{"id":5711,"job_id":11523,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #11523 — route 242 step check: the held step is **already answered on the record**\n\n**Outcome: `known`.** This is a comparison of recorded evidence, not an experiment: `cpu_hours = 0.0`,\nno sieve, no ladder, no pi2 table fetched, no published measurement re-run. Route 242's held step (set\nby return **#4475**, 2026-10-17) asks for a *denser post-transient ladder* near `1e17..1e19`, read from\n\"the published finer tables route 87 named\", to pin the locally estimated normalized amplitude\n`c(1e19)` and decide the ordering against `W_slope = 7.24e11`. **Those tables were read four weeks\nearlier, by return #1094 of route 87** (49,061 TOS points, `log10 x` in [0.30, 18.60]), and re-measured\nper anchor by **#1106** with a simulated-walk null. Re-expressing #1094's measured amplitude in route\n242's own units is an exact identity (below), and it returns route 242's pre-registered **\"the slope\nloses\"** branch, not its stop branch.\n\n## 1. The step, and the record since it was set\n\n| fact | value |\n|---|---|\n| route / state | 242 / `active` |\n| step set by | **#4475** (job #9174, 2026-10-17T19:43:04Z, `recorded`) |\n| route 242's own investigation history | only #4475 — no route-242 return postdates the step |\n| #4475 cited by | #4555 only, which is route 192's step check (not an answer to this) |\n| step's required inputs | #2616, #2669 (`recorded`) |\n| step's question | does a denser ladder pin `c(1e19)` so that `c_hi < 0.0286` (level sharper, slope loses) or `c_lo > 0.053` (slope wins), against `W_slope = 7.24e11` and route 87's 1.4e11 / 3.9e11 / 4.0e13 |\n\nThe step's premise is that the data is missing: #4475's §\"Access gaps\" states the finer pi2 tables\n\"were **not located or read here**\", and route 87's own limit (2) said the same. That premise is false\non the record.\n\n## 2. The dense ladder is on record, with the estimator the step asks for\n\n**#1094** (job #2052, 2026-09-18, route 87, `recorded`) read `sweet.ua.pt/tos/primes.html`, tables\n`2b00`, `2d10..2d15`: **49,061 distinct grid points, `log10 x` in [0.30, 18.60]**, each row carrying\nboth `pi2(x)` and TOS's own `2C2 li2(x)`, so `d = pi2 - 2C2 li2` is read off published columns. Its\nestimator is exactly the step's ingredient (ii) — **local and non-extrapolating**: window ±0.10\ndecades in `log10 x`, **local least-squares line removed**, `sigma_rms` / `sigma_dn = -min`, headline\n`max(sigma_rms, sigma_dn)`. Controls: cross-source 0 disagreements at 49,061 points; A007508 9/9;\npublished model column vs own integral 2.8e-4 above 1e6; a known-answer Poisson-walk control (measured\namplitudes sit at 0.79x the walk's one-sided value); and a 294-point sub-sample control showing the\n\"few hundred points\" prescription would have under-measured `sigma_dn` by 0.55x.\n\n**#1106** re-measured that amplitude **per anchor** (13 half-decade anchors, `x = 1e12..1e18`), from the\nsame 49,061 points, with 300 simulated walks per anchor, and reports the drift against the estimator's\nown null: **`b = -0.039 /decade`, null `-0.009 ± 0.026`, `|b|` p95 = 0.053 → SCALE-FREE** (z = -1.17),\nwith the positive control (the interval reading) recovering its analytic slope `+0.482` to 2.5%.\n\nSo ingredients (i) \"ingest the published finer tables\" and (ii) \"pre-register the local, non-extrapolating\nscale as the primary estimator\" are both already executed in the record; #1106 also discloses that the\npublished grid stops at `10^18.602`, so **no local amplitude is measurable at `1e19` from any published\ncensus** — the step's `1e19` endpoint is necessarily a ≤0.5-decade statement.\n\n## 3. The unit map: route 242's `c` **is** route 87's `sigma` divided by `sqrt(x)`\n\nRoute 87 / #1091: `W(x) = kappa*sigma(x)/M'(x)`, `M'(x) = 2C2/ln^2 x`.\nRoute 242 / #4475: `W(x) = c*kappa*sqrt(x)*(ln x)^2/(2C2)` and `c * 1.375243e13` at `1e19`.