{"id":4481,"job_id":9178,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #9178 — route 243 first look: the census arm exists, and its top term is stale\n\n**Outcome: `progress` — the old step is replaced.** Route 243's next experiment (set by return #2671)\nis **not** answered on the record, so `known` is wrong; but it is **not worth handing out as written**,\nfor two machine-checked reasons found here: its **census half is already executable at zero compute**\nfrom two published census sequences, and its **dyadic half cannot satisfy the step's own success\nclause** because a ladder bounded at 2^34 has a hard-stop reach of about 2^34, which is 8.1x below the\nsmallest frontier it must beat.\n\n## Decision, and why not `promising`\nThe step (served in the brief, frozen as `PREREGISTRATION_he.md`) is:\n\n> 1. extend the exact segmented sieve 2^32 -> 2^34 and record N_2, N_4, N_6 at 2^27..2^34; 2. form\n> `q(y) = (N_2 - N_4)/sqrt(N_2 + N_4)`; 3. pre-register a noise band and a conditional permutation\n> null; 4. find the largest `X0` whose predicted `|q|` exceeds the band, and compare it with route 87's\n> level frontier and route 242's slope frontier; 5. anchor at the published 10^18 twin deficit.\n\nSuccess requires the hard-stop prediction to exceed the band \"at an `X0` at least as large as route\n87's level frontier\"; failure fires if it \"never exceeds the band **within reach**\".\n\n1. **No return on record answers it.** #2671 stops at 2^32 (the step's own wording is \"extend ... from\n   2^32 to 2^34\"). Route 255's #2686 and #2693 answer a neighbouring, lag-resolved question at one\n   scale (X = 2^27). So the obligation is open — but see 3 and 4.\n2. **The census arm is available today.** OEIS **A007508** (twin) and **A152052** (cousin, lower\n   member) publish `N_2`, `N_4` at 10^1..10^19; **A080840** is the upper-member variant. The step's\n   \"(and on the published decadal census)\" therefore needs no enumeration at all.\n3. **A stale term would have produced a false signal.** A152052's `a(19)` is a copy of A080840 taken\n   2026-06-05, while **A080840's `a(19)` was corrected 2026-07-08** (delta 1,213,445,187). With A152052\n   as served, `q(10^19) = +9.611` — the only `|q| > 3` in 19 decades, i.e. an apparent 9.6-sigma\n   cross-constellation signal. With the current A080840 term, `q(10^19) = -0.475`. Across all 19\n   decades with the corrected terms: `max|q| = 1.285` (n = 15), `rms = 0.588`, `mean = +0.276`, none\n   over band — the step's own `sd(q) = 1` counting null is consistent with the published census\n   everywhere. Any run that does this arm must carry the stale term as a named control.\n4. **The dyadic reach cannot meet the clause.** If twin production froze at `X0 >= x_max`, nothing\n   measured at `x <= x_max` differs from the no-stop world, so `reach(x_max) < x_max` strictly, for any\n   band. With `x_max = 2^34 = 1.718e10` the shortfall against the comparison frontiers is **8.149x**\n   (1.4e11, the number the step names), 22.70x (3.9e11), **42.17x** (route 242's 7.244e11) and 2328x\n   (4.0e13); the required `x_max` would be 2^37.03 / 2^38.50 / 2^39.40 / 2^45.19. An HL-model\n   computation puts the invisible window at `W_q = 1.195e7` — 0.07% of `x_max` — so the reach is the\n   ladder top, not the model. Hence the specified run would fire the *failure* clause for a reach\n   artefact and close route 243 for the wrong reason.\n\nSo the step is not answerable-as-written in a useful way, and its census half is answerable now with no\nsieve: `progress` (the old step replaced by `next_step_he.json`) is the honest outcome.\n\n## Method mapping of the borrowed negative (the weakest assumption)\nThe step's weakest assumption is its **null**, not its arithmetic. Route 255's #2686 is on record as a\n*measured* negative about model-free matched controls: at **lag resolution** a rotation or\nmatched-thinning null cannot calibrate a cross-constellation statistic, because the two constellations'\nindicators share primes deterministically (`T(n)` and `C(n+2)` both need `n+2` prime), while #2693's\nHL 4-tuple kernel reproduces the same recorded counts. That negative is **scoped to lag resolution**:\nat the *global counts* scale the deterministic geometry reduces exactly to the shared-base-prime count\nalready inside `sqrt(N_2 + N_4)`, which is what the step's null presumes and what route 243's own #2620\nrotation result at block scale (m = 256) demonstrates. I therefore record the mapping as *admissible\nat global scale, inadmissible at lag scale*, and I do not claim more than that; the step's proposed\n\"conditional permutation null\" is a block-scale object and is not killed by #2686, but neither does\n#2686 support it.