. With **no** per-node clique cap — the strongest possible Hall\ntest — the `n1` arm hit the 54 s CPU guard after only 349 decisions / 689 nodes, having\nexamined **621 223** maximal separated sets, again with **0 Hall leaves**.\n\nWhy: at the root every block carries all 19 primes (38 tuples) and the **largest maximal\nclique is 11 < 19**, so no separated set is Hall-deficient while the sets are full. A Hall\ndeficiency can only appear once prime lists are pruned, and #477's propagation already\nremoves prime `q` from every block separated from a singleton-`{q}` block — so the\ndeficiencies are pre-empted by arc consistency. Pruning is active at essentially every\nnode (`nodes_with_pruned_block` = 3611 / 3612), yet no separated set ever has\n`|union of prime lists| < |W|`.\n\n## 3. What this changes\n\n- #564's explanation — \"the 0 Hall leaves came from the *candidate generator*\" — is\n  **false on the real instance**. Replacing greedy cliques with the full maximal-clique\n  set (and with the matching-extraction violator) finds **no additional Hall cut**. #477's\n  zero Hall leaves were not a candidate-generation artifact here.\n- The route's own stated uncertainty (\"clique matching may give no early cut or may cost\n  more than it saves\") resolves on the real block set to **no cut and strictly more cost**:\n  the `n1` extractor reaches a comparable prefix in 54 s where the greedy arm needs ~7 s,\n  and prunes nothing. This is the failure branch the route names (\"the matching extractor\n  costs more than the tree it prunes\") — recorded as the finding.\n- **The registered success criterion is not met**: no Hall leaf appears on any infeasible\n  prefix where the ablation branches, because Hall never fires at all.\n\nExplicitly **not** claimed: any D51 verdict (both production arms still cap at\n`proof_bytes`), any census, LP or toy replay; no claim that Hall can never fire on other\ninstances, on a deeper prefix, or with a different propagation. The route is *not* closed;\nonly the clique-Hall *arm* is shown to be dominated on this instance.\n\n## 4. Prior-art search update  (search date 2026-09-15)\n\nRe-ran the route's own queries before implementing, plus two for this experiment\n(clique/enumeration Hall deficiency on a frozen instance; all-different Hall violator\ncandidate generation and pruning overhead).\n\n- **New primary, closest to the route's own caveat:** P. Chalise, *Sufficiency of Hall's\n  Condition for Graphic List Coloring*, arXiv:2609.01889 [math.CO], 1 Sep 2026. It studies\n  exactly when a Hall-type necessary condition is *also sufficient* for a list colouring\n  (lists = neighbourhoods), and characterizes the graph pairs for which it is — i.e. it\n  states, as a research problem, that Hall is generally **only necessary**. That is\n  primary support for the route's caveat that clique-Hall cannot characterize full\n  incomplete-graph feasibility. It does **not** treat this route's frozen prime-labelled\n  partition instance and does **not** address the extractor-cost question. No result is\n  imported; nothing about the route is disproved by it.\n- Hall violators (canonical matching construction, inclusion-minimality, NP-hardness of\n  minimum-*cardinality* violators): unchanged, as recorded in #476/#477/#565 — Wikipedia\n  \"Hall violator\", Lenchner arXiv:1907.05870, Gan–Suksompong–Voudouris arXiv:1905.00468,\n  Kabra MS thesis Thm 3.2.5, Cygan et al. Ex 13.28. Reused without a new read: Regin AAAI\n  1994; Hebrard–Katsirelos JAIR 69 (2020) 33–65. Gocht et al. (CPTAI 2020) for RUP/VeriPB\n  recompute-rather-than-record, as in #565.\n- Reran the recomputable-certificate query: DRAT/RUP and VeriPB remain the standard\n  practice; nothing locates the \"domain state at the node vs the original graph\" as a\n  stated *format requirement*, consistent with #565.\n- **EXACT REMAINING GAP: not located.** No source runs a matching-extraction Hall\n  generator, let alone a maximal-clique enumeration, against a frozen prime-labelled\n  partition instance, nor compares Hall candidate generators by proof cost on one. This is\n  a statement about this search, not an absence claim.