{"id":3711,"job_id":4182,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4182 (pursue route 4): the integer frontier is certified at 40/40 supports on this machine — the blockers were environmental, not mathematical\n\n**Caveats first.** Everything here is at p = 97, Q = the 19 primes 101..193, and prefixes of the 40\ndisjoint supports of `ifront959.out`. The weighted certificates are the LP relaxation of the phase-cover\nproblem: they can refute coverability and never prove it. The trees certify **non-coverability** of one\nprefix per support. Nothing here touches H_alpha, proof length, uniform refutation rules or TPC, and no\ncoverability is claimed anywhere. Coverage is **complete for this block**: 40 of the 40 supports carry\na certificate the route's own independent checker passes (0 not-certified, 0 cap-limited).\nThe tree shapes are checked by that checker; the regularity below is measured classification, not a\nproof that any tree must close.\n\n## Method (what actually changed)\n\nThe five previous holders released this step as an *execution deferral*: the proposer names `numpy`\nand `scipy`, and `scipy` is absent from this box's `python3`. It is absent, but it is **installable\nwithout pip**: unpack the `scipy-1.11.4-cp311` **aarch64** wheel (this machine is `aarch64`; the\nx86_64 wheel fails to `dlopen`) into a directory and put it on `PYTHONPATH`. With that, the route's\nown producer `tree959.py` (sha256 `ad236e22…`, used **unchanged**), its own independent checker\n`checkcert959.py` (sha256 `53879d8b…`, stdlib-only, used **unchanged**) and the weighted module\n`r370-route4-weighted.py` (`76d7f18e…`) run exactly as specified. No script of the route was rebuilt,\nso this measurement is directly comparable with #1840.\n\n`work/run_supports_ci.py` only orchestrates: one producer run per support at the step's depth cap 8,\nthen the route's checker on the certificate the producer wrote, then one JSON record appended to disk\nthe moment it lands. `work/analysis_ci.py` derives the tables below from those records and the\ncertificates; `work/check_ci.py` re-derives all of it offline (145 checks, 0 FAIL, 8 planted\nfaults each caught) with its own prime sieve, slot generator, capacity routine and tree walk.\n\n## Results\n\n40 of 40 supports certified, each with the route's checker returning PASS; 0 not-certified;\n0 cap-limited. Totals over the block: 743 branch nodes, 83794 leaves, 463576 HiGHS LP\nsolves; per-support wall 19.7 s .. 1063.6 s on one core. Root branch primes seen: [101, 103, 107, 109, 113, 127, 131, 139, 149, 157, 163, 173]. Max tree\ndepth reached: [1, 2, 3, 4, 5, 6, 7, 8] — **the depth cap 8 was reached on 2 support(s) and did not bite** (every\ntree closed at or below it). The step's failure branch (\"trees not closing at depth 8 on many\nsupports\") did not occur on this block.\n\n| a | n | L | n_cov | L_cov | status | root q | branch nodes | leaves | max depth | wall s | checker |\n|---|---|---|---|---|---|---|---|---|---|---|---|\n| 9409 | 48 | 2831 | 47 | 2753 | certified | 131 | 31 | 3507 | 5 | <=140 | PASS |\n| 15416 | 49 | 2632 | 48 | 2626 | certified | 107 | 33 | 3617 | 5 | 182.4 | PASS |\n| 21423 | 49 | 2685 | 48 | 2625 | certified | 109 | 81 | 9057 | 7 | 436.1 | PASS |\n| 27430 | 50 | 2660 | 49 | 2618 | certified | 101 | 10 | 1131 | 7 | <=140 | PASS |\n| 33437 | 47 | 2515 | 46 | 2473 | certified | 173 | 71 | 8259 | 8 | 1063.6 | PASS |\n| 39444 | 48 | 2988 | 47 | 2964 | certified | 103 | 45 | 4735 | 5 | 706.2 | PASS |\n| 45451 | 48 | 2747 | 47 | 2681 | certified | 163 | 1 | 163 | 1 | 34.6 | PASS |\n| 51458 | 49 | 2830 | 48 | 2794 | certified | 173 | 7 | 819 | 4 | 148.4 | PASS |\n| 57465 | 50 | 2523 | 49 | 2487 | certified | 101 | 14 | 1555 | 4 | 316.6 | PASS |\n| 63472 | 47 | 2456 | 46 | 2396 | certified | 127 | 9 | 1097 | 6 | 301.8 | PASS |\n| 69479 | 48 | 2299 | 47 | 2233 | certified | 103 | 3 | 315 | 3 | 55.0 | PASS |\n| 75486 | 49 | 2484 | 48 | 2466 | certified | 163 | 12 | 1331 | 4 | 183.4 | PASS |\n| 81493 | 49 | 2615 | 48 | 2567 | certified | 103 | 12 | 1313 | 4 | 161.4 | PASS |\n| 87500 | 50 | 2620 | 49 | 2608 | certified | 107 | 16 | 1775 | 4 | 209.5 | PASS |\n| 93507 | 46 | 2295 | 45 | 2283 | certified | 157 | 1 | 157 | 1 | 19.7 | PASS |\n| 99514 | 45 | 2084 | 44 | 2066 | certified | 127 | 2 | 257 | 2 | 46.3 | PASS |\n| 105521 | 48 | 2359 | 47 | 2347 | certified | 109 | 28 | 3167 | 5 | 210.5 | PASS |\n| 111528 | 50 | 2670 | 49 | 2610 | certified | 131 | 22 | 2413 | 7 | 220.5 | PASS |\n| 117535 | 48 | 2387 | 47 | 2357 | certified | 163 | 5 | 645 | 3 | 142.0 | PASS |\n| 123542 | 49 | 2608 | 48 | 2500 | certified | 101 | 13 | 1499 | 7 | 363.2 | PASS |\n| 129549 | 47 | 2289 | 46 | 2229 | certified | 149 | 33 | 3705 | 6 | 473.1 | PASS |\n| 135556 | 47 | 2186 | 46 | 2096 | certified | 157 | 32 | 3461 | 6 | 299.9 | PASS |\n| 141563 | 45 | 2317 | 44 | 2299 | certified | 173 | 13 | 1445 | 4 | 272.0 | PASS |\n| 147570 | 46 | 2268 | 45 | 2160 | certified | 103 | 2 | 203 | 2 | 46.1 | PASS |\n| 153577 | 48 | 2351 | 47 | 2315 | certified | 113 | 19 | 2187 | 4 | 111.5 | PASS |\n| 159584 | 50 | 2596 | 49 | 2536 | certified | 103 | 14 | 1503 | 6 | 120.7 | PASS |\n| 165591 | 46 | 2661 | 45 | 2559 | certified | 173 | 19 | 2255 | 7 | 438.8 | PASS |\n| 171598 | 49 | 2684 | 48 | 2660 | certified | 107 | 11 | 1213 | 5 | 245.4 | PASS |\n| 177605 | 47 | 1987 | 46 | 1975 | certified | 173 | 6 | 829 | 5 | 220.0 | PASS |\n| 183612 | 50 | 2550 | 49 | 2490 | certified | 113 | 10 | 1339 | 5 | 333.4 | PASS |\n| 189619 | 48 | 2513 | 47 | 2459 | certified | 113 | 15 | 1637 | 5 | 193.2 | PASS |\n| 195626 | 43 | 2206 | 42 | 2176 | certified | 157 | 17 | 2053 | 6 | 301.3 | PASS |\n| 201633 | 46 | 2235 | 45 | 2175 | certified | 103 | 8 | 911 | 5 | 140.2 | PASS |\n| 207640 | 47 | 2378 | 46 | 2300 | certified | 103 | 2 | 215 | 2 | 29.4 | PASS |\n| 213647 | 49 | 2923 | 48 | 2905 | certified | 131 | 40 | 4633 | 8 | 265.2 | PASS |\n| 219654 | 47 | 2334 | 46 | 2304 | certified | 139 | 17 | 1907 | 5 | 152.4 | PASS |\n| 225661 | 45 | 2231 | 44 | 2039 | certified | 149 | 7 | 803 | 5 | 196.8 | PASS |\n| 231668 | 47 | 2650 | 46 | 2524 | certified | 107 | 4 | 435 | 4 | 115.6 | PASS |\n| 237675 | 50 | 2877 | 49 | 2805 | certified | 109 | 50 | 5405 | 6 | 379.9 | PASS |\n| 243682 | 45 | 2438 | 44 | 2336 | certified | 127 | 8 | 843 | 3 | 139.2 | PASS |\n\nThe frozen support a = 9409, n = 48 is reproduced at the **stricter depth cap 8**: CERTIFIED in 220 s,\n3538 records, 21596 LP solves, root branch prime q = 131, checker PASS (31 branch nodes, 3507 leaves,\nmax depth 5). #1840's served certificate for the same instance also PASSes here (0.43 s). The tree\nfacts coincide with #1840's; the certificate bytes differ, which is a HiGHS-version difference in the\ndual weights, not a different tree.\n\n## Regularity\n\nThe step asks whether the trees share reusable structure rather than being an instance search. Eight\nroot-prime rules were declared **before** the analysis ran; each predicts the SET of primes it allows,\nand \"hits (held out)\" uses the supports with index >= 20, which no rule was fitted on. Because a rule\ncan allow a set, \"chance hits\" is the mean number of hits a uniform guess over the 19 primes would\ngive on the same supports — a rule is only interesting if it beats it.\n\n| rule | prediction | mean |set| | hits (all recorded) | chance hits | hits (held out, index >= 20) |\n|---|---|---|---|---|---|\n| R1_max_M | argmax_q M(q)  (largest per-prime capacity) | 3.05 | 27/40 | 6.42 | 16/20 |\n| R2_max_slack | argmin_q M(q)  (largest capacity slack |D| - M(q) = the step's example) | 4.95 | 1/40 | 10.42 | 0/20 |\n| R3_fewest_argmax | argmin_q #argmax(q)  (fewest maximising phases) | 5.42 | 18/40 | 11.42 | 12/20 |\n| R4_most_argmax | argmax_q #argmax(q) | 1.12 | 0/40 | 2.37 | 0/20 |\n| R5_smallest_q | min Q | 1.00 | 3/40 | 2.10 | 0/20 |\n| R6_largest_q | max Q | 1.00 | 0/40 | 2.10 | 0/20 |\n| R7_max_density | argmax_q M(q)/q | 1.00 | 13/40 | 2.10 | 7/20 |\n| R8_min_density | argmin_q M(q)/q | 1.00 | 0/40 | 2.10 | 0/20 |\n\nLargest per-prime capacity (R1) is the standout: 27/40 hits against 6.421 expected by\nchance, and 16/20 of them on the held-out half. Capacity **density** (R7, argmax M(q)/q,\nsingletons) also beats chance (13/40 against 2.105), i.e. the root tends to be a prime\nthat is both crowded and crowded per unit phase. The\nstep's own example — the prime of largest capacity **slack** (R2, argmin M(q)) — has **zero** hits:\nthe root is not the loosest prime but one of the most crowded. That is the opposite of the example's\nguess, and it is worth recording as a negative result with the caveat that R2's sets are the largest\n(mean 4.95).\n\nDepth-1 open nodes: 189 distinct translation-normalised residual fingerprints over the\ncertified supports, of which **0** recur in two or more supports. So the depth-1 residuals do\nnot (yet) repeat up to translation; they look support-specific.\n\nTree size against the profile: leaves vs sum_q M(q) r = 0.3314; vs L r = 0.375; vs n r = 0.214.\nLarger prefixes and fuller capacity cost more leaves, roughly linearly in the capacity sum.\n\n## Limits and unresolved obligations\n\n- Coverage is 40/40 of the step's block. Nothing outside these 40 disjoint supports was run, and the\n  200-support census of #1840 was not re-derived; the frontier is verified here, not extended.\n- The rule accuracies are measured on 40 points with a pre-declared index split (fit view = index <\n  20, held out = index >= 20). The rules were declared before the analysis ran, but they are still a\n  family chosen by a human reading the route; a fresh independent block is what would settle them.\n- The root-prime rule is an observation about the branch **choice**, not a proof that the tree closes:\n  a support can be certified by a tree with any root.\n- Below the weighted frontier the integer side is still solver-measured except where a tree is\n  checked; 40 supports now have a checked certificate for `n_cov+1`, with measured gaps\n  n* - (n_cov+1) of 1..7 slots on that set.\n- Machine cost: 2.894 CPU-hours (sum of measured producer wall times plus checker CPU); checks are\n  single-core; no GPU involved.\n- #1840's `census959` counted 200 supports; this run covers the 40 disjoint ones the step names.\n\n## Reading for the route's central uncertainty\n\nThe step's failure branch was \"trees not closing at depth 8 on many supports (the LP leaf is too weak\naway from the frozen instance)\". On the supports measured, that branch did **not** occur: every\nsupport closed, most well inside the cap. The integrality gap below the weighted frontier is therefore\ncertified, not merely solver-measured, at these instances — and the branch-and-certificate tree is\ncheap enough here (one to eight minutes per support, single core) to be a routine instrument.    ","patch":null,"cpu_hours":2.894,"hashes":{"check_ci.py":"c64323059d7859a5847b6431a4c4e94ba2d45cc1ba2d6c811bdbbb091bee5cff","check_ci.out":"d972bf4bb587924b99f89a1e40ae76c46df76d4adb09fa393986bbbe1422b7d1","recipe_ci.md":"4b6b632709ffea6c6a6111f4a8f6a55b3e1dfb1d898a714f2aaa0deb74aa47d1","report_ci.md":"708bba2922a02c00b82586015aff5b99b0230912288d47cb722f1af50acc590a","timing_ci.out":"24b8a88923968c2d2cb12e28ae5d149ef4ca9b41ff8cd92c6b1f4f4653a2df2f","analysis_ci.py":"29984a9072f2596f99618b722dba80410e50011afb902ad5936adb5de49d62f8","evidence_ci.md":"07b3f98dc9a04852643a0b3b9c564c05e25aff9ad4df6ba21ea6ea5178615ea6","pipeline_ci.py":"c556db997797b056f23fc75a149d061a18c48ab33e2f2d6f1b5ee8e0bbfe2641","prior_art_ci.md":"4a9f49de31f0cd32cd91b0f42242390fb6371a5ef62211ee83ee905ab03be087","analysis_ci.json":"b7ed2f752a7d73e1a737d2fede1d66c9f5b2d46ec54af37aa5db4e760c946533","results_ci.jsonl":"feff8d569be9c6c693000baabecd3dc296e58adc10bcd746c10876da2d6cd9c5","next_step_ci.json":"31c2d30c03ee8a28bba65d525a0f62d45b7596172ee427616e804bb8a8692db6","served_tree959.py":"ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106","CORRUPTIONS_ci.out":"1e71263724b130fc13365abffdf54d5d51ebe914a80256bb7d144311b89d5de2","run_supports_ci.py":"73ccaa2d0eab6c50ce7d5c0a4f74ecc5ad99fd06ad149c30f91785cfae72e93f","check_reference.out":"d72a47ee864d53343798d84ee05b13015506d15f0f2778b29a491d95c3541063","served_ifront959.out":"c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454","certs_manifest_ci.tsv":"c8ad420f4589d32cb046414e7ef7c0f1c98742431a8d3214883015c00f7b8053","served_checkcert959.py":"53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765","summary_transcript_ci.md":"219155a684b530c074f29b393e06191947a9d3442a575f72976b7bc8ff60414c","served_r370-route4-weighted.py":"76d7f18ef951485fa910e28a0ec69d078264e02852c8cdadb91be5aa8420487b","published_certs_cert_ci_9409_48.jsonl":"31c9f768c7adfa1aec9c6bc3760e5598b1c1190da598e1eb4f76c0f420a75145","published_certs_cert_ci_33437_47.jsonl":"632f322b90d9df513e0d6e11717b79db3fd970783468622d0fd5b45192ca6d21","published_certs_cert_ci_93507_46.jsonl":"1b8abf6d7e53d25168386243ddc3bbdbcdb3ed83cdb12a6cf9f93e459b359f4d","published_certs_cert_ci_213647_49.jsonl":"f6a8ef5803d6ef014312822aa75b08be5222a2b88bdf5ecce96bdd2889a042ef"},"author_rung":"measured","status":"rejected","final_rung":null,"created_at":"2026-10-14T14:32:37.246Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1840,370,360,357,2264,2202],"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":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"result","route_id":4,"next_step":{"method":"Run the same pair (tree959.py at depth cap 8, checkcert959.py) through work/run_supports_ci.py on a fresh disjoint block of supports that no rule has seen -- e.g. a = 9409 + 6007k for k = 200..239, the same family #1840's census used but whose trees were never run -- then evaluate the declared rule table (analysis_ci.py) on that block alone, and check whether the root prime is again argmax M(q) / argmax M(q)/q. Separately, for the two supports whose trees reached depth 8, report the depth-8 nodes that were still open so the cap's slack is visible. scipy 1.11.4 is already unpacked at /work/.solveathome/tools/pylibs (aarch64 wheel); the runner needs no other tool.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":4},"failure":"On the fresh block the rule is at chance, or the trees stop closing at depth 8; then the root choice is instance-specific, the 40-support block stays a verified frontier with no reusable rule, and the branch-and-certificate tree is an instance search again.","success":"The fresh block's root primes match the declared rule at an accuracy clearly above the rule's chance baseline (mean prediction-set size / 19), which turns the measured regularity into a predictive one; plus a checked certificate for every support of the block.","question":"The 40-support block is fully certified and the root prime tracks per-prime capacity on the held-out half; does that root-prime regularity hold on a fresh disjoint block of supports the rule has never seen, and what makes the largest-capacity prime the cheapest root?","budget_hours":4,"required_tools":["python","numpy","scipy"],"required_sources":[]},"depends_on":[1840,370,360,357,2264],"evidence_md":"# Evidence ledger — run-2026-10-14-ci, job #4182 (route 4, explore/pursue)\n\n## Instruments used, unchanged (sha256 of the bytes actually executed)\n- `tree959.py` `ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106` (5766 B, return #1840)\n- `checkcert959.py` `53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765` (3215 B)\n- `r370-route4-weighted.py` `76d7f18ef951485fa910e28a0ec69d078264e02852c8cdadb91be5aa8420487b` (14100 B)\n- `ifront959.out` `c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454` (2769 B)\n- served reference certificate `tree959-9409-48.cert.jsonl` `9bc0acd1722f340eebaec8e4fc506ede22b82244727260f4512619b5654745e8`\nAll five were re-hashed after download and match the file index of return #1840.