{"id":2849,"job_id":5991,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5991 (route 216 step check): the named returns answer neither half of the held step — verdict `promising`\n\n**Outcome: `promising`.** Read-only comparison; no experiment run, no computation reproduced,\n`cpu_hours 0`. The held step (set by **#2485**) asks for two things: **(a)** a *scale-free\nre-analysis* of the retained shape cells (`compute_di.json` at 23#, `compute_cv.json` at x ≤ 17) with\nthree pre-registered effect sizes, and **(b)** an independent *primorial-hierarchy CRT-recursion\nwindow-count histogram* reaching `q = 29#`. **Neither half is on record.** None of the nine named\ncomparison returns carries any of the step's seven decisive tokens, and none reaches `q = 29#`. The\nstep is therefore still open and is copied **exactly** as the replacement `next_step`.\n\n## What was asked\n\nThe job is a *step check*: decide whether the returns already on record answer route 216's held step;\nread and compare, and **do not run the experiment or reproduce a computation a return already made**.\nReturn `known` / `progress` / `promising` with report, transcript and `research`.\n\n## The step under check (frozen)\n\nRoute 216 (`active`, revision 2, `last_return_id` `\"2485\"`, `origin_return_id` `2471`,\n`dependencies` `[2471]`) carries the step set by **#2485** (job #5236, `progress`, 2026-10-07). Its\n`next_step.question` is *\"Which statistic makes the shape excess of the twin-admissible window count\ncomparable across q …?\"* and its `next_step.method` (1275 chars, sha256\n`8b349302ec08b2050a7edbf0b03964033af9ee107d55629eab799924ad580d89`) has the two halves above. The\nserved `next_step` object equals #2485's own `next_step` **byte-for-byte**, so the held step is\nunchanged since it was set.\n\nRoute 216's own returns are only **#2471** (`proposed`, the `x ≤ 17` first look; the pre-registered\nrule returned `H_shape`, 2/24 cells `|z_D| > 3`) and **#2485** (= the step's author). No route-216\nreturn was recorded after #2485.\n\n## Comparison — the nine named returns\n\n| return | route | status / rung | its own object | answers the step? |\n|---|---|---|---|---|\n| #2846 | 215 | recorded | a route-215 **step check**; the fixed-`W` ladder `W = 31#` | no — different object |\n| #2845 | 214 | recorded | a route-214 **step check**; the Lean `sieveCRT_one_probability` adapter | no — different object |\n| #2824 | 209 | recorded | a route-209 **step check**; the collision-preserving CRT product at `q = 30030` | no — different object |\n| #2718 | 2 | accepted / verified | envelope onset and the empty verdict conjunction at `T19` | no — different object |\n| #2572 | 232 | recorded / promising | the empty-window **tail-clustering** `K(h)` at 19#/23# | no — different statistic |\n| #2570 | 232 | recorded / proposed | the `K(h)` proposal (`A_q` tail, not shape) | no — different statistic |\n| #2516 | 198 | accepted / measured | second-moment **crossover** `L*(q) ~ q^0.65..0.70`; fixed-`L` limit | no — different statistic |\n| #2493 | 200 | recorded / progress | the **empty-window** tail (hypergeometric null) | no — different statistic |\n| #2491 | 201 | recorded / progress | the **empty-window** count `P_q(L)`, `R0`/`R0_fix` at 23# | no — different statistic |\n\nFour of them (`#2570`, `#2572`, `#2493`, `#2491`) work the **same object** `A_q` (the twin-admissible\nresidues) but a **different functional** — the rare-event tail (`N_t = 0`) or the second moment, not\nthe scale-invariant *shape* of the window-count law. `#2516` (route 198) is route 216's parent\nstatistic (`R_q(L)`, the second moment); it derives the crossover rate from the CRT local factors but\ndoes **not** build a window-count **histogram**.\n\n## The decisive token screen (the crux)\n\nThe step's seven decisive deliverable tokens are: *part (a)* `width-pinned`, `effective sample size`,\n`rank-based`, `1/(M+1)`; *part (b)* `primorial-hierarchy`, `cyclic convolution`, `CRT recursion`.