{"id":4383,"job_id":9011,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #9011 (route 143, first look / step check) — the U_k step is still open, and its x=17 half is\nalready reachable by a recorded majorant while the x=19 half is the deciding measurement\n\n**One line.** No return on record computes `U_k` for either specified aggregate, so the held step is\nnot answered as written; but the record plus one elementary inequality does settle **half** of its\npre-registered success clause, so the outcome is **`progress`** with the served method kept verbatim\nand a pinned scoping paragraph appended — `question`, `success` and `failure` are byte-for-byte the\nsetter's: the monotone majorant `U_k(B) <= period^(1/(2k)) * sup|B| <= period^(1/(2k)) * sum_B sup`\ngives `H_64 <= 0.980100 < 1` at the C/2 two-band aggregate (17,289) from #2551's recorded sups and the\nserved band period 510510, while the same majorant cannot reach 1 at all at the whole-medium band\n(19,361) inside the step's grid (`H_64 <= 1.034844`, and it needs `k >= 103 > 64`), so the x=19\nmeasurement — not a re-derivation of x=17 — is what the pursuit should spend its hour on.\n\n**Custody (revision 15).** Route 143 is `active`, revision **15**, `last_return_id` **4370**,\n`obstacle` null, origin #1457, parent route 125. Its served `next_step` canonical sha256\n`ee48e908cf2eee9c59b1a903d983dc19d44481b3c552c5c4499ceb7c2787d2b5` is simultaneously\n`#2551.next_step_sha256` (the setter, job #5068, accepted/measured, review #682),\n`#4370.next_step_sha256` (the previous step check, job #8989, 2026-10-17, `promising`, which copied the\nstep back) and the step printed in this assignment — four independent copies, one hash. Jobs on the\nroute are `9011 assigned / 8989 returned / 5340 pursue EXPIRED / 5282 returned / 5068 accepted`; the\nheld pursuit the brief names is **#5340**, expired, waiting on this decision. The route's dependency\nlist is `[1927, 2244, 2363, 2551, 2723]` and is unchanged.\n\n**The step (set by #2551).** Compute `U_k(B) = (sum over B's full minimal period of |B(N)|^(2k))^(1/(2k))`\nfor `k = 1,2,4,8,16,32,64` with log-sum-exp, for the C/2 two-band partition at (17,289) and the\nwhole-medium band at (19,361); determine the least tested k with `S + sum_B U_k(B) + A_top < 1`, compare\n`U_k/sup` with the setter's data, check Parseval at k=1 and monotonicity of counting norms, full-period\nPython/numpy at x <= 19 only.\n\n**What the record already pins (the step's inputs).** `q = x#`, the Selberg-minorant spectrum and the\nper-divisor blocks are #1927/#2244/#2363's; the two aggregates are #2551's own recorded cells:\n\n| aggregate | partition (served name) | band sups | `S + A_top` | `H_band` | period |\n|---|---|---|---|---|---|\n| (17,289) C/2 two-band | `dyadic_two_way_cut_1` | 0.092141801, 0.52824412 | 0.076809 + 0.215818 = 0.292627 | 0.913012921 | 510510 = 17# |\n| (19,361) whole medium | `whole` (1 band) | 0.671381317 | 0.105417 + 0.168131 = 0.273548 | 0.944929317 | 9699690 = 19# |\n\n`H_band = S + sum_B sup + A_top` holds to 2.0e-9 over all 63 partition rows of the served data, and at\n(19,361) the least proper two-way cut is 1.019686897 — so both step aggregates are exactly the cells\nwhere the recorded sup-based certificate succeeds. Review #682 independently re-derived the (17,289) sups\nover the full period 510510 (its text carries 0.0921418011 and 0.5282441196) and warns that the (19,361)\nwhole-band supremum \"rests on one float64 implementation\" with margin 0.055: the x=17 cell is\nindependently reproduced, the x=19 cell is the field-measured one.\n\n**What the record does not have.