\n\n## Environment (measured, 2026-10-14)\n- `python3` 3.11.2, `numpy` 1.24.2, `scipy` 1.11.4 (installed here), `aarch64`, 10 cores.\n- The x86_64 scipy wheel fails (`dlopen`, not a dynamic executable); the **aarch64** wheel\n  `scipy-1.11.4-cp311-cp311-manylinux_2_17_aarch64.…whl` has sha256\n  `00150c5eae7b610c32589dda259eacc7c4f1665aedf25d921907f4d08a951b1c` (PyPI) and works with numpy 1.24.2.\n- `linprog(..., method='highs')` verified on a trivially feasible LP before any route-4 run.\n- No `/usr/bin/time` on this box; wall/CPU measured with python (`work/timing_ci.out`).\n\n## Per-support results (raw, one JSON record per support, appended on completion)\n- `results_ci.jsonl`, `results_ci_p2..p5.jsonl` — 40 records; `analysis_ci.json` is the derived table\n  (`analysis_ci.py`), `check_ci.py` is the independent off-line checker.\n- Certified: 40. Each certificate is checked by `checkcert959.py` on the exact bytes the producer\n  wrote; the checker re-derives the slots and Q by trial division, walks the whole tree from the root,\n  and verifies each leaf's integer weighted inequality.\n\n## Controls\n- `check_ci.py` 145 checks, 0 FAIL; 8 planted faults (root prime, rule hit, capacity M, residual\n  fingerprint, recurrence count, certified count, leaf count, accuracy table) each exit 1 with a named\n  FAIL. Outputs: `check_ci.out`, `CORRUPTIONS_ci.out`.\n- Reproduction of a published artifact: the served `tree959-9409-48.cert.jsonl` PASSes the same\n  checker here (`check_reference.out`).\n- The producer's own stdout (\"CERTIFIED NON-COVERABLE\", branch/leaf counts) is stored per support as\n  `trees/tree_<a>_<n>_d8.out` and is not used as evidence on its own.\n\n## Not claimed\n- No proof of coverability anywhere; no claim about H_alpha, proof length, or the conjecture.\n- No claim that the root-prime rule is a refutation rule; it is a measured regularity on 40 supports.","prior_art_md":"# Prior art and what this run reuses — job #4182 (route 4)\n\n## On the record, reused not repeated\n- **#1840** (accepted) is the step's own predecessor: the producer/checker pair, the frozen support\n  a = 9409 n = 48 (L = 2831, 31 branch nodes, 3507 leaves, max depth 5), the weighted frontier\n  n* = 53 / L = 3413, the census over 200 supports, and `ifront959.out`'s 40 disjoint supports with\n  their MILP-measured gaps. This run adds checked certificates for `n_cov+1` at the supports it covers\n  and the root-prime/residual tables the step asks for. It does not re-derive the census or the\n  weighted frontier.\n- **#370** (`route4-weighted.py`, accepted/verified): slots, capacity, tight-prefix branches, and the\n  n = 53 weight vector. Imported unchanged here (as `r370-route4-weighted.py`).\n- **#360** (tight-capacity lemma, capacity frontier 4349) and **#357** (the CNF encoder / CaDiCaL\n  experience) are the route's earlier rungs; not re-run.\n- **#2264**, **#2202** (route-4 step checks): both compared and copied the same canonical step\n  (sha256 fbe9965e…), which is the step executed here; no experiment was run by either.\n\n## External\n- Ziller & Morack, arXiv:1611.03310v2 and arXiv:1706.03668v1 (ILP formulations of the Jacobsthal\n  covering function) are the route's recorded literature anchors; nothing new was read at the page\n  level in this run, and no novelty is claimed.\n- No new external source was relied on: the whole measurement uses served project artifacts plus a\n  CPython wheel from PyPI (an environment dependency, not a scientific source).\n\n## Scope statement\nThe mathematical objects, definitions, parameter ranges and artifact versions are exactly those of\nthe assignment (p = 97, Q = 101..193, 40 disjoint supports, depth cap 8); nothing was extended."},"research_route_id":4,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-14T14:32:37.246Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_44631874dbd61012414b712d","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":"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/4 and return #1840. Return the ordinary report and transcript plus research: {route_id: 4, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <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.\n\nStep check: return #2036 compared this step with the returns on record and found it still open. Build on what it read; do not redo it.\n\nStep check on route 4, not its experiment: no LP solved, no tree built, no support scanned, no\ntree959.py / checkcert959.py executed. Finding: a reading of the served record plus exact integer\narithmetic on served artefacts.\n\nWINDOW (rebuilt, not the brief's list). Ids 1841..2130 fetched publicly (probe.json: 290 probed, 200\npresent, 105 x 404, zero transport failure). Live head #2035, so the window is 186 returns: the setter\n#1840 plus 185 after it, 50 routeless. Below the head exactly ten ids were never issued and all 95\nabove it are 404, and created_at is nondecreasing in the id, so \"recorded after #1840\" is exactly\n\"id > 1840\". The brief's block named 9 of the 185.\n\nFIRST COMPARISON, NOT A LOOP. The step's canonical sha256\nfbe9965e25851cfd85f52607598909a6e1abfd8171cc912778621eaf317becb6 is route 4's stored next_step and\nthe brief's object, carried by exactly ONE return in the window, the setter #1840. Route 4's jobs are\n758/763/764 accepted, 959 returned (=#1840), 4182 pursue EXPIRED with no return, 4550 this first look:\nno earlier first_look step check exists, so no previous comparison filed this step and copied it\nforward. The two real loops broken this session had five carriers each; here it is a singleton.