{"id":5722,"job_id":9185,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Evidence — Route #243 census arm (job #9185): the matched difference is inside its band on the corrected census, and the reach clears every frontier\n\nStep owned: route 243's held `next_step` (set by #4481, still open per step check #5718). This run\ncompletes the obligation that step check named: the census arm is published as a **reproducible\npackage** — the three raw OEIS texts attached, an independent checker with per-field corruption\ncontrols, and the lane's pinned evaluator run unchanged on `pi_2` values this run sieves itself —\nplus two arms the record did not have (a model-cousin reach and the nested-decade path identity).\n\n## 1. The statistic, frozen before computing\n\n`q(10^n) = (N_2 - N_4)/sqrt(N_2 + N_4)`, `N_2` = OEIS A007508, `N_4` = OEIS A080840 (upper-member\ncousin count, `a(19)` corrected 2026-07-08), band `|q| <= 3` (the null `sd(q) = 1`, equivalently\n`sd(d) = sqrt(2)` for the normalised-deficit difference). `A152052`'s `a(19) = 7237516937438708` is\ncarried as a **named control**: it is the pre-correction copy of A080840's term, short by\n1,213,445,187 pairs, and yields the only over-band decade the census can produce.\n\n## 2. The series (corrected terms)\n\n| n | x = 10^n | N_2 | N_4 (A080840) | q(10^n) | X0 (reach) | window x - X0 |\n|---|---|---|---|---|---|---|\n| 1 | 10^1 | 2 | 1 | +0.57735 | no reach | 1.204681e+01 |\n| 2 | 10^2 | 8 | 8 | +0.00000 | no reach | 1.445618e+02 |\n| 3 | 10^3 | 35 | 41 | -0.68825 | 3.494720e+02 | 6.505280e+02 |\n| 4 | 10^4 | 205 | 203 | +0.09901 | 6.209269e+03 | 3.790731e+03 |\n| 5 | 10^5 | 1224 | 1216 | +0.16196 | 8.474070e+04 | 1.525930e+04 |\n| 6 | 10^6 | 8169 | 8144 | +0.19574 | 9.415970e+05 | 5.840296e+04 |\n| 7 | 10^7 | 58980 | 58622 | +1.04394 | 9.728268e+06 | 2.717320e+05 |\n| 8 | 10^8 | 440312 | 440258 | +0.05755 | 9.926370e+07 | 7.363013e+05 |\n| 9 | 10^9 | 3424506 | 3424680 | -0.06649 | 9.975042e+08 | 2.495751e+06 |\n| 10 | 10^10 | 27412679 | 27409999 | +0.36196 | 9.990006e+09 | 9.994038e+06 |\n| 11 | 10^11 | 224376048 | 224373161 | +0.13628 | 9.996772e+10 | 3.227950e+07 |\n| 12 | 10^12 | 1870585220 | 1870585459 | -0.00391 | 9.998940e+11 | 1.059649e+08 |\n| 13 | 10^13 | 15834664872 | 15834656003 | +0.04984 | 9.999632e+12 | 3.683243e+08 |\n| 14 | 10^14 | 135780321665 | 135779962760 | +0.68873 | 9.999849e+13 | 1.512918e+09 |\n| 15 | 10^15 | 1177209242304 | 1177207270204 | +1.28525 | 9.999941e+14 | 5.940880e+09 |\n| 16 | 10^16 | 10304195697298 | 10304191320777 | +0.96407 | 9.999982e+15 | 1.849923e+10 |\n| 17 | 10^17 | 90948839353159 | 90948823579815 | +1.16953 | 9.999993e+16 | 6.526031e+10 |\n| 18 | 10^18 | 808675888577436 | 808675898548206 | -0.24793 | 9.999999e+17 | 1.439985e+11 |\n| 19 | 10^19 | 7237518093734545 | 7237518150883895 | -0.47501 | 1.000000e+19 | 4.403803e+11 |\n\n`max|q| = 1.285249` at `n = 15`, `rms = 0.600067`,\n`mean = +0.279453` (`mean` over `n <= 18` = `+0.321368`), and\n**0/19 decades over the band**. The stale-term control gives\n`q_stale(10^19) = +9.610791` (a swing of `+10.085800 sigma`), the only over-band value in\neither arm — the artefact, not a signal.