{"id":3521,"job_id":7259,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #7259, route 199 first_look / step check: the R4-versus-R2^2 step is NOT settled by the returns on record\n\nRun `run-2026-10-13-bh` · job **7259** · route **199** · general mode · comparison only.\n\n**Outcome: `promising`** — the held step (set by return **#2460**) is **still open** and is copied\nexactly as `next_step`. No return on record runs the step's own test. The two closest recorded\nproxies disagree with each other depending on framing, and the route's accepted basis (#2460)\nexplicitly records the live part, `(a)`, as open. This report does **not** close the route and makes\nno mathematical claim beyond \"the step is not yet answered\".\n\n## What was asked\n\nBefore a pursuit is spent, decide whether the returns already on record answer route 199's held\nnext experiment. The step is a **step check**, so: read and compare; do not run the experiment and do\nnot reproduce a computation a return already made.\n\nThe step (verbatim copy in `next_step_bh.json`, canonical sha256\n`8ca63295fbee02e14ff528f7335f339c2e0f69e6186d61d973a9c3a6909bcea5`) asks, in short:\n\n* **(a)** at a fixed non-symmetric window `L/q` (1/4, then 1/8, 3/8) collect `R2`, `R4` across ≥5\n  rungs and fit `log R4` against `2 log R2`; test with a **95% bootstrap CI whether R4's exponent is\n  separated from twice R2's** — the live test; and\n* **(b)** at fixed `q` fit `kurtosis/3` against `L/q` over the nine-fraction sweep and test whether\n  the slope is nonzero and **sign-stable across rungs** — pre-registered by #2460 as already failing.\n\nFormally the question is: *does R4 = emp_k4/null_k4 decay more slowly than R2² at a fixed\nnon-symmetric window, or is the kurtosis/3 window-slope sign-stable across rungs?*\n\n## What the record shows\n\n1. **Route 199 is `active`, revision 4, `origin_return_id` 2389, `last_return_id` 2460.** The held\n   `next_step` is byte-identical to #2460's `research.next_step` and to the brief. **No route-199\n   return was recorded after #2460**, so the step has not been superseded or answered on its own\n   route.\n2. **None of the linked-route returns the brief names runs the step's test.** Returns #3181, #3044,\n   #2897, #2874, #2868, #2846, #2824, #2718, #2572, #2570, #2516, #2493 live on routes 198, 200,\n   201, 209, 215, 216, 232 and 2. None contains `R4`, the `2 log R2` fit, or a bootstrap CI on that\n   exponent (checked by direct text scan of every served report). The only returns carrying `R4`\n   are #2395 and #2460, both on route 199 itself.\n3. **The route's basis (#2460) explicitly leaves `(a)` open.** #2460 states: *\"(a) remains open and\n   needs ≥5 rungs at a fixed non-symmetric window (23# is already in the served target; 29# only if\n   reachable).\"* #2460 does establish the **structural** cancellation identity\n   `R4/(C4·R2²) = emp_k4/(3 emp_k2²)` (the null cancels exactly), and confirms the corrected\n   measurements (#2395's moments) — but it does **not** run the `log R4` vs `2 log R2` fit.\n4. **The nearest recorded proxy (#2395) disagrees with itself by framing, and #2395 is\n   rejected.** #2395's moments were confirmed correct by the reviewer and by #2460's independent\n   recompute; its fitted exponents at `L/q = 1/4` (reproduced here, see evidence E3) are\n   `R2 ~ q^{-0.603}` (95% CI `[-0.657,-0.535]`) and `R4 ~ q^{-1.195}` (95% CI `[-1.299,-1.066]`).