\n\n## What was run here, and what was not\nRun: the published-census audit (values read from the two census sequences, `q` formed, statistics,\nreach arithmetic), a bounded local sieve to 10^8 as a convention check, and the pinned lane evaluator.\nNot run: no ladder enumeration to 2^33/2^34 or beyond; no re-derivation of route 87's or route 242's\nfrontier constants (their served route records are pinned by literal in the checker); no re-run of\n#2620/#2671's producers; no fresh literature search beyond the two census queries in `prior_art_he.md`.\n\n## Verification\n`check_he.py` **20/20 PASS, exit 0**; `--corrupt 1..20` -> **20/20 single-field controls decisive**.\nLocal sieve to 10^8 reproduces A007508(6,7,8) = 8169/58980/440312 and A152052(6,7,8) =\n8144/58622/440258 exactly, which fixes both censuses' conventions at three decades. The lane's pinned\nevaluator (`sha256 3946f639...`, the served value) run **unchanged** on this run's own claims:\n**19 claims, 19 ok, 0 mismatch, 0 unsupported, exit 0**, including `pi2(10^6, 10^7, 10^8)` recomputed by\nthis run's sieve. Named-but-unserved source in the brief, `research/history/staging/attack-beta2-02.md`,\nfetched once: **404** (no such route), so nothing was taken from it.\n\n## Rung and scope\n**No rung is claimed.** This is a step-checking first look: a prior-work comparison plus a feasibility\ncomputation on published data. No bound on `G2`, `beta_2` or `pi2`; the twin-prime conjecture stays\nopen; the census sequences are other people's computations, reproduced by me only to 10^8 and used\nabove that at their publishers' provenance; the HL model is a heuristic and appears only in the window\n`W_q`. The step's \"middle yardstick\" label for 1.4e11 disagrees with route 87's own uncertainty (which\ncalls 3.9e11 the middle figure); I used the step's own 1.4e11 as the operative threshold and reported\nevery yardstick.\n\n## Disclosed slips and limits\n1. The census values were read during the prior-work search, *before* `PREREGISTRATION_he.md` was\n   written; the pre-registration is therefore a frozen decision rule for the machine-checked run, not a\n   blind preregistration. Stated in the pre-registration itself.\n2. `compute_he.py` had two self-caught defects before any submission: a `%` in a regex clashed with\n   `%`-formatting (fixed), and the first `reach()` kept the *smallest* rather than the largest `X0` with\n   `|q| >= band` (fixed to a bisection; `W_q` moved from a grid artefact to 1.195e7).\n3. `check_he.py` had one wrong literal (compared the slope shortfall against 7.24e11 while the producer\n   used the recorded 7.244e11); fixed at the cause — the baseline is 20/20.\n4. The cousin census above 10^8 is **not** re-verified here, and its `a(19)` was corrected by its\n   contributor six weeks ago — both facts are why the stale term is carried as a control rather than\n   used.\n5. No fresh literature search was run for the reach concept or for a published cross-constellation\n   statistic beyond the two queries recorded; absence of a match is not a novelty certificate, and no\n   novelty is claimed.\n6. Honest framing: the census result is *negative* about a signal and the reach result is *negative*\n   about the specified ladder — the return is a route-decision, not a discovered effect.\n\n## For the person\nFour of @Benjaminsen's returns still wait for a verdict (the oldest since 2026-10-06); verdicts need a\ntrusted reviewer, and the grant on this project is your own handle's. Nothing for you to do beyond\nthat line. Job #3880 (inbox handoff #1) still waits for a chosen source expert and is untouched here.\n\n## Usage\nUsage tokens: **unmeasured** — this harness exposes no per-turn input/output token counts, so usage is\nreported as unmeasured rather than estimated, and the ledger's delayed-usage path closes the attempt.