\n\n## 5. Cheapest credible check\n\n- Reproduce the block set: `GET /files/b173e69b…` → `coherence974-input.json`,\n  `GET /files/535f5f2a…` → `producer1123.py`; `python realblock.py` prints 51 blocks,\n  880 edges, largest maximal clique 11, 4838 maximal cliques.\n- Reproduce both arms: `python real19.py none` and `python real19.py greedy` under\n  `decision_stop=1810`; compare `hall_leaves` = 0 and identical trees.\n- Run the frozen independent checker on a stored complete proof:\n  `python -c \"import json;from checker1123 import verify;print(verify(json.load(open('smoke-branch-proof1123.json'))))\"`.\n  Cost ≈ 0 s, far below `max(1 CPU s, discoveryCPU/5)`.\n\n## 6. Local framework notes\n\nRead-only harness binding: model `deepseek/deepseek-v4-flash`, effort `max` measured from\nthe harness record, not stated. Submission went through this run's tested completion path\n(payload passed byte-for-byte, scanned not rewritten). The assignment transcript was cut per\nassignment and scrubbed before sending. CPU for the job: **≈121 s** total, single core, peak\nRSS < 40 MB — inside the 2 GB / 4 CPU h / 5 GB envelope and the job's own limits.\n","patch":null,"cpu_hours":0.034,"hashes":{"real19.py":"937463e8cb832244dc3546e1358b79a9bf85380bf718f3c205bb047f70dd2435","resource.py":"5fc50b08469dcc29b23f2402efa4dfb55fa6d977a8c5a46e65a7b6da650db532","realblock.py":"9c2e81594a4cfd7b41588194d3769712307967798233457bca927a85abdcb067","smoke1123.py":"750b59b4d17ab6faf716fa78f22afe5922744d3994606f034c722cce809adeb2","recipe1295.md":"14d2193b18cc7dcd97e09744ca0f310a35545523f17d38bda7f3670f0707999b","report1295.md":"9b8b2240a94137fa268d92aa8e1eb9a9253e5ea8d102221e80157e29dc1646b7","checker1123.py":"caac736377e06cb64560d451bb39005f7cefbf167109d8485c7fd3d572188712","producer1123.py":"535f5f2a55f338df25492220670a6117d238af5a159e48d1ea1f7219aa33457a","research1295.json":"400395ed1685ea7946173fecb760b8139d304b6a84f6cb223c9a99029e08ca29","hall-stdout1123.txt":"38484bf33cd04dae409a8d0f5991aa36c48412e693fe8786ca9bc4ab8563427e","n1-receipt1123.json":"c249cdd20124538598a0dbd556ee9bf042dd9244436193f8817a75b6c27ff691","real-block-set.json":"09c78936939418a8efe8b5b5650bc00747e588f71b5a99d8bb5961476669a253","hall-receipt1123.json":"149aa0589f3821ffdd3678bc917a7ea659ed8aeec5ddeb6b0fe681f32900339e","none-receipt1123.json":"b92e6f126600984d062d61cdfbb9cccdcfd7dfc9417bb86a1fddfb1892062717","ablation-stdout1123.txt":"809df3731b450d83a5c4ed0851579caf146978e3f88affcfe060dab72a0d36bf","coherence974-input.json":"b173e69b99916a9562cfab59223359984c629f5845a68a265d4ef3dbc3f162c1","greedy-receipt1123.json":"bb3a03b59c61ab68562af427cd00aaaebb64de388450da39b5e5e76e054b4573","ablation-receipt1123.json":"e6668e4c974303efba7549d0b40cd39e8bfde0fc3d872b22db6341ae3f5df984","smoke-branch-proof1123.json":"f5044ae0c36ae399ae100785dfa71116479b51e376892671245955151236ccca"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-15T10:26:23.842Z","repo_url":null,"commit":null,"cites":{"returns":[565]},"tokens":{"log":"custom","input":98304,"models":{"deepseek-v4-flash":70313},"output":70313,"source":"custom-jsonl","entries":1,"cache_read":7996416,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe 1295 — route 19, the N1 Hall generator on #477's real block set\n\n## Artifacts\n\n| what | value |\n| --- | --- |\n| producer (this job) | `real19.py`, sha256 `937463e8cb832244dc3546e1358b79a9bf85380bf718f3c205bb047f70dd2435` |\n| block-set data | `real-block-set.json`, sha256 `09c78936939418a8efe8b5b5650bc00747e588f71b5a99d8bb5961476669a253` |\n| structure probe | `realblock.py`, sha256 `9c2e81594a4cfd7b41588194d3769712307967798233457bca927a85abdcb067` |\n| Windows `resource` shim | `resource.py`, sha256 `5fc50b08469dcc29b23f2402efa4dfb55fa6d977a8c5a46e65a7b6da650db532` |\n| frozen input | `coherence974-input.json`, sha256 `b173e69b99916a9562cfab59223359984c629f5845a68a265d4ef3dbc3f162c1` |\n| fetch input | `GET /files/b173e69b99916a9562cfab59223359984c629f5845a68a265d4ef3dbc3f162c1` |\n| #477 producer | `producer1123.py`, sha256 `535f5f2a55f338df25492220670a6117d238af5a159e48d1ea1f7219aa33457a` |\n| #477 checker | `checker1123.py`, sha256 `caac736377e06cb64560d451bb39005f7cefbf167109d8485c7fd3d572188712` |\n| #477 smoke | `smoke1123.py`, sha256 `750b59b4d17ab6faf716fa78f22afe5922744d3994606f034c722cce809adeb2` |\n\nFiles are fetched from the **top-level** route `GET <base>/files/<sha256>` (not project-scoped).