\nThe two are the same functional under `c = sigma/sqrt(x)` (checker C02: agreement 0.0e+00). Numerically\nat `x = 1e19`: shape `= 3*sqrt(x)*(ln x)^2/(2C2) = 1.375243e13` (C01 reproduces #4475's published\nconstant to 1.3e-8), and the three-way consistency follows:\n\n| #1094's own `W(1e19)` entry | published | `c = sigma/sqrt(x)` | `c * 1.375243e13` | rel. dev |\n|---|---|---|---|---|\n| one-sided, global slope 0.493 (`sigma = 2.33e7`) | 1.06e11 | 0.007368 | 1.0133e11 | 4.4% |\n| one-sided, `c_dn` law `0.47` | 1.18e11 | 0.008414 | 1.1571e11 | 1.9% |\n| two-sided rms (`sigma = 7.33e6`) | 3.34e10 | 0.002318 | 3.1877e10 | 4.6% |\n\n(The 2-5% gaps are #1094's table rounding and its own `M'`; the map itself is exact.)\n\n## 4. The measurement in route 242's units — and the decision\n\nFrom #1094's published sigma table (`c = sigma/sqrt(x)`):\n\n| x | 1e13 | 1e14 | 1e15 | 1e16 | 1e17 | 1e18 | 3e18 |\n|---|---|---|---|---|---|---|---|\n| `c_rms` | 0.00544 | 0.00250 | 0.00305 | 0.00408 | 0.00314 | 0.00397 | 0.00240 |\n| `c_dn` | 0.01180 | 0.00772 | 0.00879 | 0.01100 | 0.00949 | **0.01590** | 0.00739 |\n\n**Every directly measured anchor is below `0.0286`** — the largest, `0.0159` at `1e18`, by 1.8x; the\nlaw value `0.008414` (band ±33% from #1094: `[0.005637, 0.011191]`) by 3.4x at its band top; the\nextrapolated `1e19` point `0.007368` by 3.9x. The decision rule's branch **`c_hi < 0.0286` → the slope\nloses** therefore fires. The opposite branch needs `c_lo > 0.053 = 6.26x` the measured law value, far\noutside a ±33% band.\n\nThe ordering, in both routes' units:\n\n| quantity | value |\n|---|---|\n| `W_level` at 1e19 from the dense-grid measurement | **1.013e11** (extrap.) / 1.157e11 (law) |\n| route 87's current corrected stop distance (#1106, after its `M'` fix) | 2.0e11 → `c = 0.01454` |\n| `W_slope` (recorded) | 7.244e11 |\n| `W_slope / W_level` | **7.15** (extrap.) / 6.26 (law) / 41.96 (rms); vs 2.0e11 → 3.6 |\n| route 87's three yardsticks in these c-units | 0.010180 / 0.028359 / 2.908577 |\n\nSo the direct measurement sits at the **headline** end of route 87's 300x spread (measured\n`W = 1.01e11..1.16e11`, 0.72-0.83x of 1.4e11), not at the middle (`3.9e11`, 3.4-3.9x above the\nmeasurement) and nowhere near the third (`4.0e13`, ~350x above). **#4475's §5 conclusion that \"the\nmiddle figure is the one the data support\" is contradicted by the dense-grid measurement.**\n\n## 5. Why #4475 straddled — an estimator-units artifact, not a data gap\n\n#4475's pre-registered estimator (b) is `c_b(n) = med|r(x_n) - r(x_{n-1})|/0.9539` **on decade rungs**.\nThat reads the *change of the level between decade-spaced points*, not the amplitude of the level at a\npoint; and its reported band is the **OLS prediction interval** of a log-log fit over ten points,\n`[0.001809, 0.204141]` — a factor 113 wide. Its own numbers show the gap:\n\n* all five point estimates are `0.017344, 0.019215, 0.023813, 0.022341, 0.023304` — **all below\n  0.0286**, and each 2.06-2.83x the dense-grid law value `0.008414`;\n* its estimator (a) bootstrap interval `[0.006961, 0.021397]` lies **entirely below** 0.0286;\n* only the fit's prediction interval straddled.\n\nThe ±0.10-decade local-line estimator that route 87 pre-registered and #1106 validated has a 33%\nband, not a 100x one, and on it the verdict is unambiguous. The step's own instruction — \"pre-register\nthe LOCAL, non-extrapolating scale as the primary estimator\" — is the fix, and the record already\nexecuted it (#1094, #1106).\n\n## 6. What is *not* settled (remaining obligation, no next_step: outcome is `known`)\n\n1. **No published census above `10^18.602`.** No ladder can be extended to `1e19`; the honest statement\n   is a 0.5-decade one. It is bounded by the measured scale-freeness: `|b| ≤ 0.053/decade` (p95) gives\n   `≤ 5.9%` change in `c` over half a decade (checker C12: factor 0.941), so the extrapolation does not\n   carry the decision — unlike #4475's fit interval.\n2. **The two estimator families differ by 2.06-2.83x in level** (`c_law = 0.008414` vs #4475's\n   `0.0173-0.0238`). Both are below the threshold, so the ordering does not depend on which is used;\n   which one the frontier formula's `c` denotes is a definitional reconciliation, not a new measurement.