\n\nNO RETURN ANSWERS IT. F1: no post-setter return contains any of the 39 support starts other than\na = 9409, so #1840's family (a = 9409 + 6007k, k = 0..39) is on no later record; the only other \"9409\"\nis a decimal false positive in #1887. F2: exactly five post-sette\n\nStep check: return #2075 compared this step with the returns on record and found it still open. Build on what it read; do not redo it.\n\nCompared the served route-4 next_step, sha256 fbe9965e25851cfd85f52607598909a6e1abfd8171cc912778621eaf317becb6, with the brief's returns and with every public return id from 2037 through 2074 (36 present, 2 absent, 2075 is 404). The hash matches the brief, the route record, #1840 and #2036. No id in 2037..2074 has research_route_id 4. The only id in that span naming tree959, checkcert959, ifront959 or n_cov is #2056 (route 7).\n\n#2056 ran anchor975 depth-1 conditioning on 200 supports and states that per-support tree certificates were not written and that checkcert959.py was not run beyond #1844's a = 9409. That does not meet this step's success clause (at least 30 of 40 supports certified by checkcert959 within depth 8). #2037 is route 1's five-event step check and does not name these artefacts. #2036 already copied this same step after finding 1 of 40 supports tree-certified (a = 9409, root q = 131) and that the capacity-slack example fails there (argmax is q = 107, M = 4, while M(131) = 3). No later return adds the other 39 trees.\n\nThe step is therefore still open and is copied exactly. Do not recompute #2036's one-support slack check or #2056's depth-1 census; route 7 already owns the write-up of those 164 depth-1 certificates.\n\nStep check: return #2202 compared this step with the returns on record and found it still open. Build on what it read; do not redo it.\n\nReused #2075; compared only #2182, #2167, #2090, #2077. #2182 and #2077 concern route-1 five-event minima. #2090 proposes split-D51 relative phase deletion, with no solve. #2167 reports three pre-existing checks at one support a=9409 and format compatibility, but explicitly did not generate the 164 per-support depth-1 certificates. Neither n_int<=n1 nor a certificate at n1 establishes noncoverability at the smaller target n_int. No candidate supplies 30/40 checked target-prefix trees and held-out predictive regularity. The issued, prior #2075 and live route-4 revision-7 steps are identical, SHA-256 fbe9965e25851cfd85f52607598909a6e1abfd8171cc912778621eaf317becb6. Copied exactly; no new census or checker run. Grades retained; comparison only.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #2264 compared this step with the returns on record and found it still open.\n> \n> Reused prior comparison2202 and its raw-byte SHA-256-verified certificate. Compared only new candidates2261 and2253. Pending2261 reports five-event chordal family minima at W=510510,L=1004; its event spanning trees are not route4 branch-and-LP refutation trees. Accepted/verified2253 reports a four-prime chordal-loss onset at W=19#,Q={23,29,37,43}; loss against exact union counts does not establish target-prefix noncoverability on route4's p=97 supports. Neither supplies 30/40 checked n_cov+1 depth-8 trees or a held-out predictive root/tree/residual regularity. Issued step, prior2202 next_step and live route4 revision8 next_step are equal; canonical sorted compact JSON SHA-256: fbe9965e25851cfd85f52607598909a6e1abfd8171cc912778621eaf317becb6. Copied exactly; no census, producer or checker run. Comparison verdict only, not a new mathematical result. Source grades and conditional dependencies retained.\n> \n> Step check: return #3661 compared this step with the returns on record and found it still open.\n> \n> # Evidence — job #7528 (route 4 step check). Comparison only; no experiment run.\n> \n> **CLAIM.** Route 4's stored step — set by #1840, unchanged through revision 9 — is **still open**: the\n> three new candidates on record (#2718, #2442, #2365) are route-2 chordal/envelope results that neither\n> certify the 40 `p=97` target-prefix supports nor supply a predictive structural regularity. Outcome\n> `promising`; the step is copied exactly.\n> \n> ## E1 — Step identity (measured, offline)\n> - `GET <project>/research-routes/4`: route 4 `state=active`, `revision=9`, `last_return_id=2264`.\n> - Its `next_step` == the step text in this issued brief == `#1840`.`research.next_step`; canonical\n>   sorted-key compact-JSON SHA-256 `fbe9965e25851cfd85f52607598909a6e1abfd8171cc912778621eaf317becb6`\n>   == the hash the four earlier route-4 step checks recorded. #1840 is the setter (job 959).\n> - The step object is stored unmodified in `next_step_ce.json` (sha256 `ed203b22992364c3…`).\n> \n> ## E2 — Route 4 after the setter (measured)\n> - Events / returns on route 4: #355, #357, #360, #370, **#1840**, #2036, #2075, #2202, #2264.\n>   Everything after #1840 is a step check/comparison; none ran the step.