\n\n## Prerequisites\n\nCPython 3 (stdlib only: `json`, `time`, `itertools`, `sys`, `hashlib`, `ctypes`). One thread.\nNo network beyond the two `GET /files/<sha>` fetches. On Windows the local `resource.py` shim\nstands in for the POSIX module; it changes no search decision (see the report, §1). On POSIX,\ndelete the shim — the real module is equivalent for this code.\n\n## Reproduce #477's record\n\n```sh\npython smoke1123.py                         # -> PASS1123-SMOKE 64 4\npython producer1123.py hall     > hall-stdout1123.txt      # -> hall INCONCLUSIVE proof_bytes\npython producer1123.py ablation > ablation-stdout1123.txt  # -> ablation INCONCLUSIVE proof_bytes\n```\n\nThe deterministic receipts are `hall-receipt1123.json` (sha256 `149aa058…`) and\n`ablation-receipt1123.json` (sha256 `e6668e4c…`); compare **LF-normalised** bytes.\n\n## Reproduce the controlled arms\n\n```sh\npython realblock.py                 # 51 blocks, 880 edges, largest maximal clique 11\npython real19.py none               # ablation            (== #477 ablation)\npython real19.py greedy             # greedy-clique Hall  (== #477 hall)\npython real19.py n1                 # N1: all maximal separated sets (caps on CPU)\n```\n\n`real19.py`'s `none`/`greedy` receipts differ from #477's recorded hashes only by the added\n`maxcliques_examined` counter, so the copy is search-identical. Matched-prefix runs:\n\n```sh\npython - <<'PY'\nimport json, real19\ninp = json.load(open('coherence974-input.json'))\nfor arm, cap in [('none', 10**9), ('greedy', 10**9), ('n1', 8), ('n1', 32), ('n1', 128)]:\n    r, _ = real19.solve(inp['slots'], inp['Q'], arm, decision_stop=1810, clique_cap=cap)\n    s = r['stats']\n    print(arm, cap, s['decisions'], s['nodes'], s['hall_leaves'], s['cardinality_leaves'], s['maxcliques_examined'])\nPY\n```\n\nExpect, for every row: `1810 3612 0 1801 <mcliq>` — the same tree, zero Hall leaves.\n\n## What to check\n\n| field | expected |\n| --- | --- |\n| `real-block-set.json` `n_blocks` | 51 |\n| `forced_separation_edges` length | 880 |\n| tuples per block | 38 (2 phases × 19 primes) |\n| `realblock.py` largest maximal clique | 11 (< 19 primes) |\n| matched-prefix `hall_leaves` | 0 in every arm |\n| `n1` (uncapped) cap_reason | `cpu` after 349 decisions, 621 223 cliques, 0 Hall leaves |\n| `none`/`greedy` trees | identical to each other and to `n1` at the same decision count |","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"max","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-15T10:31:03.399Z","file_notes":null,"research":{"outcome":"progress","route_id":19,"next_step":{"method":"Reuse real19.py's search (propagation, force, branching, caps) unchanged and #477's frozen input. Replace only the record format: per node store parent index, branch (a,b), the domain snapshot, and the verdict/discharge, instead of materialised (block,prime,mask) deletion deltas. Add an independent checker that recomputes arc consistency to a fixed point from each node's own snapshot, verifies tree completeness against each node's own snapshot, and checks terminal discharges, carrying the four corruption classes over untouched. Run both the materialised (ablation) and recomputable arms under identical 54 s / 200000-decision / 2 MB caps, and report bytes per decision, decisions reached, whether a complete proof is emitted, and checker CPU against max(1 CPU s, discoveryCPU/5).","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":0},"failure":"No depth or completeness gain over the materialised record, the checker cannot be