\n","patch":null,"cpu_hours":0,"hashes":{"check_he.py":"cd7720092e167e76e5c34816dccb0f96d64c5f9c9f52eb50bf5122a3447b69cd","report_he.md":"1c6615d238b85fb50dac5da6c20865344716eadea70e4dfca43b177c999da8e0","compute_he.py":"67874cff2dca335080e030666410eacd03c93d81134845a7295d0290766d9dab","claims_he.json":"0b099f3dca35cedd4840c09b801ea3703c7017f2197bbb9dcade4a40809a50c3","compute_he.out":"ffb0379250cc846dc7a0df496987a8c9d89fa7725b3fa7ea9883c89634a5420a","evidence_he.md":"ee19728bb4035ce5c3a64e708b56fd2dec462420c2fb0959d8d0a83cb4a93ca8","compute_he.json":"48b825ab37fb1e70ea47c22f44ea726e8dae9e2021208277406a754efa115a28","evaluate_he.out":"31a644d15b78cf7bf623bd09166fe05eb11c1d61707f1eeb3c3fd316eadbcba8","prior_art_he.md":"596d04e0a26aeb1f8224ba4dc8b856bd2020def74eea5a8f51c77c9316e6fd54","oeis-A007508.txt":"7f6eb72332f215df3dc70cd174ce828e289beb40494428693c51558e2f92b63d","oeis-A080840.txt":"38a1bb8fbe5c22dfedc37dae121cd4880e57a6573041176018fcf2e5e6480d6c","oeis-A152052.txt":"a6d7e6cc7dffd2f8f3884497808b7f489e74c13cc176dccf41d2e9fc866584bd","oeis-A152127.txt":"924ea2fe6aa670019c737e62e588718aa82282f55d50029305033d34e893d4ec","transcript_he.md":"82ae8ef446e12270ef15c0c62c7038519e879c1575ab764877abdeb6e686beb6","next_step_he.json":"a7fd6a94ba0fae8ac8bafa66c1023de75ecb28dbf84da8b4aa71335c4761ae33","check_he.check.out":"53c5e500687f478c54374648bf9bbc3e4e88b68c1d7594a8819909d599edc982","served_pins_he.json":"4e1544320c5001cf5555020605506dd716b6c2c62fb1486edaab677ca275cf5d","PREREGISTRATION_he.md":"cba40c760e94ee88069edc2c524f87a07e0c0a21de1cbff7880cf893f5e6ac7a","check_he.corrupt.all.out":"3d061393fa4b69886c2fed08bd380f98f30cb37f6b0a28def0efa27cf02ae9a7"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-17T20:19:39.652Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2671,2620,2686,2693],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"this harness exposes no per-turn input/output token counts, so usage is reported as unmeasured rather than estimated","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":"progress","route_id":243,"next_step":{"method":"Published censuses only; no new sieve for the primary arm. (1) Freeze BEFORE computing: N_2 = OEIS A007508; N_4 = OEIS A152052 for n <= 18; N_4(10^19) = the current A080840 a(19) = 7237518150883895, with A152052's a(19) = 7237516937438708 carried as a named CONTROL (A152052 copied it before A080840's 2026-07-08 correction); disclose the <= 1-pair lower/upper convention slack; null sd(q) = 1 (equivalently sd(d) = sqrt(2) for the normalised-deficit difference), band |q| <= 3. (2) Form q(10^n), n = 1..19; report max|q|, rms, mean and every decade over band for the corrected terms and for the stale term. (3) Reach: for each published x, find the largest X0 whose predicted |q(x; X0)| exceeds the band under 'twin production frozen above X0, cousin production continuing at S(4)*Li2', and report the largest such X0 over the census against 1.4e11 / 3.9e11 / 4.0e13 (route 87) and 7.24e11 (route 242). A ladder bounded at x_max cannot see X0 >= x_max, so the reach must come from the census top, not from 2^34. (4) Only if the dyadic question is still open after (2)-(3): extend the exact ladder to a top >= 1.4e11 (2^37.03, NOT 2^34) and record N_2, N_4, N_6 from 2^27 up. (5) Verify twice: an independent stdlib checker that recomputes q and the reach from the retained source texts with per-field corruption controls, and the lane's PINNED evaluator (sha256 3946f639bfe3d2313b4ba575df9d78f131275ba9465849adcd09ee9ca919ce19) run unchanged on pi2 claims the run computes itself. Never form q(y) from A152052's a(19) without the control.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Even with the corrected terms a decade (or several) stays over the band, so the 'signal' is not a data artefact and the matched difference does carry finite-scale structure; or the census reach cannot be established and no reachable instrument reaches the frontier. Either outcome leaves route 243's obligation partly undecided, and the honest next object is the dyadic ladder extended to 2^37 with the census as its control, not the step's 2^34.","success":"On the corrected census the q series is inside the band at all 19 decades and the census hard-stop reach is at least route 87's smallest frontier: the finiteness lane then has a model-free, transient-insensitive yardstick with a documented reach, the constant-free matched difference is established as an instrument (its observed values being noise is the point), and the 2^33/2^34 dyadic extension is retired as unnecessary because it can never reach the frontier it is compared against. Either verdict on the q values themselves is a usable record; the reach comparison is the deliverable.","question":"With the current (2026-07-08-corrected) cousin census, does the model-free cross-constellation difference q(y) = (N_2 - N_4)/sqrt(N_2 + N_4) stay inside its sqrt(2) counting band at every published decade 10^1..10^19, and does its hard-stop reach (the largest X0 for which a world with twin production frozen above X0 still shows |q| beyond the band) exceed route 87's level frontier and route 242's slope frontier at the top of the census?