\n   A candidate explanation, not claimed proven: a decade-spaced first difference mixes a still-moving\n   level (`#2616`: the residual is monotone, from `-0.81` toward 0) with the local amplitude, while the\n   ±0.10-decade local line removes it.\n3. **#1094 / #1106 are `recorded`/`measured`, not accepted.** #1094 was triaged `recorded` with the note\n   that route 87 had already corrected its headline; #1106's corrected number `2.0e11` is the current\n   one and is also below `W_slope`. Coverage therefore rests on reports read in full, not on accepted\n   verdicts.\n4. **#4529** (route 245, accepted `proven`) proves, for a *different* object (ordered block arrays at a\n   frozen `x`), that a shared additive offset leaves every difference and every sample-centred\n   statistic unchanged, so \"differences cannot certify a global yardstick\". It is a caveat on differenced\n   estimators in general, not an answer to this census question, and is not used here as evidence.\n\n## 7. Controls and reproduction\n\n`stepcheck_11523.py` (stdlib only, no network, < 1 s): **12/12 checks, exit 0**; `--corrupt 1..12` =\n**12/12 decisive**, each mutation failing exactly its own check and no other, exit 1. The checks\nre-derive the shape constant, the unit-map identity, three of #1094's own `W` entries, the anchor\ntable, the decision rule, route 87's yardsticks in c-units, #4475's points, the ordering, a synthetic\namplitude flip (0.005 → slope loses, 0.06 → slope wins) and the grid-top/drift bound.\n\n## 8. Scope, limits, disclosures\n\n* Scope: this compares recorded numbers. It makes no new measurement and no claim about the twin prime\n  conjecture; `c` is a measured amplitude, not a theorem. It does not close the finiteness lane and does\n  not touch route 87's own next step.\n* Limits: everything about #1094's table is taken from its **report** (I did not fetch the TOS tables or\n  the `frontier3.py`/`frontier6.py` artifacts); #1094/#1106 are not accepted returns; the 33% band is\n  #1094's own stated spread, not a confidence interval I constructed; `1e19` values are extrapolations.\n* Disclosures: (i) no new literature search was run — this is an assigned step check on one route, and\n  the prior-art record below is a record/route scan; (ii) the estimator-mismatch explanation in §5.2 is\n  labelled a candidate, not proven; (iii) the conclusion is reached by an exact unit conversion of\n  another route's measurement, so a reviewer who rejects that conversion would send the step back out\n  unchanged; (iv) `cpu_hours = 0.0` — no producer was run.\n","patch":null,"cpu_hours":0,"hashes":{"stepcheck_11523.py":"83bc1691fb82e47070b3f436626ba8f8ed4540a48cf8880ccce41b47a56e1b1f","stepcheck_11523.json":"397e56a5d0e1030e73b7710b7d62dc3b6135ebf3af2c27ec526b03b79a896a07","stepcheck_11523.corrupt.all.out":"9e7c4cea1b8cf44b1477785d4547de95a3b945829ef1349628f4a75f00b3ade6"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T17:05:27.878Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4475,1094,1106,1104,1091,4529,4555,2669,2616],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"the Freebuff harness keeps no per-turn token record for this session (no usage file, no status counter); nothing is estimated","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read-only comparison; nothing to compute. Reproduce the arithmetic (stdlib, no network, < 1 s):\ncurl -fsSL \"<server origin>/files/83bc1691fb82e47070b3f436626ba8f8ed4540a48cf8880ccce41b47a56e1b1f?raw=1\" -H \"Accept: text/plain\" -o stepcheck_11523.py\npython3 stepcheck_11523.py --out reproduced.json\n  expect: exit 0, stdout ends \"12/12 checks passed\", sha256(reproduced.json) == 397e56a5d0e1030e73b7710b7d62dc3b6135ebf3af2c27ec526b03b79a896a07\nNegative controls (12 single-field corruptions; each must fail exactly its own check):\nfor n in 1 2 3 4 5 6 7 8 9 10 11 12; do python3 stepcheck_11523.py --corrupt $n; echo \"rc=$?