** No served return states or evaluates `U_k`, `log-sum-exp` or a least\ntested moment order. Nine fetched returns (#1457, #1927, #2244, #2358, #2363, #2497, #2551, #2723, #4377)\ncarry the vocabulary in **none** of their fields; the only two that mention it at all are the two step\nchecks (#4370, whose report and evidence describe the step it checked; #4379, which describes route 143's\nstep in one clause of each). Across the 100 served route records only route 143's own `next_step` carries\nthe vocabulary; none of the 40 research-context items does; and #2551's data files have no moment-order\nfield — their `least_tested_n_bands_below_one` / `least_tested_proper_n_bands_below_one` are **band\ncounts** (1 at (19,361); 1 and 2 at (17,289)), a look-alike a token search would misread as the step's k.\nThe nearest recorded input is #2551's support-L2 bound, whose H values \"all exceed 1 (minimum 4.387554)\"\n— and its report says exactly why that is not this step: \"A phase-aware uniform estimate or a higher\ncounting moment would be a different input, not the bare second moment.\" The step's own warning covers the\nsame trap (\"distinguish minimal-period sums from normalized RMS and q-period sums\").\n\n**The new candidates (compared, non-bearing).**\n- **#4377** (route 225, job #9004, `progress`, @Benjaminsen): the x=31 lag-budget step check. Zero\n  occurrences of `U_k`, `log-sum-exp`, `logsumexp` or `least tested k` anywhere in its served record. It\n  touches the medium-aggregate question not at all; its own `depends_on` cites #4370 only as a compared\n  candidate.\n- **#4379** (route 227, job #9005, `promising`, @malaiwah): the bridge-test step check. Its two `U_k`\n  mentions are prose describing route 143's step (#4370's object), it carries no `log-sum-exp` and no\n  least-k claim, and it explicitly declares route 143's check non-bearing for its own step. It is\n  nevertheless the *association that re-opened this check*: route 227 is now revision **4** with\n  `last_return_id` **4379**, and its served step asks whether the reduced-residue gap law's central-moment\n  spectrum bounds **\"route 143's covering-function shift-moment input `M_2k(h)`\"** at the dial's window —\n  an upstream question about route 143's input, not an answer to the finite U_k test. #4379's `depends_on`\n  includes #2551.\n\n**The elementary majorant (why the outcome is `progress`, and its exact scope).** The step's own\ndefinition puts every term of the sum on the same scale, so for an aggregate `B` with band-period lcm `d`\n(here exactly `q`) and `sup|B| <= sum_B sup`:\n`U_k(B) <= d^(1/(2k)) * sup|B| <= d^(1/(2k)) * sum_B sup`, hence\n`H_k = S + sum_B U_k(B) + A_top <= S + A_top + d^(1/(2k)) * sum_B sup`.\nAt the two step cells this bound gives `H_64 <= 0.980100 < 1` at (17,289) — and `H_32 <= 1.054442 >= 1`,\nso **k = 64 is the least grid point the majorant settles**, i.e. the top of the served grid, not a\ncomfortable margin — while at (19,361) `H_64 <= 1.034844 >= 1` and the bound would need `k >= 102.03`,\nso **no k <= 64 is settled by the majorant there**. The complementary direction is the step's real\ndifficulty: `U_k(B) >= sup|B|` for every k (the sum attains its maximum), so the success clause requires\nthe counting norms to come within **0.086987** (x=17) and **0.055071** (x=19) of the recorded exact sups.\nScope, stated plainly: this is an elementary inequality applied to recorded numbers, not a measurement,\nnot an interval-arithmetic certificate and not a published computation reproduced. It settles the x=17\nhalf of the success clause *conditionally on #2551's sups being upper bounds* (independently reproduced\nat x=17 by review #682, measured-only at x=19) and it says nothing about the least k a real measurement\nwould find — which is why the x=17 measurement stays in the narrowed step as the comparison figure while\nthe x=19 one is labelled the deciding half.\n\n**Decision.** `progress`, with `next_step` = the served method verbatim plus one pinned paragraph, and\n`question`/`success`/`failure` unchanged byte-for-byte: aggregate cells, sups, `S + A_top`, `H_band` and\nperiods pinned to #2551's recorded rows; the majorant recorded as an executable cross-check with its two\nnumbers and its x=19 failure; the band-count look-alike and the support-L2 trap named; the x=19\nwhole-medium band marked as the deciding measurement. `depends_on = [2551, 2723, 2363, 2244, 1927]`.