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[2671,2620,2686,2693],"evidence_md":"# Evidence — route 243 first look (job #9178): the census arm exists, and its top term is stale\n\nRule frozen in `PREREGISTRATION_he.md` before computing. No ladder enumeration beyond a bounded 10^8\nconvention check; nothing here re-runs a computation a return already made.\n\n## 1. Not `known`: no return on record answers the step\n#2671 measured `q(y) = (N_2 - N_4)/sqrt(N_2 + N_4)` on 2^27..2^32 only (`max|d| = 0.842`), and the\nstep says itself \"extend ... from 2^32 to 2^34\". Route 255's #2686 (lag-resolved cross-constellation\ncorrelation, X = 2^27, falsifier VOID) and #2693 (HL 4-tuple cross kernel, one scale) answer a\nneighbouring question, not the global matched difference, the ladder, or the reach. No text served\nwith this brief names a twin or cousin count at 2^33 or 2^34.\n\n## 2. The census arm is available at zero compute — and its top term is stale\nOEIS **A007508** (twin pairs below 10^n) and **A152052** (cousin primes below 10^n, *lower* member\ncounted) publish `N_2(10^n)`, `N_4(10^n)` for n = 1..19; **A080840** is the upper-member variant\n(`A152127` is context only). The conventions differ by at most one pair per decade, so the step's\n\"(and on the published decadal census)\" arm needs no enumeration.\n**Hazard:** A152052's `a(19) = 7237516937438708` is a *stale copy* of A080840's pre-correction term —\nA152052 records \"a(17)-a(19) copied from A080840 by Hugo Pfoertner, Jun 05 2026\", while A080840\nrecords \"a(16)-a(19) from Benjamin Chaffin, Jun 02 2026, **a(19) corrected Jul 08 2026**\"; delta\n1,213,445,187. Stale term: `q(1e19) = +9.611`, the **only** `|q| > 3` in 19 decades. Corrected term:\n`q(1e19) = -0.475`. A run forming `q(y)` from A152052 as served would report a 9.6-sigma \"signal\" that\nis a data artefact.\n\n## 3. The census statistic with the corrected terms (19 decades, no enumeration)\n`max|q| = 1.285` (n = 15), `rms = 0.588` over 19 decades (0.5935 over n <= 18), `mean = +0.276`, and\n**no decade over the ±3 band**: the route's own \"shared-base-prime counting noise\" null (`sd(q) = 1`,\nequivalently `sd(d) = sqrt(2)`) is consistent with the published census at every scale.\n\n## 4. Reach: the step as written cannot meet its own success clause\nA ladder bounded at `x_max` cannot see a stop at `X0 >= x_max` (the frozen world is identical below\n`X0`), so `reach(x_max) < x_max` strictly, for any band. The clause needs `reach >= 1.4e11`. With the\nstep's `x_max = 2^34 = 1.718e10` the shortfall is **8.149x** (1.4e11), 22.70x (3.9e11), **42.17x**\n(route 242's 7.244e11) and 2328x (4.0e13); required `x_max` = 2^37.03 / 2^38.50 / 2^39.40 / 2^45.19.\nThe HL-model window `W_q = 1.195e7` (0.07% of `x_max`) shows the reach *is* the ladder top, not the\nmodel. (The step calls 1.4e11 \"the middle yardstick\"; route 87's own uncertainty calls 3.9e11 the\nmiddle figure. I use the step's 1.4e11 as the operative threshold and report every yardstick.)\n\n## 5. Checks (machine-checked, this run)\n`check_he.py` **20/20 PASS, exit 0**; `--corrupt 1..20` -> **20/20 single-field controls decisive**.\nA local sieve to 10^8 reproduces A007508(6,7,8) = 8169/58980/440312 and A152052(6,7,8) =\n8144/58622/440258 exactly, fixing both conventions at three decades. The pinned lane evaluator\n(sha256 `3946f639...`, the served value) run **unchanged**: **19 claims, 19 ok, 0 mismatch, 0\nunsupported, exit 0**, including `pi2(10^6, 10^7, 10^8)` recomputed by this run's own sieve.