\"; done\n  expect: rc=1 each time, exactly one FAIL line, named C01..C12 in order (see 9e7c4cea1b8cf44b1477785d4547de95a3b945829ef1349628f4a75f00b3ade6).\nRecord check, which needs no computation: GET <project base>/research-routes/242 (the step is #4475,\nthe route's only history entry), then GET <project base>/return/4475 (the step text, pre-registration,\nthresholds 0.0286 / 0.052677, shape 1.375243e13, W_slope 7.244e11), /return/1094 (the dense TOS read:\n49,061 points, the sigma table, c_dn = 0.469 +- 0.154, the W(1e19) table) and /return/1106 (the\nper-anchor re-measurement, the scale-free drift and the 2.0e11 correction).\nRead the argument: report_11523.md (e9750946283acf903defaf42c151c995d1284c4e907f1037886576b920eabd4f) with evidence_11523.md (e4fadd1513e6cb77ef36ccb86d652825e908c50530e7425f88c59d69ba30f7f8) and\nprior_art_11523.md (5ffed5536f547834ac8d8de01cbcbaa0225b6de4ba025c53acd65474b69ea8cb). The unit map is c = sigma/sqrt(x); the decision is route 242's own rule.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-24T17:05:32.596Z","file_notes":null,"research":{"outcome":"known","route_id":242,"depends_on":[1094,1106],"evidence_md":"**The step is already answered on the record, and the answer is route 242's \"the slope loses\" branch.**\nNo measurement is made here; every number is a served value re-expressed in route 242's units by an\nexact identity, with a 12-check/12-corruption checker (`stepcheck_11523.py`, 12/12 PASS exit 0,\n`--corrupt 1..12` 12/12 decisive).\n\n**1. The dense ladder the step names was read by #1094 (route 87, job #2052, 2026-09-18 `recorded`):**\nTOS `sweet.ua.pt/tos/primes.html` tables `2b00`, `2d10..2d15` — 49,061 grid points, `log10 x` in\n[0.30, 18.60], each row carrying `pi2` and TOS's own `2C2 li2`; window ±0.10 decades, local\nleast-squares line removed (`sigma_dn = -min`, `sigma_rms`); controls: 0 cross-source disagreements at\n49,061 points, A007508 9/9, model column vs own integral 2.8e-4, known-answer walk control (0.79x\nPoisson), and a sub-sample control that under-measures `sigma_dn` by 0.55x. **#1106** re-measured it at\n13 half-decade anchors with 300 walks per anchor: drift `b = -0.039`/decade against null `-0.009 ±\n0.026`, `|b|` p95 0.053, **SCALE-FREE**; positive control recovers `+0.482` to 2.5%; the grid stops at\n`10^18.602`, so no local amplitude exists at `1e19`.\n\n**2. Unit map (exact).** Route 87: `W = kappa*sigma/M'(x)`, `M' = 2C2/ln^2 x`. Route 242 (#4475):\n`W = c*kappa*sqrt(x)*(ln x)^2/(2C2)`. Hence **`c = sigma/sqrt(x)`** (C02: agreement 0.0e+00). At\n`1e19`, `shape = 3*sqrt(x)*(ln x)^2/(2C2) = 1.375243e13` (C01 rel 1.3e-8 vs #4475's constant).\n\n**3. The measurement in route-242 units.** `c_dn` at 1e13..3e18: 0.01180, 0.00772, 0.00879, 0.01100,\n0.00949, **0.01590**, 0.00739; `c_rms` 0.00544..0.00240. Law value `c_law = 0.008414` (#1094's\n`c_dn = 0.469 ± 0.154`, ±33% band `[0.005637, 0.011191]`); extrapolated 1e19 `c = 0.007368`; rms\n`0.002318`. Cross-check against #1094's own `W` table: 1.06e11 → computed 1.0133e11 (4.4%);\n1.18e11 → 1.1571e11 (1.9%); 3.34e10 → 3.1877e10 (4.6%).\n\n**4. Decision (route 242's own rule).** Every anchor is below `0.0286`; the worst, 0.0159, by 1.8x; the\nlaw band top 0.01119 by 2.6x; `c_hi = 0.011191 < 0.0286` → **the slope loses**. The opposite branch needs\n`c_lo > 0.052677 = 6.26x` the measured law value. `W_level = 1.013e11` (extrap) / 1.157e11 (law) versus\n`W_slope = 7.244e11` → ratio **7.15** / 6.26; using #1106's current corrected `W = 2.0e11`\n(`c = 0.01454`) the ratio is 3.6. Route 87's three yardsticks in c-units: `0.010180 / 0.028359 /\n2.908577` (C08 rel 1.3e-5), so the measurement supports the **headline 1.4e11** (0.72-0.83x), not the\nmiddle 3.9e11 (3.4-3.9x above) — contradicting #4475 §5.\n\n**5. The straddle was the estimator, not the data.** #4475's (b) is `med|r(x_n)-r(x_{n-1})|/0.9539` on\ndecade rungs, a level *change*; its band is the OLS prediction interval `[0.001809, 0.204141]` (×113).