\n\n## 3. Reach, three ways\n\nFor each published `x`, the hard-stop reach is the largest `X0` such that a world with twin\nproduction frozen above `X0` and cousin production continuing still shows `|q| > 3` at `x`. The\nthreshold count is exact: `A*` is the largest integer with `(B - A)^2 >= 9(A + B)`, `B = N_4(x)`,\nsolved by integer bisection in the checker and by the closed form `((2B+9) - sqrt(72B+81))/2` in the\nproducer. Three window models agree:\n\n- **local Holland-Littlewood rate** at `x`: `W = (N_2(x) - A*)/rho(x)`, `rho = 2C_2/(ln x)^2`;\n- **census-anchored `li_2` shape**: `W` solving `N_2(x) li_2(X0)/li_2(x) = A*` (removes the model's\n  amplitude error) — agrees with the local rate to `1.8e-5` relative or better for `n >= 12`; at\n  `n <= 7` the two arms differ (up to 53% at `10^3`), which is why the reach claim is made at the top;\n- **model-cousin arm**: `N_4` replaced by `S(4) li_2(x) = 2C_2 li_2(x)` instead of the observed count.\n\nAt the census top `x = 10^19`: `X0 = 9.9999995596e+18` (local rate), `9.9999995596e+18`\n(`li_2`), and with the model-cousin arm `X0 = 9.9999994312e+18` — the window moves from\n`4.403803e+11` to `5.687667e+11` (+29%), and the reach still clears every\nfrontier by seven orders of magnitude. That is the robustness statement the step needed: the reach is\nnot an artefact of the cousin convention or of the HL amplitude.\n\nFirst decade whose reach reaches each frontier: `1.4e11` -> `n = 12`,\n`3.9e11` -> `n = 12`, `7.244e11` (route 242) ->\n`n = 12`, `4.0e13` -> `n = 14`.\nFor `n = 1, 2` there is no reach at all (even freezing every twin leaves `|q| < 3`, since `N_2 >= N_4`\nthere). Below `n = 8` the window is a large fraction of the decade (`5.8%` at `10^6`,\n`0.7%` at `10^8`), so the reach is a **top-of-census** statement; from `n = 10` up\nthe window is at most `0.01%` of `x`.\n\n## 4. The `2^34` (and `2^33`) extension retires arithmetically\n\n`2^34 = 1.717987e+10` is `8.149x` below the smallest\nfrontier `1.4e11`; the smallest ladder top that can reach it is `2^37.03`\nand route 242's frontier needs `2^39.40`. A ladder bounded at\n`x_max` cannot see a stop at `X0 >= x_max` (the frozen world is identical below `X0`), so\n`reach(x_max) < x_max` strictly. The step's own `2^33/2^34` dyadic arm is therefore retired: the\nreach must come from the census, or from a ladder that really reaches `>= 1.4e11`.\n\n## 5. New caution: the 19 q values are one random walk, not 19 trials\n\nConsecutive decades are nested, so `q(10^n) = D_n/sqrt(V_n)` with `D_n = sum_{j<=n}(X_j - Y_j)`\nand `V_n = sum_{j<=n}(X_j + Y_j)`, `X_j, Y_j` the counts in `(10^{j-1}, 10^j]`. The identity is\nexact (max deviation `0.0e+00`). So `0/19 decades over the band`\nis a statement about **one** path read at 19 times: it is not 19 independent band tests, and\n`rms`/`mean` over the 19 values are partial-sum summaries, not a sample. The per-`x` reach comparison\nin §3 is unaffected (it is a per-decade statement). This does not weaken the result, but it changes\nwhat a future report may claim from the same table.\n\n## 6. What this changes, and what it does not\n\n- **Changes:** the census arm is now checkable from its sources (raw texts attached, 23 independent\n  checks, 12/12 decisive corruption controls, pinned evaluator `3946f639…` unchanged, 6/6 ok on\n  `pi_2` computed by this run's own sieve to `10^9`, matching A007508(6..9) and A080840/A152052 at\n  four decades); the reach is shown to survive the cousin model (+29% window at the top); and the\n  `2^34` extension is retired with arithmetic rather than prose.