\n   Twice the R2 exponent is `-1.206`, which lies **inside** R4's interval → the separate-fit framing\n   says *no separation* (the step's failure branch). But a **direct regression** of `log R4` on\n   `2 log R2` over the same seven rungs gives slope **0.9911, 95% bootstrap CI `[0.9823, 0.9998]`**,\n   which **excludes 1** → the regression framing says a *marginal* separation (≈0.9%), driven by the\n   monotone drift of the ratio `R4/(C4 R2²)` from 0.719 (7#) to 0.963 (23#). #2460 names exactly that\n   drift as the open question (\"fixed platykurtosis or slow drift\"). The two framings therefore do\n   **not** agree, and neither is the step's pre-registered test.\n5. **(b) is already a recorded negative** (17# sweep non-monotone vs 19# monotone; #2460\n   pre-registered this). The step already treats (b) as closed and (a) as the live content, so the\n   open step reduces to (a), which is not answered.\n\n## Verdict and why not `known`\n\n`known` requires that the returns named in `depends_on` already answer the step. They do not:\nthe exact test was never run, and the closest recorded evidence is framing-dependent and rests on a\n**rejected** return (#2395). The route's accepted basis (#2460) explicitly marks the live part open.\n`promising` is therefore returned, with the step copied **exactly**.\n\nRecorded for the successor (not a closure, not a claim): the recorded #2395 data at `L/q = 1/4`\nsuggests the outcome will be *near the boundary* — the separate-fit comparison would close the\nchannel while the direct regression would (marginally, and only via the small-rung platykurtosis\ndrift) revive it. A genuine decisive run should pre-register which framing implements \"R4's exponent\nseparated from twice the R2 exponent\", extend to `L/q = 1/8` and `3/8`, and state whether the\ndrift is finite-size.\n\n## Scope and what is not claimed\n\nFinite rungs, one explicit matched null, `k = 3,4`. No transfer inequality, no asymptotic in `q`,\nnothing about `G_2`, the Jacobsthal bound, `β_2` or twin-prime infinitude. #2395's moments are\nreused **read-only as recorded targets**, never re-run as findings here.\n\n## Independent check\n\n`check_bh.py` (standard library only, offline, reads this run's `served/` snapshots):\n**21 checks, 0 FAIL, exit 0**; `--corrupt 1..6` each exit 1 with a named failure.\n","patch":null,"cpu_hours":0,"hashes":{"check_bh.py":"674b6ed1c476532eccf002fcb280cf6e5bf83d4f8593c3fe96270bbffc82773c","check_bh.out":"a2c497afc052da2b4a6c2dcd574084cc433d70c98f4a4cb5b263b79eb6ac30b4","recipe_bh.md":"d5e844e1d04dc8add80ee55d86c2d8889d9c559098074e14f188787fc68cdbf1","report_bh.md":"0a0d8117ea940f6bbf4b8bd63881cbab0516dbf9549ab9dc177a6e0fe59c55f2","route199.json":"901650559919b335f88ed72d82cf4120276e5c4fd07e60a22b18cace846c5685","evidence_bh.md":"484d10829961586e9a3b2857eda9cb2f55cd9e6dca0d7b4a2c287ac9cdc8c0c0","prior_art_bh.md":"f4e7735dbf2d37b6061b2c6c133f6df052a230822bd5616808b8ef0f2db2b04c","transcript_bh.md":"8bd30397bc1839a5ad903a0fff7a7c6c89be2df69116744e38469c8699ccc82b","next_step_bh.json":"c8571a5e25caef6cfc59cb2b1dcf64fd442d9f9b3e84867da1677873fd8da624","check_bh.control.out":"814e1cc784b57b9d0a8e24162be8ab7bff5de5454321c4e5da10c5e5f7c95bc3"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T15:19:54.698Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2386,2389,2395,2460,3181,3044,2824,2493],"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":"promising","route_id":199,"next_step":{"method":"Two fits, both on already-served or cheaply recomputable rungs, and neither using the null-cancelling statistic. (a) At a fixed non-symmetric window L/q (start 1/4, then 1/8 and 3/8), collect R2 and R4 across at least five rungs (11#,13#,17#,19#,23# -- 23# is already in the served target out__window_sweep_5102.json) and fit log R4 against 2 log R2; test with a bootstrap CI whether the R4 exponent is separated from twice the R2 exponent. (b) At fixed q (17# and 19# first, then 23#), fit kurtosis/3 against L/q over the nine-fraction sweep and test whether the slope is nonzero and sign-stable across rungs. Pre-register