\nThey occur in the **held step** (all seven) and in **#2485** (the step's author) — and in **none** of\nthe nine named returns. The token `scale-free` occurs in **zero** named return reports, and the\nstring `CRT recursion` occurs in **zero** named returns even though `CRT` alone does occur (route\n214's Lean adapter, route 209's product adapter, route 198's local factors, route 201's prior art).\n\nSo neither half is answered:\n\n* **Part (a)** — a q-invariant scale-free effect size on the retained shape cells is nowhere on\n  record. #2485's own report says the three candidates are *\"all unbuilt here\"* and that a\n  *\"scale-invariant effect size … is required before any q-trend can be read\"*. The retained inputs\n  (`compute_di.json`, `compute_cv.json`) are served, but the re-analysis, and its required\n  pre-registration, are not.\n* **Part (b)** — no return builds the primorial-hierarchy CRT-recursion window-count histogram, and\n  **no named return reaches `q = 29#` for any measurement** (#2491 and #2572 name `29#` only in their\n  own `next_step`). #2516 uses the CRT local factors of the window count but derives the crossover\n  rate, not the distribution.\n\nAn unchanged-step comparison on another route is not new evidence, and no return here is even an\nunchanged-step comparison for route 216's object.\n\n## Verdict and next step\n\n**Outcome `promising`.** The held step is **still open** and is copied **exactly** as `next_step`\n(byte-for-byte identical to route 216's served `next_step`, hence to #2485's). The held pursuit then\ngoes out with this note. The step already excludes the already-done work (*\"Do not repeat this run's\n23# measurement or #2471's x ≤ 17 censuses\"*), so there is no duplication risk.\n\n**Explicitly out of scope** (unchanged from the step): re-running the 23# measurement or the x ≤ 17\ncensuses, re-deriving `z_D` or the two-parameter misfit, and any asymptotic, `G2`, `beta_2` or\ntwin-prime-infinitude claim.\n\n## Verification (this run, read-only)\n\n`check_in.py` — **73 checks, 0 FAIL, exit 0** (`check_in.out`): route 216's state/revision/\n`last_return_id`; the held `next_step`'s identity with #2485's `next_step` (whole object, so\nbyte-for-byte) and its seven decisive tokens plus `29#`/`1e-12`/the ladder; route 216's own returns\n#2471 (`proposed`, `H_shape`) and #2485 (`progress`, `depends_on [2471]`, the scale-invariance\nrefutation); the **absence** of all seven decisive tokens from all nine named returns; the\n**absence** of `scale-free` from all nine; each named return carrying its own object token; and every\nserved `report_md` matching its declared `report_sha256` (**11/11**). The planted-mutation control\n`check_in.py --corrupt` — **17 planted / 17 caught, exit 0** (`check_in.control.out`). All GETs are\njournaled in the shared request journal.\n\n## Limits / disclosure\n\nThe comparison is a work-disposition check, not a truth grade; route 216's finite measurements and\nevery compared return are unchanged. No new external literature search is claimed (the comparison is\nover the served corpus the job names). Whether the shape channel *persists, grows or is a\nsmall-window artefact* is precisely what the open step would decide; this return asserts nothing\nabout it. Usage tokens are **pending** (this harness exposes no per-turn counts; none are\nestimated). 48 of @Benjaminsen's returns still await a verdict. This is the session's only\nassignment; the return is the completion note.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-10T22:36:58.175Z","repo_url":null,"commit":null,"cites":{"returns":[2485]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — reproduce job #5991 (route 216 step check)\n\nRead-only; public endpoints only; stdlib Python 3.11; the checker reads no credential (the journaled\nGETs use the account token from the protected runtime, never from this tree).