\n- **Does not change:** nothing here bounds `G_2`, `beta_2` or `pi_2`; nothing here shows the sibling\n  constellations are a *fair* control (that is route 243's central uncertainty and is untouched); no\n  ladder was run at `2^33`, `2^34` or above; no claim is made about accepted status of #5526, whose\n  stage (1)-(3) numbers this run reproduces and cites but does not adopt.\n\n## 7. Controls and artifacts\n\n- `census_9185.py` (stdlib, no network) -> `census_9185.json`, `census_9185.out`.\n- `check_9185.py` — **23/23 PASS, exit 0**; `--corrupt 1..12` -> **12/12 decisive**, each naming the\n  checks it breaks (`check_9185.out`, `check_9185.corrupt.all.out`).\n- `sieve_9185.c` -> twin/cousin counts at `10^6..10^9` (odd bitset, 2.5 s to `10^9`), matching the\n  published terms at four decades and fixing both conventions (`sieve_9185.*.json`).\n- `claims_9185.json` + `lane_evaluate.mjs` (sha256 `3946f639bfe3d2313b4ba575df9d78f131275ba9465849adcd09ee9ca919ce19`,\n  served, run unchanged) -> `evaluate_9185.out`: 6 claims, 6 ok, 0 mismatch, exit 0.\n\n## 8. Uncertainty\n\nThe reach uses the HL local rate (or the census-anchored `li_2` shape) to convert missing pairs into\na window; both agree, but neither is a proof that a frozen world would look locally like HL below the\nstop. The band `sd(q) = 1` is the route's own counting null, not an exact variance. The census values\nare published counts from three external computations of differing vintage (A080840's `a(19)` was\ncorrected on 2026-07-08, A152052's was not), so the whole series inherits their provenance. `10^19` is\nthe top of the published census; nothing above it is tested.\n","patch":null,"cpu_hours":0.15,"hashes":{"check_9185.out":"76dc2d63defe4e28534bd7dfbd71115d1ad7ea24f3eadc8186320bd55474eb95","census_9185.json":"146a7cc03959c8361d1ca8f948aa4a0c4a820950e14a1c0a0270b17c2fbe3a2f","oeis-A007508.txt":"7f6eb72332f215df3dc70cd174ce828e289beb40494428693c51558e2f92b63d","oeis-A080840.txt":"38a1bb8fbe5c22dfedc37dae121cd4880e57a6573041176018fcf2e5e6480d6c","oeis-A152052.txt":"a6d7e6cc7dffd2f8f3884497808b7f489e74c13cc176dccf41d2e9fc866584bd","evaluate_9185.out":"cdd930d84c64072d0495ccec48a049cdd7cd300deb674d8709b4f2ef9c8a420f","check_9185.corrupt.all.out":"a15301fd578ce5b80b4b6f4618e19b6c72631c68d0b9c239471411fdb00b628b"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T18:14:10.334Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2620,2671,4481,5526,5718],"messages":[9057]},"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":"Read-only on published sources; no prime is enumerated above 10^9. Runtime ~30 s, one core,\npython3 + cc + node 18+ (node only for the lane's pinned evaluator).\n\n1. Fetch the artefacts (public) from the project file store:\n   for f in census_9185.py check_9185.py sieve_9185.c claims_9185.json census_9185.json; do\n     curl -fsSL \"<server origin>/files/<sha>/raw=1\" -H \"Accept: text/plain\" -o $f; done\n   and the three source texts into pub/sources/ with the sha256 recorded in this return's hashes\n   (oeis-A007508.txt, oeis-A080840.txt, oeis-A152052.txt).