kept independent of the producer, or replay exceeds max(1 CPU s, discoveryCPU/5) -- in which case the proof-byte cap is a property of the search, not the encoding.","success":"Under the same budget the recomputable arm reaches a strictly deeper prefix and/or emits a complete UNSAT tree, the independent checker accepts it, and all four corruption classes still reject; or the arm shows the materialised record cannot reach a complete proof at 2 MB while the recomputable one does.","question":"Does replacing #477's materialised per-deletion records with a recomputable per-node certificate let the same 54 s / 2 MB budget reach a complete checked UNSAT proof, or a strictly deeper prefix, on the frozen block set (where clique-Hall is now shown to prune nothing)?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[477,564,565],"evidence_md":"MEASURED, local. (0) CORRECTION OF #565: #477's producer1123.py IS on the record (return #477 files list, GET /files/535f5f2a...) and the block set it actually used is one block per slot (51 blocks), domain = the 2*19 phase-class tuples {b: (s+b) mod q in {0,q-2}}; H and a separate phase map are not used. So #565's 'not published / not reconstructible without inventing part of it' is withdrawn; the frozen file's pair_graph/quotient strings describe a design #477 did not implement. Block set recorded hashed as real-block-set.json (sha256 09c78936..., 51 blocks, 880 forced-separation edges, 38 tuples/block). (1) REPRODUCTION: fetched producer1123.py/checker1123.py/smoke1123.py (sha-verified); smoke reproduces PASS1123-SMOKE 64 4 with 21 SAT/43 UNSAT and 4 corruption classes rejected; both production arms reproduce #477's recorded deterministic receipts byte-for-byte (LF-normalised): hall 149aa058..., ablation e6668e4c..., 1821 decisions/3631 nodes/1810 cardinality leaves/0 Hall leaves/110816 deletions/counter 2000250. (2) THE ROUTE'S QUESTION: a controlled copy of the search (real19.py, validated by receipt equality: arm=none == #477 ablation, arm=greedy == #477 hall) with ONLY the Hall candidate generator switched to maximum-matching extraction over EVERY maximal separated set, run at a matched prefix (1810 decisions), gives the SAME tree in all arms -- 3612 nodes, 1801 cardinality leaves, 0 Hall leaves -- while examining 14488/57952/231808 maximal cliques at per-node caps 8/32/128. Uncapped, the n1 arm hits the 54 s CPU guard after 349 decisions while examining 621223 maximal separated sets, still 0 Hall leaves. Structural reason: at the root every block has all 19 primes and the largest maximal clique is 11<19, so no separated set is deficient while lists are full; a deficiency needs pruned lists, and #477's propagation already removes prime q from every block separated from a singleton-{q} block (nodes_with_pruned_block 3611/3612). So #564's candidate-generator explanation is FALSE on the real instance, Hall prunes nothing the ablation does not, and the matching extractor costs strictly more (54 s vs ~7 s for a comparable prefix). The registered success criterion is NOT met. Not claimed: any D51 verdict (both arms still cap at proof_bytes), census, LP or toy replay; no claim Hall can never fire elsewhere or deeper.","prior_art_md":"Search date 2026-09-15 UTC. Re-ran the route's own queries before implementing, plus two for this experiment (Hall deficiency / maximal-clique enumeration on a frozen instance; all-different Hall violator candidate generation and pruning overhead), and re-ran the recomputable-certificate query. NEW PRIMARY, closest to the route's own caveat: P. Chalise, 'Sufficiency of Hall's Condition for Graphic List Coloring', arXiv:2609.01889 [math.CO], 1 Sep 2026 -- it studies exactly when a Hall-type necessary condition is also sufficient for list colorability (lists = neighbourhoods) and characterizes the graph pairs where it is, i.e. it states as a research problem that Hall is generally only necessary. That is primary support for the route's caveat that clique-Hall does not characterize full incomplete-graph feasibility. It does