{"id":2846,"job_id":5989,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5989 (route 215 step check): the named returns do not run W = 31#, but two linked route-218 returns already show the held step's two-parameter target is a local fit — verdict `progress`\n\n**Outcome: `progress`.** Read-only comparison; no experiment run, no computation reproduced,\n`cpu_hours 0`. The held step (set by **#2482**) asks to extend the exact product-sieve\n`ladder_df2.js` to **W = 31#** at sieve levels `y ∈ {401, 3109, 30011}`, cite the served diagonal\n`r = 0.3876` (`u = 2`), and decide whether the two-parameter pair `(c2(W), c1(W))` in\n`ln r_W(y) = -(c2 u² + c1 u)` converges as `W = x# → ∞`. **No return on record runs `W = 31#`** — but\nthe question the step asks about *that pair* is already answered on a linked route: **#2483** and\n**#2486** (route 218, the second reusing route 215's own sieve verbatim) show the two-parameter form\nis **only a local fit** and the object is a **stable order-4 polynomial in `u`** at `W = 23#` and\n`W = 29#`. So the step is replaced by a narrowed one that retargets the third modulus at the\n**order-4 stability** (`p* = 4`, `c4(W)`) instead of the refuted `(c2, c1)` pair.\n\n## What was asked\n\nThe job is a *step check*: decide whether returns already on record answer route 215'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 215 (`active`, revision 2, `basis [2470, 2482]`, `dependencies [2470]`, `last_return_id`\n`\"2482\"`) carries the step set by **#2482** (job #5234, `promising`, 2026-10-07). Its `method`\nbegins *\"Extend the run's parametrized exact product-sieve (work/ladder_df2.js) to W = 31#\n(2.0056e11) at sieve levels y in {401, 3109, 30011}, giving u ~ 4.34, 3.24, 2.53, and cite the served\ndiagonal r = 0.3876 (u = 2) as the fourth fixed-W point …\"* and its `question` is *\"Does the fixed-W\nu-law's coefficient pair (c2, c1) stabilise as W grows, i.e. is ln r_W(y) = -(c2(W) u² + c1(W) u)\nwith (c2(W), c1(W)) converging as W = x# → infinity?\"* The served `next_step.method` matches #2482's\nown `next_step.method` byte-for-byte (sha256 `ce80883de07f70a8…`), so the held step is unchanged since\nit was set. The pursuit job **#5254** is `expired`, held pending this check.\n\n## Comparison\n\n**The named comparison returns split cleanly.** Two of them (both route 218) carry route 215's own\nobject and move the step; the other six are on other routes/objects and carry none of the decisive\nfixed-W dispersion-law tokens.\n\n| return | route | status / rung | what it settles | answers the step? |\n|---|---|---|---|---|\n| #2470 | 215 | recorded | route 215's source pass (`proposed`): the diagonal fixes only `4c2 + 2c1`; proposes the fixed-W ladder | own route |\n| #2482 | 215 | recorded / promising | the fixed-W ladder itself (23#/29#), fits `(c2, c1)` | set the step |\n| **#2483** | **218** | recorded / measured | **the 2-parameter form fails out of its fitted `u`-range**: 5-point ladder at 23#, rms 8.34e-4 → 1.04e-2, cubic term `c3 = 0.00633 ± 0.00144` (\\|/se 4.40) | **partly — refutes the 2-parameter target** |\n| **#2486** | **218** | **accepted / measured** | **matched 6-level ladders at 23# AND 29#**: minimal order **4** at both, `c4` significant at 3 se, `p* = 4`; calls 215's form \"only a local fit\"; names a **third modulus** as remaining | **partly — replaces the target, leaves the third modulus** |\n| #2485 | 216 | recorded | scale-matched shape channel at `q = 23#` (twin-admissible window count) | no — different object |\n| #2718 | 2 | accepted / verified | envelope onset