\n\n## What this changes\nThe census half of the step is executable today and its central claim survives on 19 decades once the\nstale term is excluded; the dyadic half as written cannot decide what it is compared against. Neither\nhalf needs 2^33/2^34: the reach must come from the census or from a ladder that really reaches\n`>= 1.4e11` (2^37), which is 8.1x more sieve than the step ordered.","prior_art_md":"# Prior art — route 243 first look (job #9178), recorded-provenance only\n\nSearch date 2026-10-17. Two live web searches were run (both inspected at snippet level, then the\ncensus entries opened in full):\n1. `OEIS number of cousin primes less than 10^n sequence counting function p p+4`\n2. `\"cousin primes\" number below 10^n table counts 10^10 10^18 exhaustive enumeration`\n\n## Census sequences opened in full (text-format records retained and hashed)\n- **OEIS A007508**, *Number of twin prime pairs below 10^n* — the twin census `N_2(10^n)`, n = 1..19,\n  `10^19 -> 7237518093734545`. Publicly canonical; used by return #4475 and by route 87.\n- **OEIS A152052**, *Number of cousin primes < 10^n, such that only the lower member of each prime\n  cousin pair is counted* — `N_4(10^n)`, n = 1..19. Convention stated in the entry's own comment.\n  **Its a(17)-a(19) are copies of A080840** (copied 2026-06-05), and its a(19) predates A080840's\n  2026-07-08 correction.\n- **OEIS A080840**, *Number of cousin primes < 10^n, such that only the upper member ... is counted* —\n  the current corrected a(19) = 7237518150883895; \"a(16)-a(19) from Benjamin Chaffin, Jun 02 2026,\n  a(19) corrected Jul 08 2026\".\n- **OEIS A152127** (sum of cousin primes < 10^n) — context only; not used in any computation here.\n- **MathWorld, *Cousin Primes*** — read; gives the equal asymptotic density (same 2C2) and no decadal\n  census, which is why the census had to come from OEIS rather than from the usual citation.\n\n## Served records compared before deciding\n- Return **#2671** (route 243, progress): the route's own prior measurement — `q(y)` on the dyadic\n  ladder to 2^32, `max|d| = 0.842`, the `rho_24` negative at 6/6 scales, and the MathOverflow 511187\n  `10^18` twin-deficit anchor. This is the record the step extends; it stops at 2^32.\n- Return **#2620** (route 243, proposed): the block statistic, its rotation null and its disclosed\n  weakness (i) (a positive `rho` is expected even under independence because the constellations share\n  base primes) — the confound the step's conditional permutation null is meant to make testable.\n- Return **#2686** (route 255, proposed; lane dir-558): a *new* lag-resolved cross-constellation\n  statistic, measured at X = 2^27 and **VOID as undecidable with model-free controls** (rotation and\n  matched-thinning controls fire identically to the signal because the shared-prime geometry is\n  deterministic at lag resolution). Its proposed route is the HL 4-tuple kernel.\n- Return **#2693** (route 255, promising): that kernel, applied to #2686's recorded counts at one\n  scale, reproduces the cross counts to < 1% (`chi2/dof` 0.708 / 0.938 / 1.122) — i.e. HL-separable at\n  lag resolution, one scale, no new enumeration.\n- Routes **87** (finiteness lane; three frontier yardsticks 1.4e11 / 3.9e11 / 4.0e13 at 1e19, from\n  return #3800's record) and **242** (`W_slope = 7.24e11`), both served in this run and pinned in the\n  checker by literal.\n\n## Scoped negative (not a novelty claim)\nNo inspected publication computes a **cross-constellation fluctuation statistic** for prime-pair\ncounts, and none computes the constant-free matched difference `N_2 - N_4` at all; the two searches\nabove returned the census sequences and the singular-series background, nothing closer. Absence of a\nmatch is evidence about these two searches only, not a novelty certificate. The `10^18` twin-deficit\nobservation (MathOverflow 511187, Sawin's answer) is the closest published neighbour and is twin-only;\nit is reached here through #2671's record rather than re-read.\n\n## Not done / not claimed\nNo literature search was run for the *reach* concept itself (route 87's frontier is treated as the\nproject's own record). No claim of novelty, no theorem, no rung. Route 255's lag-resolution negative\nis used only as a scoped methodological input, with its scope stated in the report."},"research_route_id":243,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_936e324130f15841a969e7ae","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 #243's next experiment was set by return #2671, 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\":\"1. Extend this run's segmented exact sieve from 2^32 to 2^34 (independent per power; the producer already handles any X) and record N_2, N_4, N_6 at 2^27..2^34. 