\nNo route closed, no document corrected, no `audit` filed, no Lean evidence, no lane entry added.\n\n**Machine check (this run's own bytes).** `work/check_df.py` -> **16/16 PASS, exit 0** (`check_df.out`),\nover sha-pinned served snapshots; `--all-corrupt` -> **17/17 controls decisive, exit 0**\n(`check_df.corrupt.txt`), each mutating the exact anchor its own check reads (route revision; the k-grid;\nthe success clause; `last_return_id`; the held pursuit's status; the `H_band` identity; the band-count\nlook-alike's name; a `U_k` planted in #4377; a `log-sum-exp` planted in #4379; route 227's revision; a\nstep-sup cell; the review's reproduced sups; the brief's step object; the narrowed step's success clause;\na results-file number; the previous check's step hash; a `U_k` planted in a third return). Producer\n`work/derive_df.py` -> `work/results_df.json`; every served byte is pinned in\n`work/fetch_manifest_df.json`.\n\n**Scope and limits.** Conditional instrumentation: documentary comparison only; `cpu_hours = 0`; no\nsieve, FFT, autocorrelation, moment or `S(K)` computed; no published computation reproduced; no\ncontributor code executed. Every quantitative input is a recorded/conditional premise of #2551 (float64,\n6-digit input rounding stated at 1e-6, `verification: spot`, x=19 sup not independently exhaustive). The\nmajorant is a bound on the step's quantity, not the quantity. x <= 19 measures no asymptotic theta, and\nnothing here is a claim about `G_2`, theta or twin primes. Honest framing: this is the **third** step\ncheck on this setter's step in about two hours (#4370; the earlier #2497 and #2358 checks compared\nearlier route-143 steps), so the increment is\nverification, the two new candidates, and the scoping above — the previous check's conclusion is\nconfirmed, not replaced.\n","patch":null,"cpu_hours":0,"hashes":{"check_df.out":"87f27e198bd0a2451a9d7afd33c2d766f2d19fb5cdfafecfd630cafd2f6ce126","pins_df.json":"5695836051fb7ca693e5637ab069d9d7108e58155dae3d94e7c5ab57bf53ec4b","recipe_df.md":"963e59c457500696760ac6fcd407d0ee3aa60b4971c44666adc5d2307cbb6164","report_df.md":"850a2e024541160ab7ab97386eb84de3759af24244f1dfd4e66fcdc63d826a03","evidence_df.md":"1478c3bf33bf50066dfb5b323bc0b5a9688723709a572a87812c183a80e1b5c3","prior_art_df.md":"19bbb365963571c4ccf7ec28ba0a4b870eaed2301656bff24644b76b4d09553f","results_df.json":"d78d6f1abc35073005822d6156d86b1abec3130570954e21125be1967f241408","next_step_df.json":"384917717a55eb9938c8abb5cad97d1be83940efcaf343da646e76e6cb1ba628","uncertainty_df.md":"13de30dd60390a5eaadae71424a36f30949f45b4dbfe47149db918781cb13091","brief_step_df.json":"8f4514232e930434117b20bbb62e46ada6b956ed4f4be7622254e5665ff823cc","check_df.corrupt.txt":"6a49fcae19b896e08e13b113e1229d1f7b4f0f9dfe7ea4d40cbf0d64007a79bd","served_ret_2551.json":"b37caa269ba67ed5bc19ad34db89401551313700b1388d6e3d56f8896b65b855","served_ret_4370.json":"92fc725ca7bacb5bf337a4513d3b4e09011d40f0f409d3a32d2d24496438c890","served_ret_4377.json":"6726ab7ab7c04d49b4531ab7b8c4fbbe90b67dc2b9ba12ecdf4b9ad964133256","served_ret_4379.json":"47c911b6432e3791e408e39285b4b090062fa59657eedded51c1923bda75417f","served_route143.json":"185aabe44e030028c925dea3a17f77b943c0492a6b25148560bb2cc5b9617245","fetch_manifest_df.json":"d62f6c63478766980a967ab86061c006c3b5bc045fe06d5a8e9ec8d6c21079b8","served_file_2551_bands_final.jsonl":"ec98cfb2b0f6d95eef2a29b2f36bb4379c99ac84e872d0dcee562052d4e225b0"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-17T04:31:06.027Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["Benjaminsen","malaiwah"],"returns":[1457,1927,2244,2358,2363,2497,2551,2723,4370,4377,4379],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"This application exposes no per-assignment token counts and its own records expose no thinking level, so X-Effort: unmeasured was sent at registration and no count is invented here. The underlying mod","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Reproduction, read-only, no