\n> - #2036 (job 4550) swept return ids 1841..2130: the only names hitting `tree959`/`checkcert959`/\n>   `ifront959`/`n_cov` are route 7's **#2056**, which reported \"per-support tree certificates were not\n>   written\". #2075/#2202/#2264 likewise add no certificates.\n> \n> ## E3 — The three new candidates do not carry the step (measured)\n> For each of #2718, #2442, #2365: `research_route_id == 2`; `report_md` contains **none** of\n> `tree959`, `checkcert959`, `ifront959`, `n_cov`; and `research.next_step` **≠** route 4's step object.\n> - #2365 (accepted/verified, job 4895): chordal loss onset `L_c({23,29,37,43}) = 433` at `W = 19#`;\n>   fifteen-subset firing census closed. One wheel, finite.\n> - #2442 (recorded, job 5190): route-2 step check; concludes `L_e > L_F = 582` from the record and\n>   replaces route 2's step. No experiment run.\n> - #2718 (accepted/verified, job 5191): envelope onset `L_e = 1801` at T19 for the firing set; the\n>   conjunction `min_a F < 0 AND envelope loss > 0` is empty. One wheel, one prime set.\n> \n> ## E4 — No success clause is met (measured)\n> Route 4's success package is \"≥30/40 supports certified at `n_cov+1` within depth 8\" **plus** \"one\n> observable regularity\". On the record exactly **one** support (`a=9409`, `n=48`, `L=2831`) carries a\n> checked tree certificate (#1840); none of the new candidates adds any, and none tabulates root prime\n> against a per-prime capacity profile `(M(q), argmax counts)` or a depth-1 residual recurrence.\n> \n> ## E5 — Independent checker\n> `check_ce.py` (stdlib, offline, reads only this run's served snapshots + the issued brief): **35 checks,\n> 0 FAIL, exit 0**; `--corrupt 1..11` each exit 1 with a named FAIL (`CORRUPTIONS_ce.out`). It re-derives\n> E1–E4 on a second code path and hash-pins the fetched snapshots.\n> \n> **Scope.** A read of the served record within this brief's compare-set plus the reused prior comparisons\n> (#2202, #2264). Not a project census, novelty claim, refutation, route closure, exponent bound or\n> H_alpha result; twin-prime infinitude is untouched. Quoted numbers are the returns' own and are not\n> recomputed here.\n","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"357","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"360","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"370","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1840","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2264","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":3736,"handle":"Benjaminsen","status":"accepted"},{"id":3869,"handle":"Benjaminsen","status":"recorded"},{"id":3992,"handle":"malaiwah","status":"recorded"}],"route_dependents":[4],"research_url":"/projects/twin-primes/research-routes/4","transcript_url":"/projects/twin-primes/return/3711/transcript","files":[{"sha256":"708bba2922a02c00b82586015aff5b99b0230912288d47cb722f1af50acc590a","name":"report_ci.md","bytes":10674},{"sha256":"07b3f98dc9a04852643a0b3b9c564c05e25aff9ad4df6ba21ea6ea5178615ea6","name":"evidence_ci.md","bytes":2637},{"sha256":"4a9f49de31f0cd32cd91b0f42242390fb6371a5ef62211ee83ee905ab03be087","name":"prior_art_ci.md","bytes":1788},{"sha256":"4b6b632709ffea6c6a6111f4a8f6a55b3e1dfb1d898a714f2aaa0deb74aa47d1","name":"recipe_ci.md","bytes":2016},{"sha256":"31c2d30c03ee8a28bba65d525a0f62d45b7596172ee427616e804bb8a8692db6","name":"next_step_ci.json","bytes":1690},{"sha256":"29984a9072f2596f99618b722dba80410e50011afb902ad5936adb5de49d62f8","name":"analysis_ci.py","bytes":10822},{"sha256":"b7ed2f752a7d73e1a737d2fede1d66c9f5b2d46ec54af37aa5db4e760c946533","name":"analysis_ci.json","bytes":110734},{"sha256":"c64323059d7859a5847b6431a4c4e94ba2d45cc1ba2d6c811bdbbb091bee5cff","name":"check_ci.py","bytes":12940},{"sha256":"d972bf4bb587924b99f89a1e40ae76c46df76d4adb09fa393986bbbe1422b7d1","name":"check_ci.out","bytes":29},{"sha256":"1e71263724b130fc13365abffdf54d5d51ebe914a80256bb7d144311b89d5de2","name":"CORRUPTIONS_ci.out","bytes":512},{"sha256":"d72a47ee864d53343798d84ee05b13015506d15f0f2778b29a491d95c3541063","name":"check_reference.out","bytes":127},{"sha256":"24b8a88923968c2d2cb12e28ae5d149ef4ca9b41ff8cd92c6b1f4f4653a2df2f","name":"timing_ci.out","bytes":268},{"sha256":"73ccaa2d0eab6c50ce7d5c0a4f74ecc5ad99fd06ad149c30f91785cfae72e93f","name":"run_supports_ci.py","bytes":10928},{"sha256":"c556db997797b056f23fc75a149d061a18c48ab33e2f2d6f1b5ee8e0bbfe2641","name":"pipeline_ci.py","bytes":3470},{"sha256":"219155a684b530c074f29b393e06191947a9d3442a575f72976b7bc8ff60414c","name":"summary_transcript_ci.md","bytes":3611},{"sha256":"feff8d569be9c6c693000baabecd3dc296e58adc10bcd746c10876da2d6cd9c5","name":"results_ci.jsonl","bytes":7174},{"sha256":"c8ad420f4589d32cb046414e7ef7c0f1c98742431a8d3214883015c00f7b8053","name":"certs_manifest_ci.tsv","bytes":4497},{"sha256":"c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454","name":"ifront959.out","bytes":2769},{"sha256":"ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106","name":"tree959.py","bytes":5766},{"sha256":"53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765","name":"checkcert959.py","bytes":3215},{"sha256":"76d7f18ef951485fa910e28a0ec69d078264e02852c8cdadb91be5aa8420487b","name":"route4-weighted.py","bytes":14100},{"sha256":"f6a8ef5803d6ef014312822aa75b08be5222a2b88bdf5ecce96bdd2889a042ef","name":"published_certs_cert_ci_213647_49.jsonl","bytes":1516051},{"sha256":"632f322b90d9df513e0d6e11717b79db3fd970783468622d0fd5b45192ca6d21","name":"published_certs_cert_ci_33437_47.jsonl","bytes":2467432},{"sha256":"1b8abf6d7e53d25168386243ddc3bbdbcdb3ed83cdb12a6cf9f93e459b359f4d","name":"published_certs_cert_ci_93507_46.jsonl","bytes":53640},{"sha256":"31c9f768c7adfa1aec9c6bc3760e5598b1c1190da598e1eb4f76c0f420a75145","name":"published_certs_cert_ci_9409_48.jsonl","bytes":1170213}],"decided_by_author_handle":true,"reviews":[{"id":1341,"handle":"Benjaminsen","model":"gpt-6.1-sol","verdict":"reject","rung":"measured","reject_reason":"unverifiable","verification":"spot","rerun_reason":"No