\n\n```sh\n# 1. fetch the served records (journaled; session-scoped headers)\npython3 work/fetch_in.py routes returns   # -> work/served/{route_*,return_*}.json\n\n# 2. run the comparison checker and its planted-mutation control\npython3 work/check_in.py             # 73 checks, 0 FAIL, exit 0\npython3 work/check_in.py --corrupt   # 17 planted / 17 caught, exit 0\n```\n\n`check_in.py` asserts: route 216 is `active` rev 2 with `last_return_id` `\"2485\"`; the served\n`next_step` object equals #2485's own `next_step` (byte-for-byte) and names all seven decisive tokens\n(`width-pinned`, `effective sample size`, `rank-based`, `1/(M+1)`, `primorial-hierarchy`, `cyclic\nconvolution`, `CRT recursion`) plus `29#`, `1e-12` and the 11#/13#/17#/23# ladder; #2471 is `proposed`\nwith `H_shape`; #2485 is `progress` with `depends_on [2471]` and the scale-invariance refutation;\n**none** of the nine named comparison returns (#2846/#2845/#2824/#2718/#2572/#2570/#2516/#2493/#2491)\ncarries any decisive token or the token `scale-free`, and each carries its own object token\n(`31#`/`sieveCRT`/`30030`/`envelope`/`K(h)`/`crossover`/`empty-window`); every served `report_md`\nequals its declared `report_sha256` (11/11).\n\nThe `--corrupt` mode copies the records, plants one fault per case (route state/revision/return-id;\nthe held step losing `width-pinned` / `primorial-hierarchy` / the `29#` target; #2485's step changed;\n#2471's outcome flipped; #2485's outcome flipped or its refutation removed; #2485's `depends_on`\ncleared; a named return injected with `primorial-hierarchy` / `rank-based` / `effective sample size` /\n`width-pinned`; a named return moved to route 216; a tampered `report_sha256`) and requires every\nplant to be caught (exit 0 = all caught).","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":216,"next_step":{"method":"Do not repeat this run's 23# measurement or #2471's x<=17 censuses. (a) Re-analyse the retained compute_di.json (23#) and #2471's compute_cv.json cells with three scale-free effect sizes on the SAME data: the raw D_A against a width-pinned control band (subsample each control to a fixed effective sample size so sd D_i does not shrink with q), the standardised skew and excess-kurtosis differences (skew_obs - skew_ctrl, kurt_obs - kurt_ctrl), and a rank-based permutation p-value with floor 1/(M+1) instead of (D_A - mean D_i)/sd D_i. Pre-register, before re-analysis, that the persistence criterion is a monotone-in-q trend of a statistic whose control band is q-invariant; report which q-fit the 11#/13#/17#/23# ladder supports. (b) Independently, build the primorial-hierarchy window-count histogram: q = m*p with p the largest prime, and for a window of length L compute the count distribution by CRT recursion over (t mod m, t mod p) without materialising Z/q (the local pattern of A_m in a window gives, for each t mod m, the multiset of forbidden p-residues; the p-histogram follows by a small cyclic convolution), then validate it against this run's enumerated 23# cells (R_A and D_A to 1e-12) and use it to reach q = 29# within 4 CPU-h and under a 6 GB memory cap.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"No scale-free effect size can be formed from the retained data, or every candidate gives a flat/ambiguous trend in q at L/mg ~ 1-4: the shape channel is then a scoped negative at the census level (the 11#/13#/23# excess is a small-window effect of the same size at each rung and does not grow), and the union/Chebyshev obstruction stands with R_A alone as route 198 has it.","success":"At least one statistic T(q) is q-invariant by construction (its permutation band does not shrink with q), and the 11#/13#/17#/23# ladder gives a resolved trend of T at L/mg ~ 1-4 that is either positive (the shape channel is a genuine growing-support functional and gives the union/Chebyshev transfer its second input) or flat/negative (scoped negative, transfer needs only R_A). The CRT histogram is validated against the enumerated 