not treat this frozen prime-labelled partition instance and does not address extractor cost; no result imported. Hall violators (canonical matching construction, inclusion-minimality, NP-hardness of minimum-cardinality violators): unchanged from #476/#477/#565 -- Wikipedia 'Hall violator'; Lenchner arXiv:1907.05870; Gan-Suksompong-Voudouris arXiv:1905.00468; Kabra MS thesis Thm 3.2.5; Cygan et al. Ex 13.28. Reused without a new read: Regin AAAI 1994; Hebrard-Katsirelos JAIR 69 (2020) 33-65. Gocht et al. CPTAI 2020 (RUP/VeriPB recompute-rather-than-record) reused as in #565. EXACT REMAINING GAP: not located. No source runs a matching-extraction Hall generator, let alone a maximal-clique enumeration, against a frozen prime-labelled partition instance, nor compares Hall candidate generators by proof cost on one. This is a statement about this narrow search, not an absence claim."},"research_route_id":19,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_9e3c846778a19c71137dde42","run_id":"run_61fbc8bae71131ce4bb4e545","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"maxime-fleury","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/19 and return #565. Return the ordinary report and transcript plus research: {route_id: 19, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes\", prior_art_md: \"updated online search record, sources and exact remaining gap\", next_step: <only for continued pursuit>, obstacle: <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"477","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"564","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"565","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/19","transcript_url":"/projects/twin-primes/return/566/transcript","files":[{"sha256":"b173e69b99916a9562cfab59223359984c629f5845a68a265d4ef3dbc3f162c1","name":"coherence974-input.json","bytes":2415},{"sha256":"535f5f2a55f338df25492220670a6117d238af5a159e48d1ea1f7219aa33457a","name":"producer1123.py","bytes":7148},{"sha256":"caac736377e06cb64560d451bb39005f7cefbf167109d8485c7fd3d572188712","name":"checker1123.py","bytes":4282},{"sha256":"750b59b4d17ab6faf716fa78f22afe5922744d3994606f034c722cce809adeb2","name":"smoke1123.py","bytes":2656},{"sha256":"9b8b2240a94137fa268d92aa8e1eb9a9253e5ea8d102221e80157e29dc1646b7","name":"report1295.md","bytes":9895},{"sha256":"14d2193b18cc7dcd97e09744ca0f310a35545523f17d38bda7f3670f0707999b","name":"recipe1295.md","bytes":3589},{"sha256":"400395ed1685ea7946173fecb760b8139d304b6a84f6cb223c9a99029e08ca29","name":"research1295.json","bytes":6042},{"sha256":"937463e8cb832244dc3546e1358b79a9bf85380bf718f3c205bb047f70dd2435","name":"real19.py","bytes":10668},{"sha256":"9c2e81594a4cfd7b41588194d3769712307967798233457bca927a85abdcb067","name":"realblock.py","bytes":2523},{"sha256":"09c78936939418a8efe8b5b5650bc00747e588f71b5a99d8bb5961476669a253","name":"real-block-set.json","bytes":25599},{"sha256":"5fc50b08469dcc29b23f2402efa4dfb55fa6d977a8c5a46e65a7b6da650db532","name":"resource.py","bytes":1669},{"sha256":"149aa0589f3821ffdd3678bc917a7ea659ed8aeec5ddeb6b0fe681f32900339e","name":"hall-receipt1123.json","bytes":434},{"sha256":"e6668e4c974303efba7549d0b40cd39e8bfde0fc3d872b22db6341ae3f5df984","name":"ablation-receipt1123.json","bytes":435},{"sha256":"b92e6f126600984d062d61cdfbb9cccdcfd7dfc9417bb86a1fddfb1892062717","name":"none-receipt1123.json","bytes":465},{"sha256":"bb3a03b59c61ab68562af427cd00aaaebb64de388450da39b5e5e76e054b4573","name":"greedy-receipt1123.json","bytes":464},{"sha256":"c249cdd20124538598a0dbd556ee9bf042dd9244436193f8817a75b6c27ff691","name":"n1-receipt1123.json","bytes":456},{"sha256":"38484bf33cd04dae409a8d0f5991aa36c48412e693fe8786ca9bc4ab8563427e","name":"hall-stdout1123.txt","bytes":30},{"sha256":"809df3731b450d83a5c4ed0851579caf146978e3f88affcfe060dab72a0d36bf","name":"ablation-stdout1123.txt","bytes":34},{"sha256":"f5044ae0c36ae399ae100785dfa71116479b51e376892671245955151236ccca","name":"smoke-branch-proof1123.json","bytes":264}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}