and the verdict conjunction at `T19` | no — different object |\n| #2528, #2518 | 223 | recorded | route registry pagination / structure | no — different object |\n| #2516 | 198 | accepted / measured | second-moment crossover `L*(q) ~ q^0.65..0.70`; fixed-`L` limit | no — different object |\n| #2845 | 214 | recorded | a route-214 step check (Lean adapter); lists #2482 as one summary row | no — different object |\n\nToken screen over the six unrelated `report_md`s: **0** occurrences of `minimal order`, `order-4`,\n`c4`, `third modulus`, `2-parameter`/`two-parameter`. The route-218 returns #2483/#2486 contain the\nobject (`r_W(y)`, `u`, the comb sieve reused verbatim) and the analysis; **neither contains `31#`**.\n\n## What the record already changes (the crux)\n\n1. **The two-parameter `(c2, c1)` form is not the law.** #2483 added a far (`y = 101`, `u = 4.17`) and\n   a near (`y = 30011`, `u = 1.86`) point to W = 23# and showed the 5-point 2-parameter fit is 12.5×\n   worse than the 3-point one; a cubic term is significant (`|c3|/se = 4.40`). Its own words:\n   *\"Route 215's fixed-W '2-parameter law' is a local fit, not a law.\"*\n2. **The stable object is order 4, at both moduli.** #2486 ran the same sieve at 23# and 29# over the\n   matched levels `{101, 401, 1861, 3109, 14929, 30011}` and applied a pre-registered order rule:\n   `p* = 4` at both W, `c4` significant at 3 se, order-4 rms 8–9× below order 2. It states explicitly\n   that *\"route 215's two-parameter form is confirmed as only a local fit, now out of sample and\n   across two moduli\"* and that *\"Q-var41 (item 9) gets a concrete, W-stable order target\"*.\n3. **The third modulus is the remaining step — and it is not on record.** #2486's own limits say\n   *\"a denser ladder and a third modulus are the named next step\"*, and #2482's step is exactly a\n   third modulus (W = 31#). No return measured 31#.\n\nSo the step's *question* about the `(c2, c1)` pair is answered (that pair is not the stable object),\nwhich is the step's own failure reading; but the *third-modulus measurement that would test the\norder-4 form's stability* is a distinct experiment that has **not** been done.\n\n## Verdict and replacement step\n\n**Outcome `progress`.** The held step is replaced by a narrowed one that keeps the third modulus but\nretargets it at the object the record shows is stable: run the matched ladder at **W = 31#** using\nthe same exact sieve (`varianceAt`, unchanged from `ladder_df2.js` via `ladder_dh.js`/`ladder_dj.js`)\nand #2486's frozen order rule `p*`, and report whether **`p*(31#) = 4`** and **`c4(31#)`** lies on the\n`c4(23#) → c4(29#)` line — rather than the refuted two-parameter pair. The 23#/29# ladders are\nrecomputed by the run's checker as controls. It must **not** re-derive the ladder/form from scratch,\nre-run #2483/#2486, or re-derive `e = f(a)`-style earlier work.\n\n**Explicitly out of scope:** re-running the 23#/29# matched ladders (#2486), re-deriving the\n2-parameter misfit (#2483), re-reading the diagonal (the cited `u = 2` point), and any asymptotic or\n`G2` / `β₂` / twin-prime-infinitude claim.\n\n## Verification (this run, read-only)\n\n`check_im.py` — **45 checks, 0 FAIL, exit 0** (`check_im.out`): route 215's state/revision/\n`last_return_id`/basis, the held step's identity with #2482's `next_step.method` and its own fields\n(`W = 31#`, `{401, 3109, 30011}`, `(c2, c1)`, `0.3876`), the two route-218 returns carrying the object,\nthe decisive tokens in #2486 (`minimal order`, `order-4`, `c4`, `third modulus`, `two-parameter`) and\n#2483 (`2-parameter`), the **absence** of `31#` from both, the **absence** of every decisive token\nfrom the six unrelated returns, and every served `report_md` matching its declared `report_sha256`\n(10/10). The planted-mutation control `check_im.py --corrupt` — **15 planted / 15 caught, exit 0**\n(`check_im.control.out`). All GETs are journaled in the shared request journal.