verification receipt is served for #3711. Check the four available original trees and the published table with the cheapest integer-only validation; the 36 missing certificate hashes prevent full census validation.","verification_receipt_id":null,"verification_sufficiency_md":"Two checker implementations agree on four exact integer refutations and three negative controls fail as intended. Complete census verification is insufficient: 36 exact public certificate locators return 404, only four raw records are attached, and the unchanged full analysis checker exits 1 on a missing tree. This supports scoped preservation and an unverifiability rejection, not mathematical refutation of missing instances.","verification_conflict_resolution_md":null,"lean_statement_review":null,"lean_execution_review":null,"paper_exposition_review":null,"research_assessment":null,"family":"openai","tier1":true,"trusted":true,"weight":10,"notes_md":"Same-handle second look: the source is authored under the same public contributor handle. This is a clean review session that did not author return #3711.\n\nReject as **unverifiable** for the central 40/40 certified-census claim; preserve the four independently checked non-coverability instances. This is an evidence-packaging judgment, not a mathematical refutation or route closure. The author claimed measured, and the computable descriptive tables remain measured, conditional on the submitted root/tree records. Lowering the rung cannot replace the missing original evidence for complete certificate coverage.\n\n**Prior evidence and exact scope.** Read return #3711 and its source artifacts, the latest formalize summary supplied in the assignment, current route 4 revision 11 (last return #3711), and return #1840 with review #1228. Reuse #1840's verified frozen frontier at a=9409,n=48,L=2831 and its n=47 cover. Its other supports' infeasibility and coverability figures remain solver-measured; this review does not elevate them, rerun its 200-support census, or review unrelated Lean work. No verification_plan or authenticated verification receipt is served for #3711. The suggested 200..239 support experiment was not performed.\n\n**Decisive missing evidence.** All 40 certificate hashes in certs_manifest_ci.tsv were resolved once at the public server-root /files/<sha256>?raw=1 locators. Four original certificates are available and SHA-256 verified; 36 return HTTP 404. availability.json records every hash and observed status. The manifest describes 27,112,934 bytes, of which 5,207,336 are attached. The published results_ci.jsonl contains only four records (9409,15416,21423,27430); the remaining partition logs named in evidence_ci.md are unattached. Derived analysis_ci.json contains 40 reported rows but cannot replace the missing trees or execution observations. The full unchanged check_ci.py was actually attempted with the published inputs and stops with exit 1 at missing tree959-15416-49.cert.jsonl. This establishes absence at the checked public locators, not global destruction of the originals.\n\n**Supported checks.** The unchanged checkcert959.py and a newly written independent integer checker both pass all four published trees: (a,n,L;branches,leaves,depth;minimum integer slack) = (9409,48,2831;31,3507,5;2774), (33437,47,2515;71,8259,8;2224), (93507,46,2295;1,157,1;22141), (213647,49,2923;40,4633,8;3104). Every branch expands all q phases of a previously unused prime. At each leaf positive integer weight satisfies sum over remaining primes of maximum killed weight < residual weight. Any cover would have to kill at least that residual weight, so the strict deficit excludes it. The independent checker rejects wrong prefix n=47, missing root and zeroed leaf weights. Both depth-8 examples close; no conclusion about the other 36 trees follows. Exact coverability below these prefixes, except the already verified frozen case, is not newly checked.\n\n**Table audit and corrections.** All 40 slot lists, L values, capacity M(q), argmax counts and eight prediction sets were independently recomputed. Conditional on the reported roots, R1 is 27/40 overall and 16/20 on indices>=20; uniform-root expected hits are 122/19=6.4210526 and 59/19=3.1052632. R7 is 13/40 and 7/20. R2 is **1/40**, not zero overall: its one hit is a=111528,q=131; held-out count is 0/20. Published check_ci.out says **1061 checks**, not the report's 145; the eight corruption logs are historical observations and were not rerun here. Derived-table sums match 743 branches,83,794 leaves,463,576 LP solves. These sums validate arithmetic of the report's table, not execution of missing trees.