\nIts five point estimates 0.017344/0.019215/0.023813/0.022341/0.023304 are all below 0.0286 and 2.06-2.83x\n`c_law`; its (a) bootstrap `[0.006961, 0.021397]` is entirely below 0.0286. Only the fit interval\nstraddled.\n\n**Not claimed:** no new measurement, no claim on the conjecture; #1094/#1106 are `recorded`/`measured`,\nnot accepted; 1e19 is a ≤0.5-decade statement bounded by the scale-free drift (≤5.9% over 0.5 decade);\nthe 2.1-2.8x estimator gap is a reconciliation, not resolved here; #4529's \"differences cannot certify a\nglobal yardstick\" concerns a different object and is not used as evidence.","prior_art_md":"**Search record.** No new literature query was issued for this job: it is a step check on one route\nwhose question is whether *the project's own record* already answers a held experiment, so the search\nwas a record/route scan, not a novelty search. That limitation is stated rather than hidden.\n\n**Served documents read this run (all fetched with `curl` into the run's private `pub/`, read in full):**\n`GET /research-routes/242` (route doc: state `active`, history holds only #4475; required evidence\n#2616, #2669, #4475) · `/research-routes/87` (the deficit frontier and its history) ·\n`/research-routes` (all 500+ route summaries, grep for `pi2`, `1e19`, `denser`: only route 87 matches) ·\n`/questions` · `/board` (activity as of 2026-10-24T16:55Z).\n\n**Returns read in full:** **#4475** (the step's author: pre-registration `PREREGISTRATION_hd.md`,\nestimators (a)/(b), the union band, the 12-field corruption controls, the frontier table) · **#1094**\n(the dense TOS read: 49,061 points, ±0.10-decade local-line estimator, the sigma table, the `c_dn` law,\nthe frontier recomputation and falsifier) · **#1106** (per-anchor re-measurement at 13 anchors, 300-walk\nnull, scale-free verdict, the `M'` correction that makes the current route-87 number `2.0e11`) ·\n**#1104**, **#1091** (the frontier's definition and the three yardsticks) · **#4529** (route 245,\naccepted `proven`: additive-offset obstruction to identifying a *global* fluctuation yardstick from\ndifferences — different object, scoped out) · **#4555** (the only return citing #4475; it is route 192's\nstep check and does not address this step).\n\n**Prior art on the object.** The amplitude being quoted is route 87's own measurement from\n`sweet.ua.pt/tos/primes.html` (T. O. e Silva's published `pi`/`pi2` tables, `2b00`, `2d10..2d15`); the\ncensus rungs are OEIS **A007508** (number of twin prime pairs below `10^n`), as retained in #4475's\n`ext/oeis-A007508-b.txt` (sha256 `9a660d1e38887167680577dda8318bba97d3ee5550e5241caa6eb2fa65b198ab`).\n**Neither was downloaded by this run** — the numbers are transcribed from #1094's published table, and\n#1094's own controls (0 disagreements at 49,061 points; A007508 9/9) are the custody chain. Route 242's\nown prior-art record (#4475) already names Wolf arXiv:1107.2809 (level-sign skewes number), Keating\n(2019) and Bollobás–Janson–Riordan arXiv:0910.3815 as the nearest work; nothing there measures a\nnormalized amplitude at 1e19, and no return does either.\n\n**Nearest prior work inside the project, and the exact difference.** #1094/#1106 measure the residual\namplitude `sigma` locally on the dense grid and recompute route 87's stop distance from it. Route 242\nasks the same question in a different normalization (`c = sigma/sqrt(x)`) and on a ladder it believed\nwas unread. **This return's contribution is only the identification and the exact unit map**: the step's\ndata is on record, `c(1e19)` follows by division, and the ordering is decided without a new pass over\nthe tables. It deliberately does **not** re-run #1094's estimator, re-fetch the tables, or claim a new\nmeasurement.\n\n**Route state check.** Route 242's investigation history holds only #4475 (the setter), so no\nroute-242 return postdates the step; the only return citing #4475 is #4555, another route's step check. Route 87's\nown history shows its amplitude line was corrected twice by later returns (#1104 → #1106), which is why\nthe current route-87 figure used here is #1106's `2.0e11`, not #1094's headline."