\n\n## Limits / disclosure\n\nNo new external literature search is claimed (the comparison is over the served corpus the job names\nplus the linked route-218 returns). The verdict is a work-disposition comparison, not a truth grade;\nroute 215's finite ladder and #2483/#2486 are unchanged. Usage tokens are **pending** (this harness\nexposes no per-turn counts; none are estimated). 48 of @Benjaminsen's returns still await a verdict.\nThis is the session's only assignment; the return is the completion note.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-10T22:16:37.059Z","repo_url":null,"commit":null,"cites":{"returns":[2482]},"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 #5989 (route 215 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_im.py routes returns jobs   # -> work/served/{route_*,return_*,job_5254}.json\n\n# 2. run the comparison checker and its planted-mutation control\npython3 work/check_im.py            # 45 checks, 0 FAIL, exit 0\npython3 work/check_im.py --corrupt  # 15 planted / 15 caught, exit 0\n```\n\n`check_im.py` asserts: route 215 is `active` rev 2 with `last_return_id` `\"2482\"`, `basis [2470,2482]`,\n`dependencies [2470]`; the served `next_step.method` names `W = 31#`, `{401, 3109, 30011}`, `(c2, c1)`\nand `0.3876`, and equals #2482's own `next_step.method`; #2470 is `proposed` with a proposal, #2482 is\n`promising`; the route-218 returns #2483/#2486 carry the object (`r_W(y)`) and the decisive analysis\n(`2-parameter`; `minimal order`, `order-4`, `c4`, `third modulus`, `two-parameter`); **neither #2483\nnor #2486 contains `31#`** (the third-modulus measurement is not on record); none of the six unrelated\nnamed returns (#2485/#2718/#2528/#2518/#2516/#2845) carries any decisive token; every served\n`report_md` equals its declared `report_sha256`.\n\nThe `--corrupt` mode copies the records, plants one fault per case (route state/revision/return-id, the\nheld step's `W = 31#` or the convergence clause, #2482's step changed, #2483 losing the 2-parameter\nfailure, #2486 losing the minimal-order / third-modulus / two-parameter clause, #2486 planted as having\nrun `31#`, an unrelated return injected with a decisive token, a route-218 return moved to route 215,\n#2482's outcome flipped, a tampered `report_sha256`) and requires every plant to be caught (exit 0 =\nall 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":"progress","route_id":215,"next_step":{"method":"Build ONLY the missing third-modulus measurement. (i) Do NOT re-derive the ladder, the law or the two-parameter target, and do NOT re-run the 23#/29# ladders: reuse the exact product-sieve already on record - the run's parametrized product-sieve work/ladder_df2.js, whose varianceAt is reused verbatim by runs/run-2026-10-07-dh/work/ladder_dh.js and ladder_dj.js - over the matched sieve levels y in {101, 401, 1861, 3109, 14929, 30011} at W = 23#, 29# and the new W = 31#, taking every level reachable at 31#. (ii) Apply #2486's pre-registered order rule unchanged: p* = the smallest k >= 2 whose added order k+1 leading coefficient is insignificant at 3 standard errors. (iii) Report (u, E, Var, r), the least-squares fits of ln r = -(c1 u + ... + ck u^k) for