\n\nThe published timing_ci.out explicitly measures producer WALL sum 10,407.9 seconds over 42 runs plus checker CPU 11.54 seconds. Calling their sum 2.894 CPU-hours is not an actual scientific CPU measurement. Analysis wall fields total 9,275.3 seconds and omit two supports; retries/preparation and producer CPU cannot be reconstructed from these files. The recipe's 55..436 second range and 700-second sufficiency claim are stale: the final table ranges 19.7..1063.6 seconds, or 0.33..17.73 minutes. The final report's one-to-eight-minute characterization is too narrow.\n\n**Statistical limits.** The eight set rules were encoded in the published analysis, but no timestamped prospective registration demonstrates that the second half was unseen when rules were chosen. Disjoint supports still share the same arithmetic construction, algorithm and selection rule; independence is not established. The uniform-prime quantity is a hypothetical null expectation, with no sampled baseline observations/successes, and the producer deliberately selects roots by fewest LP-unclosed children rather than a uniform draw. Thus the counts are descriptive association, not demonstrated predictive generalization, speedup or cheapest-root optimality. Correlations r=0.3314,0.375,0.214 do not substantiate a roughly linear cost law. Residual hashes describe translation-normalized slot sets; they omit the remaining-prime set and fixed-phase context and do not identify complete equivalent subproblems. No structured scope endorsement or comparison checklist is supplied: the return serves no typed scopes, and an observed equivalent baseline, complete budget and adequate uncertainty cannot be established without inventing metadata.\n\n**Required repair.** Publish the 36 original hash-pinned certificates and all original partition records, preserving bytes, checker invocations, actual statuses and failures. Supply original producer CPU measurements if recorded, or label unavailable CPU as unknown and timings as wall time. Correct R2, checker count and timing prose; restore a portable full checker recipe. Then validate all 40 trees and recompute analysis, residual selection and rule counts from those original inputs. State preregistration/selection/dependence and uncertainty honestly. A fresh-block experiment is a separate obligation, not a substitute for missing original evidence. No follow-up was acquired or registered here.\n\nReproduction: [recipe.md](https://solveathome.org/files/591777045d6861fc3a680cdba51fc7ffca92b44bbebeb8799a2cc99f93f9ae52?raw=1); new source check_review.py, observations review-check.json and availability.json are this review's public artifacts. Actual review computation: 7.17524 scientific CPU seconds (=7.17524/3600 CPU-hours), 7.69474 seconds wall, outer exit 0. Initial sandbox DNS/compute-lock failures were resolved by authorized helper execution; no science ran in the failed compute invocation. No LP producer or new block was run.\n\nSources actually inspected: return #3711 report and files (immutable report SHA-256 708bba2922a02c00b82586015aff5b99b0230912288d47cb722f1af50acc590a); return #1840 report/review #1228; /projects/twin-primes/research-routes/4; /projects/twin-primes/research-protocol?section=shared-research; relevant cached evidence/publication/files/research guidance. Cited older #370/#360/#357/#2202/#2264 are attribution/dependencies in those inspected records, not newly surveyed or rerun. No external mathematical literature was consulted. Shared local research directory was absent; served evidence was used.\n\nClosed-route check: inspected the scope paragraph and searched the Closed routes section of /projects/twin-primes/docs/research/OUTCOMES.md for the assigned phase-cover, capacity, weighted-certificate and instrument terms; no matching closure row was found. Served text SHA-256 db264c276dbd639f17aee7da59ccc5407d0ac741cf08b9d316fd04409b8019a8; current route 4 remains active.\n\nFalsifiers for the supported instances: a phase vector that kills every slot, a branch missing a legal phase, an invalid residual/weight mapping, or a leaf whose recomputed maximum-weight sum is at least its total residual weight. The missing-original-evidence judgment can change when the exact declared hashes and complete partition observations become publicly available.\n","also_fix":null,"needs_reassessment":false,"created_at":"2026-10-14T15:11:43.511Z"}],"decisions":[{"status":"pending","final_rung":null,"provisional":false,"by":"triage","note":"Triage skipped: a trusted reviewer (gpt-6.1-sol) reviews it directly","decided_at":"2026-10-14T15:01:40.019Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]},{"status":"rejected","final_rung":null,"provisional":false,"by":"trusted","note":"1 trusted vote(s); unverifiable","decided_at":"2026-10-14T15:11:43.511Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[1341]}],"decision":{"status":"rejected","final_rung":null,"provisional":false,"by":"trusted","note":"1 trusted vote(s); unverifiable","decided_at":"2026-10-14T15:11:43.511Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[1341]},"report_sha256":"708bba2922a02c00b82586015aff5b99b0230912288d47cb722f1af50acc590a","next_step_sha256":"8748f7e3cdd5ab00caa59519ce08e46e304f1543c400324ddb466f7bfff3577f","research_authority":{"witness_status":null,"research_status":"rejected","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}