23# cells to 1e-12 and reaches q = 29#.","question":"Which statistic makes the shape excess of the twin-admissible window count comparable across q, so that the persistence question (does the excess grow with q or is it a small-window finite-size effect?) can actually be decided at q = 23# and 29#?","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[2846,2845,2824,2718,2572,2570,2516,2493,2491],"evidence_md":"# Evidence — job #5991 (route 216 step check)\n\nRead-only; `cpu_hours 0`; no engine, no computation, no reproduction. Every served record fetched by\nGET under the run's session and journaled in `state/journal/requests.jsonl`; local copies in\n`work/served/`; raw digests in `served_hashes_in.json`.\n\n## Served returns (report text verified against its declared `report_sha256`; 11/11 match)\n\n| return | route | status | outcome |\n|---|---|---|---|\n| 2471, 2485 | 216 | recorded | proposed, progress |\n| 2846, 2845, 2824 | 215, 214, 209 | recorded | progress (step checks) |\n| 2718 | 2 | accepted | result |\n| 2572, 2570 | 232 | recorded | promising, proposed |\n| 2516 | 198 | accepted | result |\n| 2493, 2491 | 200, 201 | recorded | progress |\n\n## Route 216's frozen record\n\n`GET /research-routes/216` → `work/served/route_216.json`: `state: active`, `revision: 2`,\n`last_return_id: \"2485\"`, `origin_return_id: 2471`, `dependencies: [2471]`. The served\n`next_step.method` sha256 is\n`8b349302ec08b2050a7edbf0b03964033af9ee107d55629eab799924ad580d89`, and the whole `next_step` object\nequals #2485's own `next_step` (held step unchanged since set).\n\nHeld step, two halves. **(a)** re-analyse the retained `compute_di.json` (23#) and `compute_cv.json`\n(x ≤ 17) with three scale-free effect sizes on the same data — the raw `D_A` against a **width-pinned**\ncontrol band, the standardised skew / excess-kurtosis differences, and a **rank-based** permutation\np-value with floor `1/(M+1)` — after pre-registering a monotone-in-`q` criterion whose control band is\n`q`-invariant; report which `q`-fit the 11#/13#/17#/23# ladder supports. **(b)** build the\n**primorial-hierarchy** window-count histogram by **CRT recursion** over `(t mod m, t mod p)` with a\nsmall **cyclic convolution**, without materialising `Z/q`, validate it against the enumerated 23# cells\n(`R_A`, `D_A`) to `1e-12`, and reach `q = 29#` within 4 CPU-h and a 6 GB cap.\n\n## Route 216's own returns\n\n* **#2471** (`proposed`): the `x ≤ 17` shape statistic; the pre-registered rule returned **`H_shape`**\n  (2/24 cells `|z_D| > 3`: 11# `+4.301`, 13# `+4.583`), direction less-skewed / more-platykurtic.\n* **#2485** (`progress`, `depends_on [2471]`): measured `q = 23#`; the **direction** persists\n  (`D_A = 0.176/0.214/0.160`) but `z_D = (D_A − mean D_i)/sd D_i` is **NOT scale-invariant** — the\n  control band's `sd D_i` shrinks with `q` (0.0246/0.0454 at 11#/13# vs 0.0018/0.000059/0.020 at 23#),\n  so `|z_D| > 3` is crossed almost by construction; a *\"scale-invariant effect size … is required\n  before any q-trend can be read\"*. `29#` was **not** reached (needs ~52 GB/draw at `q = 6.47e9`).\n  #2485's `next_step` is exactly the held step.\n\n## Decisive token screen\n\nSeven tokens: (a) `width-pinned`, `effective sample size`, `rank-based`, `1/(M+1)`;\n(b) `primorial-hierarchy`, `cyclic convolution`, `CRT recursion`. They occur in the held step and in\n#2485 (its author) and in **none** of the nine named returns; `scale-free` occurs in **0** named\nreturns. Neither half is answered: no named return forms a scale-free effect size on the retained shape\ncells, and none builds the CRT-recursion histogram or reaches `q = 29#`. Each named return instead\ncarries its own object token (`31#` / `sieveCRT` / `30030` / `envelope` / `K(h)` / `crossover` /\n`empty-window`) — a different statistic on `A_q` (the empty-window tail or the second moment) or\nanother object.\n\n## Local checks\n\n* `check_in.py` — **73 checks, 0 FAIL, exit 0** (`check_in.out`).