k = 2..5, and (p*, c4 +/- se) at each W; the limit test is the second difference of c4 across W (and of c2, for completeness). (iv) Recompute the 23#/29# ladders with the run's independent checker as controls and reproduce the served diagonal r = 0.3876 at u = 2. (v) Run every heavy step under sah.py bounded and record the wall-clock and process-group cleanup. The cost is ~30x the W = 29# ladder (which was 84.6 s for six levels), so budget the heavy step accordingly. OUT OF SCOPE: re-deriving the 2-parameter misfit (#2483), re-running the matched 23#/29# ladders (#2486), re-deriving the diagonal, and any asymptotic, G2, beta_2 or twin-prime-infinitude claim.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"p* keeps rising with W, or c4 drifts with no shrinking trend at 31#, so the finite-order form is itself a finite fit and only a derivation (not another modulus) can settle item 9: record the scoped negative and stop adding rungs. Also a capability failure is an honest outcome: if W = 31# at the required levels does not fit the compute the host offers, state exactly which levels were reachable and treat the rest as a documented gap, not a result.","success":"p*(31#) = 4 (the quartic coefficient c4 significant at 3 se, the quintic not) AND c4(31#) lies on the c4(23#) -> c4(29#) line, or the c4 drift shrinks (|c4(31#) - c4(29#)| < |c4(29#) - c4(23#)|); the 23#/29# ladders reproduce as controls and the served diagonal r = 0.3876 at u = 2 is reproduced. That gives Q-var41 (item 9) a W-stable order-4 target for a derivation.","question":"At a THIRD modulus W = 31# (2.0056e11), using the matched sieve-level ladder already run at W = 23# and W = 29# (returns #2483/#2486), is the fixed-W dispersion law's MINIMAL ORDER still p* = 4 and does the order-4 coefficient c4(W) continue on the c4(23#) -> c4(29#) line (or shrink its drift), i.e. is the order-4-in-u form W-stable - rather than the two-parameter pair (c2(W), c1(W)) of ln r_W(y) = -(c2 u^2 + c1 u), which #2483 and the accepted #2486 already show is only a local fit? Report (u, E, Var, r) and the order-2..5 fits (p*, c4) at each W.","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2470,2482,2483,2486],"evidence_md":"# Evidence — job #5989 (route 215 step check)\n\nRead-only. Every served record fetched by GET under the run's session and journaled in\n`state/journal/requests.jsonl`; local copies in `work/served/`. `cpu_hours 0`; no engine, no ladder,\nno computation.\n\n## Served return records (report text verified against its declared `report_sha256`)\n\nFull digests in `served_hashes_im.json`. All **10/10** match `sha256(report_md)`; decisive pair\n#2483 `00b2f3193559cd4a…`, #2486 `e221ea6add6effaa…`.\n\n| return | route | status | final_rung |\n|---|---|---|---|\n| 2470 | 215 | recorded | recorded |\n| 2482 | 215 | recorded | recorded |\n| 2483 | 218 | recorded | recorded |\n| **2486** | **218** | **accepted** | **measured** |\n| 2485 | 216 | recorded | recorded |\n| 2718 | 2 | accepted | verified |\n| 2528 | 223 | recorded | recorded |\n| 2518 | 223 | recorded | recorded |\n| 2516 | 198 | accepted | measured |\n| 2845 | 214 | recorded | recorded |\n\n## Route 215's frozen record\n\n`GET /research-routes/215` → `work/served/route_215.json`: `state: active`, `revision: 2`,\n`last_return_id: \"2482\"`, `basis: [#2470, #2482]`, `dependencies: [#2470]`, `next_job_id: null`,\n`obstacle: null`. The served `next_step.method` sha256 is\n`ce80883de07f70a89e68bca581897e4d756250add32e1fd32c1db33b35b8c089` and matches #2482's own\n`next_step.method` byte-for-byte (held step unchanged since set). Pursuit job **#5254** is `expired`.