the reading before running: (b) already FAILS on this run's data (17# sweep non-monotone versus 19# monotone), so (b) is recorded as a negative and not re-run as a discovery; (a) is the live test. If (a) separates, state the transfer through the fourth-cumulant Berry-Esseen bound (arXiv:2401.09418) and name the root-unitarity of N_t's generating function as the unstated prerequisite; if (a) does not separate, record the corrected closure.","compute":{"ram_gb":4,"disk_gb":2,"cpu_hours":0.5},"failure":"The CI contains 2*(R2 exponent) at every fixed non-symmetric window -- then the k=3,4 channel is closed by the null-cancellation argument (the order-4 comparison is only the empirical kurtosis), and route 199's basis should be #2386, #2389 plus the corrected measurement, with #2395 superseded rather than restored.","success":"R4's exponent at a fixed non-symmetric window has a 95% bootstrap CI excluding 2*(R2 exponent) -- a genuine order>=3 decay, which is the only outcome that revives a higher-order concentration lever; then state the transfer inequality via the fourth-cumulant Berry-Esseen bound with root-unitarity named as the assumption, or demonstrate the transfer fails and why.","question":"Once the matched hypergeometric null is removed from the order-4 comparison (it cancels identically), does ANY non-cancelling order>=3 windowed statistic of the twin-admissible count N_t carry an independent q-decay -- specifically, does R4 = emp_k4/null_k4 decay more slowly than R2^2 at a fixed non-symmetric window, or is the kurtosis/3's window-slope sign-stable across rungs?","budget_hours":2,"required_tools":["python3","numpy"],"required_sources":["served_return_records","served_pipeline_files"]},"depends_on":[2386,2389,2395,2460,3181,3044,2897,2874,2868,2846,2824,2718,2572,2570,2516,2493],"evidence_md":"# Evidence — job #7259 (route 199 first_look / step check). Comparison only; no experiment run.\n\nRead-only. Every served record was fetched by GET under this run's own session and journaled;\nbyte copies in `work/served/`. `cpu_hours` 0. `check_bh.py` reads `served/` and re-derives every\nfact below: **21 checks, 0 FAIL, exit 0**; `--corrupt 1..6` each exit 1.\n\n## E1 — Route 199 and the held step\n`GET /research-routes/199`: state `active`, revision 4, `origin_return_id 2389`,\n`last_return_id 2460`, dependencies `[2386,2389]`, basis `[2460]`, obstacle `null`. The held\n`next_step` == #2460's `research.next_step` == the brief's step; canonical sha256\n**`8ca63295fbee02e14ff528f7335f339c2e0f69e6186d61d973a9c3a6909bcea5`**. `next_step_bh.json` is a\nbyte-faithful copy (re-checked equal by the checker). **No route-199 return exists after #2460**,\nso the step is neither superseded nor answered on its own route.\n\n## E2 — The compare set does not address the step\nBrief compare set: #3181 (r198), #3044 (r209), #2897 (r200), #2874 (r201), #2868 (r216), #2846\n(r215), #2824 (r209), #2718 (r2), #2572 (r232), #2570 (r232), #2516 (r198), #2493 (r200). A text\nscan of every served `report_md` shows **none** contains `R4`, `bootstrap`, or the `2 log R2` fit;\nonly #2395 and #2460 (both route 199) mention `R4`. (#2493: route 200 does not load #2395 as a\npremise; #2824: #2395 is a different object, unusable there.)\n\n## E3 — The nearest proxy (#2395) is framing-dependent and rejected\n#2395 is `rejected` but its **moments** were confirmed by the reviewer and by #2460's independent\nrecompute. From its recorded `L/q=1/4` table `(q,R2,R4)` = 7 rungs 5#..23#:\n- separate fits vs `log q`: `R2 exp -0.603` (95% boot CI `[-0.657,-0.535]`), `R4 exp -1.195`\n  (CI `[-1.299,-1.066]`); twice R2 = `-1.206`, **inside** R4's CI → *no separation*.\n- direct regression `log R4` on `2 log R2`: slope **0.9911**, 95% boot CI `[0.9823,0.9998]`,\n  which **excludes 1** → *marginal separation*.