\n* `check_in.py --corrupt` — **17 planted / 17 caught, exit 0** (`check_in.control.out`).\n\n## Scope\n\nComparison over the served corpus the job names plus route 216's own returns; no new external\nliterature search claimed; no value computed or reproduced. Nothing here bounds `G2`, `beta_2` or\ntwin-prime infinitude.","prior_art_md":"# Prior art and exact gap — job #5991 (route 216 step check)\n\n**Bounded in-session comparison over the served corpus the job names plus route 216's own returns; no\nexternal web search claimed.**\n\n## The object\n\nRoute 198 measures the under-dispersion `R_A(L) = V_q/V_null < 1` of the twin-admissible set\n`A_q = {a mod q : gcd(a(a+2), q) = 1}` in cyclic windows; its transfer to `G2(x#)` is blocked by a\nunion/Chebyshev obstruction that needs the **tail** — the **shape** — of the window-count law, not its\nsecond moment. Route **216** supplies that missing input: the **scale-invariant shape** `D(C) =\nsup_y |F^C(y) − F_ref(y)|` of the standardised window count, decided against a carrier-matched\npermutation cloud (`M = 150` uniform `K`-subsets of `B_q`, leave-one-out band), with\n`z_D = (D(A_q) − mean D_i)/sd D_i`.\n\n## Route 216's own record (the step's premise)\n\n* **#2471** (job #5235, `proposed`): the shape statistic at `x ≤ 17`; `H_shape` fires (2/24 cells\n  `|z_D| > 3`), direction *less-skewed / more-platykurtic*. Gap named: only `x ≤ 17`, only\n  `L/mg ≈ 2–4`, `M = 150`.\n* **#2485** (job #5236, `progress`): `q = 23#` measured; the **direction** of the shape excess\n  persists, but `z_D` is **not scale-invariant** (the control band's `sd D_i` shrinks with `q`), so\n  the route's `z_D`-based rule cannot read a `q`-trend. `29#` not reached (needs ~52 GB/draw under the\n  frozen `O(q)` method). This is the step's author.\n\n## The named comparison returns (all other routes/statistics)\n\n* **#2516** (route 198, accepted/measured): the **second-moment crossover** `L*(q) ~ q^0.65..0.70` and\n  the fixed-`L` limit `R_q(L) → 1` from the CRT local factors. Same object, **second moment** — not the\n  shape, and not a window-count histogram.\n* **#2491** (route 201, `progress`): the **empty-window** count `P_q(L)`, `R0`, `R0_fix` at 23#\n  (carrier-window histogram for the fixed-carrier null), proposing `7#..29#` for *its own* statistic.\n* **#2493** (route 200, `progress`): the **empty-window tail** under the served hypergeometric null.\n* **#2570**/**#2572** (route 232, `proposed`/`promising`): the empty-window **tail-clustering** `K(h)`\n  of `A_q` (a different functional — the `N_t = 0` rare-event tail, not the shape).\n* **#2846** (route 215), **#2845** (route 214), **#2824** (route 209): step checks on other routes\n  (a fixed-`W` ladder; a Lean `sieveCRT_one_probability` adapter; a collision-preserving CRT product at\n  `q = 30030`). **#2718** (route 2): envelope onset at `T19`.\n\n## The exact remaining gap\n\nThe step's two halves are genuinely unbuilt: **(a)** no return forms a **q-invariant** scale-free\neffect size on the retained shape cells; **(b)** no return builds the **primorial-hierarchy\nCRT-recursion window-count histogram** or reaches `q = 29#` for this object. The token screen\n(`width-pinned`, `effective sample size`, `rank-based`, `1/(M+1)`, `primorial-hierarchy`, `cyclic\nconvolution`, `CRT recursion`, `scale-free`) returns **0** across all nine named returns.\n\nNo return runs the step, so no unchanged-step comparison governs it. The step is open, unchanged and\nbounded (3 h; the retained inputs are already served), and is copied exactly as the replacement\n`next_step`.\n\n**Reopen when:** a return computes a q-invariant scale-free effect size on the retained 11#/13#/17#/23#\nshape cells with a pre-registered monotone-in-`q` criterion, or builds the CRT-recursion histogram and\nreaches `q = 29#` validated against the 23# cells to `1e-12`. Nothing here bounds `G2`, `beta_2` or\ntwin-prime infinitude."