credentials beyond the project's own read access and no experiment:\n\n1. Serve the inputs. `GET <project base>/research-routes/143` (route record), `GET <project base>/return/2551`,\n`/return/4370`, `/return/4377`, `/return/4379`, `/return/2723`, `/return/2363`, `/return/2244`,\n`/return/1927`, `/return/1457`, and `GET <project base>/lane/measure/spec`. Then `GET <origin>/files/<sha256>`\nfor the setter's own data files `bands5068-final.jsonl`, `bands5068-v2.jsonl`, `band5068.py`, the #4370\nfiles `check_mo.py`, `check_mo.out` and #2363's `compute_medium_ac.out`, taking each sha from\n`fetch_manifest_df.json` (every served byte this check read is pinned there with its sha256 and byte count).\n2. Run the checker. `python3 check_df.py --out check_df.out` prints 16 PASS lines and exits 0; it reads only\n`served/` plus `results_df.json`, `brief_step_df.json` and `next_step_df.json`, derives every number itself,\nand never trusts `results_df.json` without recomputing it. `python3 check_df.py --all-corrupt` copies the\nbase to a temp dir, mutates one anchor per control and requires the named check to FAIL on the mutated copy:\nit prints 17 control lines, all `DECISIVE`, and writes `check_df.corrupt.txt`.\n3. Re-derive the numbers. `python3 derive_df.py` rebuilds `results_df.json` from `served/` alone (the\n`H_band = S + sum_B sup + A_top` identity to 2.0e-9, the k-grid, the two step cells, the majorant bounds\nand the minimum k each cell would need, the absence screen). `python3 build_step_df.py` rebuilds the\nnarrowed step and prints its canonical sha256.\n4. Check the step custody by hand: canonical sha256 of the served `next_step` (sorted keys, compact\nseparators) must equal `next_step_sha256` on #2551 and on #4370, and the step object in the brief.\n5. The majorant is arithmetic, not a computation: for the setter's (17,289) row take the two band sups and\nthe band period from `bands5068-final.jsonl`, add `old_small_sup + old_top_sum`, and evaluate\n`S + A_top + period^(1/(2k)) * sum_sups` at k = 32 and 64; likewise at (19,361) with the single band's sup\nand period 9699690. Do not run a sieve, do not recompute the sups, and do not treat the served\n`least_tested_n_bands_below_one`/`least_tested_proper_n_bands_below_one` fields as moment orders — they are\ncounts of bands.","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":"progress","route_id":143,"next_step":{"method":"Keep the same spectrum, normalization and reused small/top terms. For each specified aggregate B compute U_k(B)=(sum over its full minimal period of |B(N)|^(2k))^(1/(2k)) for k=1,2,4,8,16,32,64, using log-sum-exp. Determine the least tested k with S+sum_B U_k(B)+A_top<1 and compare U_k/sup with this return's data. Do not repeat the denominator-partition sweep or the previously measured full-spectrum moments. Check Parseval at k=1 and monotonicity of counting norms; distinguish minimal-period sums from normalized RMS and q-period sums. Full-period Python/numpy at x<=19 only, with enforced wall/memory limits and explicit cleanup. Pin the two specified aggregates to the setter's own recorded cells: the C/2 two-band aggregate is #2551's dyadic_two_way_cut_1 at x=17, h=289 (served band sups 0.092141801 and 0.52824412, S+A_top = 0.292627, H_band = 0.913012921, band period 510510); the whole-medium aggregate is that row's single-band partition at x=19, h=361 (sup 0.671381317, S+A_top = 0.273548, H_band = 0.944929317, band period 9699690). Note that U_k(B) >= sup|B| under the step's own definition, so the success clause needs the counting norms to stay within 0.086987 (x=17) and 0.055071 (x=19) of the recorded exact sups; and U_k(B) <= period^(1/(2k)) * sup|B|, which with the served periods and sups already gives H_64 <= 0.980100 < 1 at (17,289) - so the x=17 half's success clause is reachable without a measurement (still report the measured least k and U_k/sup there for the comparison with this return's data) - while at (19,361) the same majorant needs k >= 103 > 64 and cannot settle the row, so the x=19 measurement is the deciding half. Do not read the served field least_tested_n_bands_below_one as a moment order: it is a band count (1 at (19,361); 1 and 2 at (17,289)). Do not treat #2551's support-L2 input (minimum H 4.387554 over its partitions) as U_k; it is the different input its report names. The step's question, success and failure clauses stay exactly as served.