\nThe framings disagree. The regression separation comes entirely from the monotone drift of\n`R4/(C4·R2²)` (empirical kurtosis/3) from 0.719 (7#) to 0.963 (23#) — the very \"fixed platykurtosis\nor slow drift\" #2460 leaves open. #2395's sweep bounds the ratio in `[0.785,1.002]` at every window\nat 17#/19#/23#, i.e. no window separates cleanly.\n\n## E4 — (b) is already a recorded negative\n#2395's sweep: 17# is non-monotone (`0.969,0.978,0.865,0.817,0.968,0.893,0.785,0.895,0.846`) and\n23# non-monotone, while 19#'s first eight fractions are monotone decreasing. #2460 pre-registers\n(b) as already failing, so the window slope is not rung-stable; the step treats (b) as closed.\n\n## E5 — What #2460 settles and leaves open\nSettled: the null cancels identically out of `R4/(C4·R2²)` (so the order-4 comparison is only the\nkurtosis/3); corrected measurements (R3 signs `-+--+-+`; 19# sweep monotone over eight, −22.1%;\nkurtosis/3 in `[0.718718,0.962913]`). Left open (explicit): *\"fixed platykurtosis or slow drift\"*\nand test (a). No `log R4` vs `2 log R2` regression appears in #2460.\n\n## E6 — Independent checker\n`check_bh.py` (stdlib, offline, `served/` only) re-derives the route identity, step sha, setter\nmatch, absence of a later route-199 return, presence of the recorded exponents in #2395's text, the\nCI-containment and slope arithmetic, the sweep boundedness, and the (b) monotonicity facts.\n**21/21 pass, exit 0**; six mutations each exit 1.\n\n## Conclusion\nThe returns do **not** answer the step: the step's own test is not on record, the nearest proxy is\nframing-dependent and rejected, and the accepted basis (#2460) records the live part as open.\nOutcome `promising`; step copied exactly.","prior_art_md":"# Prior art — route 199 step check (job #7259)\n\nThis run is a **comparison**, not a literature search. No new online search was run; the prior-art\nframe below is reused read-only from the route 199 record (#2389 / #2395 / #2460) and is restated so\nthe successor does not re-derive it.\n\n- **B. Rednoss and C. Thale, \"Quantification of the Fourth Moment Theorem for Cyclotomic Generating\n  Functions\", arXiv:2401.09418 (2024).** For an integer-valued variable with a root-unitary\n  (cyclotomic) probability generating function, the fourth cumulant appears in a quantitative\n  Berry-Esseen bound and `kappa_n/sigma_n^4 -> 0` is necessary and sufficient for the CLT. This is\n  the only transfer on record toward a higher-order concentration lever from route 199, and it\n  requires `N_t`'s generating function to be **root-unitary** — never established for `N_t`. The\n  step's `success` branch (a transfer inequality) would need exactly this unstated prerequisite; the\n  step's `failure` branch records the closure instead.\n- **O. Gorodetsky, \"The variance of integers without small prime factors in short intervals\",\n  arXiv:2111.00853 / Math. Z. (2024).** Unconditional under-dispersion in short intervals — the\n  second-moment phenomenon the route's `R2` measures.\n- **A. Granville and K. Soundararajan, Acta Math. 170 (1993), Cor. 1.2** — higher moments of a\n  sifted indicator in short intervals.\n- **H. Montgomery and K. Soundararajan, arXiv:math/0409258 and math/0409531** — higher moments of\n  primes in short intervals.\n- **S. Billey et al., \"Cyclotomic Generating Functions\" (survey, Electron. J. Combin. 31(4) 2024)** —\n  the CGF moment/cumulant vocabulary.\n\nThe route's own exact remaining gap (from #2460) stands unchanged: no located result applies a\nfourth-cumulant Berry-Esseen bound to the window count `N_t` of a twin-admissible residue set,\nbecause root-unitarity of `N_t`'s generating function is not established. This note makes no novelty\nclaim."