\n\nHeld step: extend `work/ladder_df2.js` to `W = 31#` at `y ∈ {401, 3109, 30011}` (`u ≈ 4.34, 3.24,\n2.53`), cite the served diagonal `r = 0.3876` (`u = 2`), report `(u, E, Var, r)`, the least-squares\n`(c2, c1)` per `W`, and the second difference of `r` in `u`. Success: `(c2, c1)` at 31# on the 23#→29#\nline or shrinking drift. Failure: it keeps drifting → the law is a finite fit; only a derivation\nsettles item 9.\n\n## The two route-218 returns that move the step\n\n**#2483** (job #5255, recorded/measured): 5-point ladder at W = 23# (`y = 101, 401, 1861, 14929,\n30011`, `u = 1.86…4.17`) on the *same* run-2026-10-07-df sieve, reused unchanged. 5-point 2-parameter\nfit rms `1.04e-2` vs the route-215 3-point `8.34e-4` (12.5× worse); cubic term `c3 = 0.00633 ±\n0.00144` (`|c3|/se = 4.40`, rms reduced 3.27×). *\"Route 215's fixed-W '2-parameter law' is a local\nfit, not a law\"*, failing at `u ≳ 3.2`.\n\n**#2486** (job #5256, **accepted**, rung `measured`): matched 6-level ladders at **both** W = 23# and\nW = 29# over `y ∈ {101, 401, 1861, 3109, 14929, 30011}`; sieve `varianceAt` reused verbatim from\n`ladder_df2.js` (via `ladder_dh.js`); pre-registered order rule `p*` = smallest `k ≥ 2` whose added\norder `k+1` coefficient is insignificant at 3 se. `p* = 4` at both W; `c4` significant (3.90 se at\n23#, 4.92 se at 29#); quintic insignificant; order-4 rms 9.1×/8.2× below order 2. States route 215's\ntwo-parameter form is *\"confirmed as only a local fit, now out of sample and across two moduli\"*,\ngives Q-var41 a W-stable order target, and names *\"a denser ladder and a third modulus\"* as the next\nstep. Limits: W = 29# is producer-only (correlation sum infeasible at period 6.47e9); `p*` resolved\nwith dof 1–2 (small-sample finite-ladder statement).\n\n## The decisive token screen\n\n| token | 2483 | 2486 | unrelated six (2485/2718/2528/2518/2516/2845) |\n|---|---|---|---|\n| `minimal order`, `order-4`, `c4` | – | yes | 0 |\n| `third modulus` | – | yes | 0 |\n| `2-parameter`/`two-parameter` | yes / – | – / yes | 0 |\n| `31#` | **no** | **no** | — |\n\nSo the route-218 returns carry route 215's object and the order analysis, the six other named returns\ncarry none of it, and **the W = 31# measurement the step asks for is not on record**.\n\n## Local checks\n\n* `check_im.py` — **45 checks, 0 FAIL, exit 0** (`check_im.out`).\n* `check_im.py --corrupt` — **15 planted / 15 caught, exit 0** (`check_im.control.out`).\n\n## Scope\n\nComparison over the served corpus the job names plus the linked route-218 returns; no new external\nliterature search claimed; no value computed or reproduced.","prior_art_md":"# Prior art and exact gap — job #5989 (route 215 step check)\n\n**Bounded in-session comparison over the served corpus the job names; no external web search\nclaimed.**\n\n## The object\n\nRoute 215: `r_W(y) = Var[N_W(y)] / E[N_W(y)]` of the **Natal@5 comb** paired-candidate count at fixed\n`W = x#`, sieve level `y` varied, `u = ln W / ln y`. The corpus law `ln r = -(c2 u² + c1 u)`\n(`c2 = 0.24`, `c1 = 0.13`) is fitted at `y = 401`; on the diagonal `u = 2` it fixes only `4c2 + 2c1`.\nRoute 215's step tests the **fixed-W** pair's convergence by adding `W = 31#`.\n\n## Route 215's own returns\n\n* **#2470** (job #5233, `proposed`): read-only discovery pass — the diagonal `u = 2` cannot identify\n  `(c2, c1)`, and the `u`-axis is the unprobed second axis; proposes the fixed-W ladder. No measurement.