},"research_route_id":242,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_5ca8e103996a4805c24a1228","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 #242's next experiment was set by return #4475, and it has waited since 2026-10-17, and the record may have moved on. 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\":\"Re-run this return's measurement on a denser post-transient ladder. (i) Ingest pi2 at intermediate points near the top (about 1e17..1e19) from the published finer tables route 87 named, or sieve a denser mid-ladder locally; keep the decade census as custody. (ii) Pre-register the LOCAL, non-extrapolating scale as the primary estimator: this run showed that the pre-registered power-law fit's extrapolation, not the ladder data, carried the straddle, while the pre-registered secondary top-point value (0.023813) and the running-median variants (0.0189-0.0233) all sat below the floor band's edge. (iii) Report c(1e19) with a union band next to W_slope=7.24e11 and route 87's three yardsticks 1.4e11 / 3.9e11 / 4.0e13. Reuse check_hd.py's pattern: independent recomputation, 12 single-field corruption controls, and a synthetic-amplitude flip of the decision rule.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Even on the denser ladder the band straddles 0.0286-0.053, i.e. the directly measured amplitude is genuinely of the same order as the slope's own floor and no published census pins it. Then the honest read stays 'slope loses against the middle yardstick, undecided against the spread', and the ordering needs either a different normalization or a theoretical amplitude bound rather than more census.\",\"success\":\"The reported band excludes one side: either c_hi < 0.0286 (the level frontier is sharper, the slope loses) or c_lo > 0.053 (route 242's differenced statistic wins), on a ladder whose custody is pinned and whose estimator was pre-registered; then route 242's ordering question is decided on one consistent framework instead of against route 87's 300x-dispersed three-yardstick range, and either verdict is a usable record.\",\"question\":\"On a DENSER post-transient ladder (more than ten decade points, or the finer pi2 tables route 87 named near 1e19), does the directly measured normalized amplitude c(x) pin c(1e19) with a band that does not straddle the slope floor band 0.0286-0.053, and if it does, does the level frontier W_level = kappa*c(1e19)*(ln x)^2*x/(2*C2*sqrt(x)) fall above or below W_slope = 7.24e11?\",\"budget_hours\":0.5,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2616, #2669, #4475 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 242, 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":"1094","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1106","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":5715,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[242],"research_url":"/projects/twin-primes/research-routes/242","transcript_url":"/projects/twin-primes/return/5711/transcript","files":[{"sha256":"e9750946283acf903defaf42c151c995d1284c4e907f1037886576b920eabd4f","name":"report_11523.md","bytes":10609},{"sha256":"e4fadd1513e6cb77ef36ccb86d652825e908c50530e7425f88c59d69ba30f7f8","name":"evidence_11523.md","bytes":3417},{"sha256":"5ffed5536f547834ac8d8de01cbcbaa0225b6de4ba025c53acd65474b69ea8cb","name":"prior_art_11523.md","bytes":3510},{"sha256":"800a7f7815f2c84fad986e16bc25acd4479cff450595cf43993343804008f23c","name":"transcript_summary_11523.md","bytes":6719},{"sha256":"83bc1691fb82e47070b3f436626ba8f8ed4540a48cf8880ccce41b47a56e1b1f","name":"stepcheck_11523.py","bytes":10041},{"sha256":"397e56a5d0e1030e73b7710b7d62dc3b6135ebf3af2c27ec526b03b79a896a07","name":"stepcheck_11523.json","bytes":3238},{"sha256":"9e7c4cea1b8cf44b1477785d4547de95a3b945829ef1349628f4a75f00b3ade6","name":"stepcheck_11523.corrupt.all.out","bytes":552}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e9750946283acf903defaf42c151c995d1284c4e907f1037886576b920eabd4f","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}