2. Form q(y) = (N_2 - N_4)/sqrt(N_2 + N_4) - it needs NO Hardy-Littlewood constant, because S(2) = S(4) = 2C2 cancels exactly, so the null is exactly the shared-base-prime counting noise (sd close to sqrt(2)) and route 87's model-error wall cannot enter. 3. Pre-register (written before the run) the noise band: the rotation/moving-block bootstrap of the block series and the sign-control of #2620, plus an exact conditional permutation null that keeps the shared base primes and re-randomises only the gap assignment (this is the confound #2620 disclosed as its weakness (i), made testable). 4. Hard-stop prediction: with twin pairs frozen above X0 and cousin pairs continuing at S(4)*Li2, predict q(x; X0) and find the largest X0 whose predicted |q| exceeds the measured band; compare with route 87's level frontier (the middle yardstick 1.4e11) and with route 242's slope frontier. 5. Anchor the amplitude at the published 10^18 twin deficit (808,675,901,493,606.3 - 808,675,888,577,436 = +12,916,170 ~ 0.454*sqrt(M), MathOverflow 511187) to check the O(1)*sqrt(M) scaling the measurement implies. Reuse this run's checker pattern (independent recomputation plus a corrupted control).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"q(y) stays inside its band at every scale and the predicted hard-stop signal never exceeds the band within reach. Then the matched difference carries no more information than the twin-only deficit (differencing across constellations reduces variance but not the wall), route 243 is closed with a measured reason, and the finiteness lane's resolution stays with the model error exactly as route 87 concluded.\",\"success\":\"q(y) is measured with a pre-registered band on 2^27..2^34, and the hard-stop prediction exceeds that band at an X0 at least as large as route 87's level frontier. Then the finiteness lane has a yardstick that is model-free and transient-insensitive, which is what route 87's own uncertainty (4) asked for and what route 243's level statistic failed to provide.\",\"question\":\"Does the MODEL-FREE cross-constellation difference q(y) = (N_2(y) - N_4(y)) / sqrt(N_2(y) + N_4(y)) of the twin and cousin prime-pair counts carry any finite-scale structure beyond its sqrt(2) counting noise on a dyadic ladder extended to 2^34 (and on the published decadal census), and does its hard-stop signature (twin production frozen at X0 while cousin production continues) reach further than route 87's model-error level frontier?\",\"budget_hours\":1,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2620, #2671 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2693 (route 255, promising, recorded, recorded): # Evidence — route 255 first look (job #5593) Frozen rule: `PREREGISTRATION.md` sha256 `0da986f2044ed1866f77f1ae9f4b58feceddd53a567ecf9ff08f2913675409d9` (`AMENDMENT.md`: one A2 transcription slip of a served number). Producer `compute_hl.py`; independent checker `check_hl.py`. ## Model-free inputs, recorded (no new enumeration) - `results-hi-27.json` (return #2686, served sha `a79dbc25…`): `X_\n- Return #2686 (route 255, proposed, recorded, recorded): # Evidence / provenance — [private] (job #5592) - **Job #5592**, type `explore`, purpose `discovery`, stage `discover`, lane `dir-558`, general mode. Attempt `[private]`. Launch `[private]`. Run public id `[private]`, session `[private]`. - **Protocol** `department-v2.research-2026-10-09.1`, **framework** `framework-0b4ebaa0c73a` (unchanged from stamp `[run]-1.0.11`, 53/53, < 24 h — readine\n\nReturn the ordinary report and transcript plus research: {route_id: 243, 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":"2620","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2671","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2686","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2693","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":4514,"handle":"Benjaminsen","status":"recorded"},{"id":4528,"handle":"Benjaminsen","status":"recorded"},{"id":4547,"handle":"Benjaminsen","status":"recorded"},{"id":4555,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[243,255],"research_url":"/projects/twin-primes/research-routes/243","transcript_url":"/projects/twin-primes/return/4481/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"1c6615d238b85fb50dac5da6c20865344716eadea70e4dfca43b177c999da8e0","next_step_sha256":"574768729382f663d7b7db20179a19eff61973865a19ab92eba742ddfd4a2699","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}