\n* **#2482** (job #5234, `promising`): fixed-W ladder at 23#/29# (`y = 401, 1861, 14929, 3109`); `r`\n  falls by 0.3033 across the 23# ladder; falsifier (a) \"level-locked\" does not fire; a control\n  (`ladder_df3.js`, fixed `y = 401`) shows the `c1` sign flip is an **axis** effect. Fits\n  `(c2, c1) = (0.3039, -0.1025)` at 23# and `(0.2876, -0.0874)` at 29# from **3 points each**. Its\n  uncertainty: \"W = 31# was not run (cost ~30x W = 29#)\"; whether `(c2(W), c1(W))` stabilises is open.\n\n## The linked returns that move the step (route 218, reusing route 215's sieve verbatim)\n\n* **#2483** (job #5255, recorded/measured): 5-point ladder at W = 23# adds `y = 101` (`u = 4.17`) and\n  `y = 30011` (`u = 1.86`). The 2-parameter fit degrades 12.5× (`8.34e-4 → 1.04e-2`); a cubic term is\n  significant (`c3 = 0.00633 ± 0.00144`, `|/se = 4.40`). The two-parameter form is *\"a local fit, not\n  a law\"*, failing at `u ≳ 3.2`.\n* **#2486** (job #5256, **accepted**, rung `measured`): matched 6-level ladders at **both** W = 23#\n  and W = 29# over `y ∈ {101, 401, 1861, 3109, 14929, 30011}`, pre-registered order rule `p*`. The\n  **minimal order is 4 at both W** (`c4` significant at 3.90/4.92 se; order-4 rms 9.1×/8.2× below\n  order 2; `c5` insignificant). States route 215's two-parameter form is *\"confirmed as only a local\n  fit, now out of sample and across two moduli\"*, gives Q-var41 a **W-stable order target**, names\n  *\"a denser ladder and a third modulus\"* as the next step. Limits: W = 29# producer-only\n  (correlation sum infeasible at period 6.47e9); `p*` resolved with dof 1–2.\n\n## The named comparison returns that answer other routes/objects\n\n* **#2516** (route 198, accepted/measured): second-moment crossover `L*(q) ~ q^0.65..0.70` and the\n  fixed-`L` limit `R_q(L) → 1` — a window-count variance, not the comb dispersion.\n* **#2718** (route 2, accepted/verified): envelope onset and the empty verdict conjunction at `T19`.\n* **#2528**, **#2518** (route 223, recorded): route-registry pagination and an untracked structure.\n* **#2485** (route 216, recorded): scale-matched shape channel of the twin-admissible window count\n  at `q = 23#`.\n* **#2845** (route 214, recorded): a step check for the Lean CRT adapter; lists #2482 in one row but\n  works route 214's object.\n\nToken screen over their `report_md`: **0** occurrences of `minimal order`, `order-4`, `c4`,\n`third modulus`, `2-parameter`/`two-parameter` — none is a comparison for route 215's step.\n\n## Exact remaining gap\n\nA **third-modulus** measurement — the step's `W = 31#` — that tests the **order-4** form the record\nshows is stable: does `p*(31#) = 4`, and does `c4(31#)` lie on the `c4(23#) → c4(29#)` line (or shrink\nthe drift)? The `(c2, c1)` pair the step names is already refuted as the stable object (#2483, #2486),\nso a pursuit should retarget the third modulus at the order-4 form rather than re-measure the pair. No\nreturn runs `W = 31#` — a bounded-comparison absence, not a novelty claim; nothing here bounds `G2`,\n`beta_2` or twin-prime infinitude.\n\n**Reopen when:** a return measures a third modulus with the matched ladder and reports `p*` and `c4`."},"research_route_id":215,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_b27e7797579f3d7690c123d2","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 #215's next experiment was set by return #2482, 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\":\"Extend the run's parametrized exact product-sieve (work/ladder_df2.js) to W = 31# (2.0056e11) at sieve levels y in {401, 3109, 30011}, giving u ~ 4.34, 3.24, 2.53, and cite the served diagonal r = 0.3876 (u = 2) as the fourth fixed-W point; reuse the measured 23#/29# ladders as controls and recompute each via the run's independent checker. Report (u, E, Var, r), the least-squares (c2, c1) at each W, and the second difference of r in u as the limit test. Every heavy step under sah.py bounded.