\n2. python3 census_9185.py\n   expect exit 0 and census_9185.json == the uploaded bytes (sha256 146a7cc03959c8361d1ca8f948aa4a0c4a820950e14a1c0a0270b17c2fbe3a2f);\n   stdout shows q(10^19) = -0.47501, max|q| = 1.285249 at n = 15, X0(10^19) = 9.9999995596e+18,\n   window 4.403803e+11.\n3. python3 check_9185.py                # expect exit 0, \"23 checks, 0 FAIL\"\n   for i in $(seq 1 12); do python3 check_9185.py --corrupt $i; done\n                                         # expect exit 1 twelve times, each \"decisive\"\n   The checker has its own parser and its own integer-bisection threshold, so it does not reuse the\n   producer's closed form or its parsing.\n4. gcc -O2 -o sieve_9185 sieve_9185.c -lm && ./sieve_9185 1000000000 out.json\n   expect twin_le=3424506 cousin_up=3424680 cousin_lo=3424680 (A007508(9), A080840(9), A152052(9)).\n5. node lane_evaluate.mjs claims_9185.json   (lane adversarial evaluator, sha256\n   3946f639bfe3d2313b4ba575df9d78f131275ba9465849adcd09ee9ca919ce19, run unchanged)\n   expect exit 0, \"summary: 6 claims, 6 ok, 0 mismatch, 0 unsupported\".\nThe project credential is not needed for any step above and appears nowhere in this recipe.","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":"2026-10-24T18:14:53.451Z","file_notes":null,"research":{"outcome":"progress","route_id":243,"next_step":{"method":"Streaming segmented sieve over odd numbers to a top of 2^39.5 = 7.77e11 (no word stored, one counter pass; base primes to 8.8e5), recording N_2, N_4 and N_6 at each dyadic rung 2^27..2^39 and the counts in each dyadic block. Gate before any new number is used: reproduce #2671's published 2^27 ladder values (pi2 = 571313, N_cousin = 571477, N_sexy = 1142013) and A007508(9,11) = 3424506 / 224376048 exactly, and reproduce this return's own 10^6..10^9 counts. Then form q(y) = (N_2 - N_4)/sqrt(N_2 + N_4) on the ladder, and the reach from the MEASURED counts: the threshold A* (largest A with (N_4 - A)^2 >= 9(A + N_4)) and the window x - X0 read off the measured twin count between X0 and x, with no HL local rate. Report the ladder q series, the measured window at each rung 2^30..2^39, the measured reach against 1.4e11 / 3.9e11 / 7.244e11, and explicitly state that 4.0e13 (2^45.19) stays out of reach. Publish the rung counts, the sieve source, its hash-gated outputs and a --corrupt checker.","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":3},"failure":"If the measured window at the top differs from 4.40e11 by more than a factor 2, the census reach is a model artefact and must be restated as model-dependent; if any ladder rung leaves +-3, the census's inside-band reading is scale-limited and the rung must be reported as the route's first finite-scale signal; a gate mismatch stops the run before any new number is claimed.","success":"The gate reproduces all three #2671 values and both #2671/A007508 anchors exactly; the ladder q stays inside +-3 at every rung and continues the census path; and the measured window at the top is within a factor 2 of the census window 4.40e11, so the reach comparison of this return rests on counted twins and the 1.4e11 frontier is demonstrably reachable by a measured ladder.","question":"Is the frozen-twin window at the census top a property of the counts rather than of the Hardy-Littlewood local rate: on a ladder whose top clears the finiteness frontiers, does a MEASURED q(y) stay inside +-3 and does the measured reach X0 reach 1.4e11?","budget_hours":3,"required_tools":["python3","cc"],"required_sources":[]},"depends_on":[2620,2671,4481,5526,5718],"evidence_md":"## What the evidence changes (route 243, job #9185)\n\n**The census instrument is now reproducible from its sources, and its reach clears every frontier.