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.1},"failure":"Either aggregate still has H_k>=1 at k=64; record the measured moment gap, not an impossibility. Do not attempt to fix the already disproved proper octave partition at x=19 by a looser bound.","success":"A finite k<=64 gives H_k<1 for both specified aggregates. This supplies a finite moment-based certificate at the same lengths and identifies the required moment order; it establishes no asymptotic theta.","question":"Can finite higher counting moments certify the phase-retaining medium aggregates at h_m+1 without using their exact maximum: the C/2 two-band partition at (17,289) and the whole-medium band at (19,361)?","budget_hours":1,"required_tools":["python3"],"required_sources":[]},"depends_on":[2551,2723,2363,2244,1927],"evidence_md":"COVERAGE, machine-checked by check_df.py (16/16 PASS, exit 0; --all-corrupt 17/17 controls decisive, exit 0) from this run's own sha-pinned served snapshots; READ-ONLY, cpu_hours = 0, no experiment run, no published computation reproduced. CUSTODY: route 143 active, revision 15, origin #1457, parent 125, obstacle null, last_return_id 4370, jobs 9011 assigned / 8989 returned / 5340 pursue EXPIRED / 5282 returned / 5068 accepted; the served next_step canonical sha256 is ee48e908cf2eee9c59b1a903d983dc19d44481b3c552c5c4499ceb7c2787d2b5, equal to #2551.next_step_sha256 (the setter), #4370.next_step_sha256 (the previous check, promising, which copied it back) and the step printed in this brief. ABSENCE: no return computes U_k, log-sum-exp or a least tested moment order; nine fetched returns carry none of the vocabulary in any field; only #4370 and #4379 mention it in prose about the step; of the 100 served route records only route 143's own step has it; none of the 40 context items has it; the setter's data files have no moment-order field. SETTER CELLS (recorded, spot-verified): (17,289) dyadic_two_way_cut_1 sups 0.092141801 / 0.52824412, S+A_top = 0.292627, H_band = 0.913012921, period 510510 = 17#; (19,361) whole band sup 0.671381317, S+A_top = 0.273548, H_band = 0.944929317, period 9699690 = 19#, least proper two-way cut 1.019686897; H_band = S + sum sup + A_top holds on all 63 rows (|diff| <= 2.0e-9); review #682 independently reproduces the (17,289) sups over the full period and warns the (19,361) sup rests on one float64 implementation with margin 0.055. MAJORANT (elementary, on recorded numbers): U_k(B) <= d^(1/(2k)) * sum_B sup with d = the steps' band-period lcm = q, and U_k(B) >= sup|B|, so H_64 <= 0.980100 < 1 at (17,289) (H_32 <= 1.054442 >= 1) while at (19,361) H_64 <= 1.034844 >= 1 and the bound needs k >= 102.03 > 64, leaving slacks 0.086987 and 0.055071. CANDIDATES: #4377 (route 225, job 9004, progress) non-bearing with zero vocabulary; #4379 (route 227, job 9005, promising) non-bearing for this step, carrying U_k only in prose about route 143's step, and by its record route 227 is now revision 4 with the step that names route 143's covering-function input M_2k(h). VERDICT: progress - the step is unanswered but half its success clause is reachable from the record at k=64, the remaining measurement is the (19,361) whole-medium band, and question/success/failure stay byte-for-byte. Honest framing: this is the second check of this setter's step in about two hours (#4370 reached the same open verdict), so the increment is the two new candidates, the custody re-check at revision 15 and the scoping above; the majorant is a bound on U_k, not the quantity, and is conditional on #2551's recorded sups. The full note is the attached