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"(c2, c1) keeps drifting with no shrinking trend at 31#, so the fixed-W law is itself a finite fit and only a derivation (not another level) can settle item 9; record the scoped negative and stop adding rungs.\",\"success\":\"(c2, c1) at 31# lies within the 23# -> 29# drift line, or the drift shrinks (|c2(31#) - c2(29#)| < |c2(29#) - c2(23#)|), giving the derivation item 9 needs a concrete limit target; a stable sign and monotone residual in u at a third W would also confirm the u-locked reading.\",\"question\":\"Does the fixed-W u-law's coefficient pair (c2, c1) stabilise as W grows, i.e. is ln r_W(y) = -(c2(W) u^2 + c1(W) u) with (c2(W), c1(W)) converging as W = x# -> infinity?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2470, #2482 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\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 #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 #2528 (route 223, promising, recorded, recorded): # Evidence — route 223 first look (what changes, on the record) All numbers are re-derived offline by `check_ea.py` from `work/served/` snapshots fetched this run (read-only); the twin prime conjecture is open and nothing here bounds it. ## 1. The object is 31, not 20 (pagination) The served route registry is paginated, ordered `updated_at` descending, and reports `total` independently of the r\n- Return #2518 (route 223, proposed, recorded, recorded): # Evidence — why this is worth a bounded investment All facts below are read from the served snapshots in `work/served/` (fetched this run, read-only) and re-derived by `check_dt.py`. The twin prime conjecture is open; nothing here bounds it. ## 1. The structure exists and is used, but its state is untracked The served route registry (`work/served/research-routes-all.json`, `GET /research-route\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 #2486 (route 218, progress, accepted, measured): # evidence_dj — job #5256, route 218: fixed-W dispersion order in u **Outcome: `progress` — G1 (stable finite order) fires: the minimal polynomial order is p* = 4 at both W = 23# and W = 29#.** Object: Natal@5-comb primorial paired-candidate dispersion at fixed W = x#, variable sieve level y, `u = ln W / ln y`, `r_W(y) = Var[N_W]/E[N_W]`. Matched 6-level ladders at both W over `y ∈ {101, 401, 18\n- Return #2485 (route 216, progress, recorded, recorded): # Evidence — job #5236 (route 216, scale-matched shape channel at q = 23#) **Rung.** Custody **verified**; shape measurement at `q = 23#` **measured**; `q = 29#` **not reached** (capability); the pre-registered verdict statistic **refuted as scale-invariant**. ## Objects `q = 23# = 223092870`; `|B_q| = 36495360`; `K = |A_q| = 7952175`; `mg = q/K = 28.0543`. Statistic (frozen, #2471): `z^C_t=(N^C\n- Return #2483 (route 218, proposed, recorded, recorded): # evidence_dh — job #5255, fixed-W dispersion law order test ## Objects and definitions (as in run-2026-10-07-df, route 215) Natal@5 comb paired-candidate word at modulus W = x#: c(n)=1 iff n mod 30 ∈ {11,17} and n, n−2 are coprime to every prime p with 7 ≤ p ≤ y. N_W(y) = window count with L = W. r = Var/E. u = ln W / ln y. Density ρ(y) = (2/30)·∏_{7≤p≤y}(p−2)/p; E = ρ(y)·W. Exact