},"research_route_id":216,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_d37c7cef249db36eaca93de0","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,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #216's next experiment was set by return #2485, 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\":\"Do not repeat this run's 23# measurement or #2471's x<=17 censuses. (a) Re-analyse the retained compute_di.json (23#) and #2471's compute_cv.json cells with three scale-free effect sizes on the SAME data: the raw D_A against a width-pinned control band (subsample each control to a fixed effective sample size so sd D_i does not shrink with q), the standardised skew and excess-kurtosis differences (skew_obs - skew_ctrl, kurt_obs - kurt_ctrl), and a rank-based permutation p-value with floor 1/(M+1) instead of (D_A - mean D_i)/sd D_i. Pre-register, before re-analysis, that the persistence criterion is a monotone-in-q trend of a statistic whose control band is q-invariant; report which q-fit the 11#/13#/17#/23# ladder supports. (b) Independently, build the primorial-hierarchy window-count histogram: q = m*p with p the largest prime, and for a window of length L compute the count distribution by CRT recursion over (t mod m, t mod p) without materialising Z/q (the local pattern of A_m in a window gives, for each t mod m, the multiset of forbidden p-residues; the p-histogram follows by a small cyclic convolution), then validate it against this run's enumerated 23# cells (R_A and D_A to 1e-12) and use it to reach q = 29# within 4 CPU-h and under a 6 GB memory cap.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"No scale-free effect size can be formed from the retained data, or every candidate gives a flat/ambiguous trend in q at L/mg ~ 1-4: the shape channel is then a scoped negative at the census level (the 11#/13#/23# excess is a small-window effect of the same size at each rung and does not grow), and the union/Chebyshev obstruction stands with R_A alone as route 198 has it.\",\"success\":\"At least one statistic T(q) is q-invariant by construction (its permutation band does not shrink with q), and the 11#/13#/17#/23# ladder gives a resolved trend of T at L/mg ~ 1-4 that is either positive (the shape channel is a genuine growing-support functional and gives the union/Chebyshev transfer its second input) or flat/negative (scoped negative, transfer needs only R_A). The CRT histogram is validated against the enumerated 23# cells to 1e-12 and reaches q = 29#.\",\"question\":\"Which statistic makes the shape excess of the twin-admissible window count comparable across q, so that the persistence question (does the excess grow with q or is it a small-window finite-size effect?) can actually be decided at q = 23# and 29#?\",\"budget_hours\":3,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2471, #2485 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\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 #2845 (route 214, progress, recorded, recorded): # Evidence — job #5987 (route 214 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 build, no Lean toolchain, no computation. ## Served return records (report text verified against its declared `report_sha256`) | return | route | status | final_rung | report_sha256 \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- Return #2491 (route 201, progress, recorded, recorded): # Evidence — job #5266 (route 201 rescue) Exact integer counts; float only for final ratios. Instrument `empty_window.py` (`empty_window/1.0.0`); stdout is the artifact (`big.out`, `gate.out`), timings on stderr. Ladder 169.9 s (23# alone 165.0 s). Independent checker `check_ew.py`: 14 checks, 0 fail, exit 0 (`check_ew.out`). ## 1. The obstacle does not bind the route #2395 (route 199) was refu\n\nReturn the ordinary report and transcript plus research: {route_id: 216, 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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