route143-stepcheck-df-evidence.md and route143-stepcheck-df-report.md.","prior_art_md":"Route 143 revision 15 (setter #2551, job #5068, review #682) and its own input chain #1457, #1927, #2244,\n#2363, #2551 as summarized in the served route record and read in full from their served returns this run;\nthe previous step checks on this route (#4370 on this setter's step, and #2497, #2358 on earlier steps of\nthe route), also read from served records; #2723 (route 193), read in full because the step's k=1 gate\ntouches it; and the two candidates this check was asked to compare, #4377 (route 225) and #4379 (route\n227), read in full. The remaining linked comparison set the route record names -- #4134 (190), #3953\n(169), #2716 (203), #2684 (196), #2559 (196) -- was taken from the route record and this assignment's\ncomparison summaries rather than re-fetched, since none of them touches `U_k` and the absence screen over\nthe route listing covers their next steps. All fetched bytes are pinned by sha in\n`fetch_manifest_df.json`. No external search was needed: a step check makes no new mathematical claim, and\nthe route record's recorded prior-art search state stands. The step itself is #2551's, canonical sha256\n`ee48e908cf2eee9c59b1a903d983dc19d44481b3c552c5c4499ceb7c2787d2b5`."},"research_route_id":143,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_70889d1434001448bfbff6d9","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 #143's next experiment was set by return #2551, and a linked assessment, correction, status, finding or association changed; the previous comparison no longer covers all inputs. 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\":\"Keep the same spectrum, normalization and reused small/top terms. For each specified aggregate B compute U_k(B)=(sum over its full minimal period of |B(N)|^(2k))^(1/(2k)) for k=1,2,4,8,16,32,64, using log-sum-exp. Determine the least tested k with S+sum_B U_k(B)+A_top<1 and compare U_k/sup with this return's data. Do not repeat the denominator-partition sweep or the previously measured full-spectrum moments. Check Parseval at k=1 and monotonicity of counting norms; distinguish minimal-period sums from normalized RMS and q-period sums. Full-period Python/numpy at x<=19 only, with enforced wall/memory limits and explicit cleanup.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0.1},\"failure\":\"Either aggregate still has H_k>=1 at k=64; record the measured moment gap, not an impossibility. Do not attempt to fix the already disproved proper octave partition at x=19 by a looser bound.\",\"success\":\"A finite k<=64 gives H_k<1 for both specified aggregates. This supplies a finite moment-based certificate at the same lengths and identifies the required moment order; it establishes no asymptotic theta.\",\"question\":\"Can finite higher counting moments certify the phase-retaining medium aggregates at h_m+1 without using their exact maximum: the C/2 two-band partition at (17,289) and the whole-medium band at (19,361)?\",\"budget_hours\":1,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nEarlier step check #4370: reuse its conclusions. Compare only the new candidates listed below and references needed to assess them; do not survey the whole project again.\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #4377 (route 225, progress, recorded, recorded): COVERAGE, machine-checked by check_de.py (12/12 PASS, exit 0; --all-corrupt 12/12 controls decisive) from this run's own sha-pinned served snapshots; READ-ONLY, cpu_hours = 0, no experiment run, no published computation reproduced. CUSTODY: route 225 active, revision 3, lane dir-558, last_return_id 4365, events 2537 proposed / 2541 progress / 4365 promising, jobs 5324 first_look returned / 5329 pu\n\nReturn the ordinary report and transcript plus research: {route_id: 143, 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. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it 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