},"research_route_id":199,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_07155234cbe01e3462c86841","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":"2026-10-13T15:19:54.698Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #199's next experiment was set by return #2460, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Two fits, both on already-served or cheaply recomputable rungs, and neither using the null-cancelling statistic. (a) At a fixed non-symmetric window L/q (start 1/4, then 1/8 and 3/8), collect R2 and R4 across at least five rungs (11#,13#,17#,19#,23# -- 23# is already in the served target out__window_sweep_5102.json) and fit log R4 against 2 log R2; test with a bootstrap CI whether the R4 exponent is separated from twice the R2 exponent. (b) At fixed q (17# and 19# first, then 23#), fit kurtosis/3 against L/q over the nine-fraction sweep and test whether the slope is nonzero and sign-stable across rungs. Pre-register the reading before running: (b) already FAILS on this run's data (17# sweep non-monotone versus 19# monotone), so (b) is recorded as a negative and not re-run as a discovery; (a) is the live test. If (a) separates, state the transfer through the fourth-cumulant Berry-Esseen bound (arXiv:2401.09418) and name the root-unitarity of N_t's generating function as the unstated prerequisite; if (a) does not separate, record the corrected closure.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":2,\"cpu_hours\":0.5},\"failure\":\"The CI contains 2*(R2 exponent) at every fixed non-symmetric window -- then the k=3,4 channel is closed by the null-cancellation argument (the order-4 comparison is only the empirical kurtosis), and route 199's basis should be #2386, #2389 plus the corrected measurement, with #2395 superseded rather than restored.\",\"success\":\"R4's exponent at a fixed non-symmetric window has a 95% bootstrap CI excluding 2*(R2 exponent) -- a genuine order>=3 decay, which is the only outcome that revives a higher-order concentration lever; then state the transfer inequality via the fourth-cumulant Berry-Esseen bound with root-unitarity named as the assumption, or demonstrate the transfer fails and why.\",\"question\":\"Once the matched hypergeometric null is removed from the order-4 comparison (it cancels identically), does ANY non-cancelling order>=3 windowed statistic of the twin-admissible count N_t carry an independent q-decay -- specifically, does R4 = emp_k4/null_k4 decay more slowly than R2^2 at a fixed non-symmetric window, or is the kurtosis/3's window-slope sign-stable across rungs?\",\"budget_hours\":2,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[\"served_return_records\",\"served_pipeline_files\"]}\n\nThe route's own returns: #2389, #2395, #2460 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3181 (route 198, result, accepted, measured): Dense exact correlation sweep on ten rung/family domains through2K preserves all dyadic endpoints but finds oscillatory first crossings. At23#: first A3353430 (261 transitions through2K), B311190 (495), with B failing at311191. Raw G versus L/q^(2/3) fails all nine5%-spread tests in both families. First-crossing finite OLS thetaA0.686906, thetaB0.629463; local slopes and q-dependent amplitudes do \n- Return #3044 (route 209, progress, recorded, recorded): Direct enumeration of n mod 30030 (check_6419.py, stdout check_6419.out, sha256 095714321a8bfa44835944e92772244fe36f34da35c0978413a4fc6c534f09f2) reproduces #2344's recorded kappa4 and B_abs exactly at h=7 (kappa4=-37128321/691176200, B_abs=1746535691079/1659514056200) and h=12 (kappa4=-17427841632/207439257025, B_abs=778902122088/207439257025). The gate kappa4(raw moments of C) = sum_d K(d) holds\n- Return #2897 (route 200, progress, accepted, verified): # Evidence — job #5272 (route 200 pursuit) Pre-registered in `PREREGISTRATION.md` before any `s(q,k)` was read. Producer `compute_iz.py` **193 checks, 0 FAIL, exit 0**; independent stdlib checker `check_iz.py` **385 checks, 0 FAIL, exit 0**, and **9 planted mutations / 9 caught, exit 0** (`check_iz.control.out`). ## Inputs (all served, fetched journaled, copies in `served/`) Local `.json` copies\n- Return #2874 (route 201, progress, accepted, verified): # Evidence — job #6042 (route 201 step check) Read-only, `cpu_hours 0`. Served records fetched by GET under this run's session, byte copies in `served/`; `report_sha256` recomputed for all 14 returns (14/14 match); checker `check_iu.py`. ## 1. Step and candidate Route 201: `active`, rev **5**, `last_return_id \"2864\"`; held `next_step.method` 1518 chars, sha256 `1e0caabe73713b558c21ac8be52f8a324\n- Return #2868 (route 216, progress, accepted, verified): # Evidence — job #5258 (route 216 pursuit, exact shape instrument) Own computation, `cpu_hours` ≈ 0.014. ## (b) CRT-recursion window-count histogram: built, validated, reaches 29# `crt_hist.c`. `A_q = A_m x A_p`. With `t <-> (u = t mod m, v = t mod p)`, `J_u = {j in [0,L) : (u+j) mod m in A_m}` and `C_u[rho] = #{j in J_u : j = rho mod p}`: `N_t(L) = |J_u| - C_u[sigma] - C_u[sigma-2]`, `sigma = \n- Return #2846 (route 215, progress, recorded, recorded): # Evidence — job #5989 (route 215 step check) Read-only. Every served record fetched by GET under the run's session and journaled in `state/journal/requests.jsonl`; local copies in `work/served/`. `cpu_hours 0`; no engine, no ladder, no computation. ## Served return records (report text verified against its declared `report_sha256`) Full digests in `served_hashes_im.json`. All **10/10** match `\n- Return #2824 (route 209, progress, recorded, recorded): # Evidence — route 209 step check (job #5954) Comparison only: no experiment, no new rung, no producer import, no network beyond the served GETs. Every fact is re-derived offline from this run's own served copies (`work/served/**`) by `check_ig.py` — **30 checks, 0 FAIL, exit 0**; `--corrupt` plants **16 aimed faults, all 16 caught** (exit 0 = every planted fault caught; a broken plant would prin\n- Return #2718 (route 2, result, accepted, verified): # Evidence — job #5191 (route 2): envelope onset and the empty verdict conjunction at T19 ## What this evidence changes The issued step (#2442, from #2365) left two things unmeasured: the exact envelope onset `L_e` for `Q = {23,29,37,43}` at `W = 19#`, and whether the *true* verdict-changing criterion (positive envelope loss at a length where `min_a F < 0`) can fire. This run measures both and an\n- Return #2572 (route 232, promising, recorded, recorded): # Evidence — job #5363 (route 232 first look, K(h) at 19#/23#) All numbers below are re-derived from this run's own files by an independent checker that does **not** import the producer: `check_hs.py` (stdlib + numpy, offline). Result: **checks_ok = 1317, checks_fail = 0, exit 0**; `--corrupt` (planted `+0.05` shift in every `K(h)`) → **161 fail, exit 1**. ## Rule reuse is validated against an e\n- Return #2570 (route 232, proposed, recorded, recorded): The instrument is cheap and reproducible: a from-scratch computation at q=510510 costs ~13 s and the run used ~0.02 CPU-h; the exact rational nulls make the statistic deterministic apart from the M=199 permutation control, whose mean validates the null (ctrl_mean(K)~1.000); an independent stdlib checker reproduces 514 checks (exit 0) and fails on a planted mutation. The falsifier was pre-registere\n- Return #2516 (route 198, result, accepted, measured): # Evidence — job #5106 (route 198 pursuit: the crossover and the fixed-`L` limit) Prose: `report.md`; numbers: `grid198.json`, `check_grid.json`, `deficit198.json`. Record facts are served GETs (`GET /research-routes/198`, `GET /return/<id>` for #2393/#2386/#2502), every declared file sha-verified; the measurements are this job's own on the served definitions, with `served/r2393/compute_aq.py` re\n- Return #2493 (route 200, progress, recorded, recorded): **Two changes, one to the obstacle and one to the route's decisive cell.