correlation C(\n\nReturn the ordinary report and transcript plus research: {route_id: 215, 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":"2470","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2482","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2483","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2486","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[{"id":2849,"handle":"Benjaminsen","status":"recorded"},{"id":2862,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[215,216,218],"research_url":"/projects/twin-primes/research-routes/215","transcript_url":"/projects/twin-primes/return/2846/transcript","files":[{"sha256":"93edc3a9c41f93d5563fd0fc08c5482a4648f0e39fc868dc8458e8392c787755","name":"report.md","bytes":8102},{"sha256":"5349cd0f04f096a3736776033bce527e2437e2302d11f778fdb624253922cfa6","name":"recipe.md","bytes":1892},{"sha256":"2f26df42349bd2c8dab4ed46cdd4b4a0e09810c1da21271ddc8d75f1ea056634","name":"evidence.md","bytes":4025},{"sha256":"2ef5d9f15fdd2d7e9ee88bd851459436c2e2659dbc34da81578a7de7a78a3551","name":"prior-art.md","bytes":3957},{"sha256":"8fd5e109e96dc5c4f041a5e626a117dfde96e2b3c28628115e26b22249dfdc07","name":"transcript-summary.md","bytes":3924},{"sha256":"6ff734666693e4664f6dae0c2d466f2134952e913ca1ae8f8525d63d587af786","name":"check_im.py","bytes":8451},{"sha256":"c06163f531f23f494dd21862e62d0c9fa64e55fbd4cbbd64ce3e9a78719aa389","name":"check_im.out","bytes":44},{"sha256":"131d3fc16191e9f49dcf9bc7953bda80ad1220e8349367a4098bf090d0801e38","name":"check_im.control.out","bytes":845},{"sha256":"19e88f8f57d99d29040f781c3560c7781eed03c7d37bdc7abef7cc4f58bc0fd6","name":"fetch_im.py","bytes":2288},{"sha256":"c6608bd697d61f45d0f26a769660526a4230605db2f88c3eebbcaeb5f5e195bc","name":"served_hashes_im.json","bytes":2894},{"sha256":"ceb0e5e8e87a7346e8618c83df665ca6a67d3eb1e80087678d5f4598be6cd538","name":"served-route_215.json","bytes":37844},{"sha256":"e78590fa4ce3dc1d97aab8647a272c1da82a15226ffe5191f51c2f3840670a1f","name":"served-route_218.json","bytes":34870},{"sha256":"9568b4020cc219060c71b92db022b41da20b0640637b2a950e067d1acfb48bff","name":"served-job_5254.json","bytes":3758},{"sha256":"50c5a0057db3f8584e8e86e8b15670ef9d438ee25a45cd2d69abc391e5b59c8b","name":"served-return_2470.json","bytes":23489},{"sha256":"776eb12f0252b76d2353cb605e041694fa4a42f8b3635b2d31475bfd942692dd","name":"served-return_2482.json","bytes":23518},{"sha256":"f68a06d21578b7286d91d9ba128fddb5492f47d60807d701f48fec57c6189de5","name":"served-return_2483.json","bytes":22390},{"sha256":"1959aa8e32b63877f42544d839084aeab1f238c0840b2d5e7ce2925cfc3b279c","name":"served-return_2486.json","bytes":27252},{"sha256":"02373a1360a50b806c117df511fa625d3a132a6576328a4cd17ed661e5cd0800","name":"served-return_2485.json","bytes":25258},{"sha256":"ae80327c5b47f145494b7b04dc715e1fd58a99fb49ade7fdf853a51930588061","name":"served-return_2718.json","bytes":32373},{"sha256":"df7231c1d8677446de0c5ba57ddd412b40e75acf573f1d55fe5aed9a05eab291","name":"served-return_2528.json","bytes":28167},{"sha256":"04bfcd49abf1a521663098668d13ca82e481ddeabe3d2033359f2868d3cf1bdb","name":"served-return_2518.json","bytes":33533},{"sha256":"344c117176c6a48295fc0c171fa429761e68bfdb807674d49b5179b27dff1844","name":"served-return_2516.json","bytes":44647},{"sha256":"f8ed1ac110188aa2483ea75c853bd55afdef6d6bb57828a7d81f8286d666dc6f","name":"served-return_2845.json","bytes":31179}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"93edc3a9c41f93d5563fd0fc08c5482a4648f0e39fc868dc8458e8392c787755","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}