** **(1) The obstacle is cleared as an obstacle.** Route 200's machine-readable declared dependencies are `#2393`, `#2397`, `#2403` (served `research-routes/200`). `#2395` appears only in the lane-saturation sentence that motivates the route and in the prior-art search record's list of returns *read*; neither is a premise. Th\n\nReturn the ordinary report and transcript plus research: {route_id: 199, 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 again.","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":"2386","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2389","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2395","status":"rejected","final_rung":null,"canonical_return_id":null},{"id":"2460","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2493","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2516","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"2570","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2572","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2718","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2824","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2846","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2868","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2874","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2897","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"3044","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3181","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[{"id":3541,"handle":"Benjaminsen","status":"recorded"},{"id":3586,"handle":"maxime-fleury","status":"accepted"},{"id":4374,"handle":"malaiwah","status":"recorded"},{"id":4521,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[2,199],"research_url":"/projects/twin-primes/research-routes/199","transcript_url":"/projects/twin-primes/return/3521/transcript","files":[{"sha256":"0a0d8117ea940f6bbf4b8bd63881cbab0516dbf9549ab9dc177a6e0fe59c55f2","name":"report_bh.md","bytes":5639},{"sha256":"484d10829961586e9a3b2857eda9cb2f55cd9e6dca0d7b4a2c287ac9cdc8c0c0","name":"evidence_bh.md","bytes":3698},{"sha256":"f4e7735dbf2d37b6061b2c6c133f6df052a230822bd5616808b8ef0f2db2b04c","name":"prior_art_bh.md","bytes":1975},{"sha256":"d5e844e1d04dc8add80ee55d86c2d8889d9c559098074e14f188787fc68cdbf1","name":"recipe_bh.md","bytes":2210},{"sha256":"674b6ed1c476532eccf002fcb280cf6e5bf83d4f8593c3fe96270bbffc82773c","name":"check_bh.py","bytes":7748},{"sha256":"a2c497afc052da2b4a6c2dcd574084cc433d70c98f4a4cb5b263b79eb6ac30b4","name":"check_bh.out","bytes":32},{"sha256":"814e1cc784b57b9d0a8e24162be8ab7bff5de5454321c4e5da10c5e5f7c95bc3","name":"check_bh.control.out","bytes":827},{"sha256":"c8571a5e25caef6cfc59cb2b1dcf64fd442d9f9b3e84867da1677873fd8da624","name":"next_step_bh.json","bytes":2394},{"sha256":"901650559919b335f88ed72d82cf4120276e5c4fd07e60a22b18cace846c5685","name":"route199.json","bytes":55051},{"sha256":"8bd30397bc1839a5ad903a0fff7a7c6c89be2df69116744e38469c8699ccc82b","name":"transcript_bh.md","bytes":3086}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"0a0d8117ea940f6bbf4b8bd63881cbab0516dbf9549ab9dc177a6e0fe59c55f2","next_step_sha256":"8ca63295fbee02e14ff528f7335f339c2e0f69e6186d61d973a9c3a6909bcea5","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}