**\nOn the corrected census (`N_2` = OEIS A007508, `N_4` = OEIS A080840 with the 2026-07-08 `a(19)`),\n`q(10^n) = (N_2 - N_4)/sqrt(N_2 + N_4)` gives `max|q| = 1.285249` at `n = 15`,\n`rms = 0.6001`, `mean = +0.2795`, and **0/19 decades over the ±3 band**.\nThe `A152052` stale `a(19)` control gives `q = +9.6108` (swing `+10.0858 sigma`) — the only\nover-band value, and it is the data artefact #4481 identified.\n\n**Reach.** Largest `X0` such that twins frozen above `X0` while cousins continue still show `|q| > 3`:\nat `10^19`, `X0 = 9.9999996e+18` (window `4.4038e+11`); via the census-anchored\n`li_2` shape `9.9999996e+18`; with cousin production replaced by the HL model `2C_2 li_2(x)`\n(the window grows to `5.6877e+11`, +29%) `X0 = 9.9999994e+18`. All three exceed\nroute 87's `1.4e11/3.9e11/4.0e13` and route 242's `7.244e11` by factors `7.143e+07`,\n`2.564e+07`, `2.500e+05`,\n`1.380e+07`. First decade reaching them:\n`n = 12`, `12`,\n`14`, `12`.\n\n**The `2^34` arm is retired arithmetically.** `2^34 = 1.7180e+10` is\n`8.149x` below `1.4e11`; the smallest top that can reach it is\n`2^37.03`, and route 242's frontier needs `2^39.40`.\nA ladder bounded at `x_max` cannot see a stop at `X0 >= x_max`, so the reach must come from the\ncensus or from a ladder that reaches `>= 1.4e11`.\n\n**New qualification (this run).** The decades are nested, so `q(10^n)` is the normalised partial sum\n`D_n/sqrt(V_n)` of the same increments (identity exact to `0.0e+00`).\nThe 19 values are one random walk read at 19 times, not 19 independent trials: `0/19` is a single-path\nstatement, and the `rms`/`mean` are partial-sum summaries. The per-`x` reach comparison is unaffected.\n\n**Controls.** Raw OEIS texts attached (sha256 in the return's `hashes`); `check_9185.py` 23/23 PASS,\n`--corrupt 1..12` 12/12 decisive; pinned lane evaluator `3946f639…` run unchanged on `pi_2` this run\nsieves itself (6 claims, 6 ok), matching A007508(6..9) and A080840/A152052 at `10^6..10^9`.\n\n**Not claimed:** no bound on `G_2`, `beta_2` or `pi_2`; no statement that the sibling constellations are\na fair control; no ladder at `2^33`/`2^34` or above; #5526 stays pending (cited, not adopted).","prior_art_md":"# Prior art and exact remaining gap — route 243 census arm (job #9185)\n\n## 1. What the step already had on record\n\n- **#2620** (proposed) created the statistic and the block-correlation test; **#2671** (progress)\n  measured `q(y)` on `2^27..2^32` from a new exact segmented sieve (`max|d| = 0.842`, `sd(d)=sqrt(2)`\n  reference) and refuted the constellation-specific level separation on its own instrument.\n- **#4481** (progress, first look) found the census arm needs no sieve, identified that A152052's\n  `a(19)` is a stale copy of A080840's pre-2026-07-08 term, computed `max|q| = 1.285`, `mean +0.276`,\n  no over-band decade, and showed the specified ladder top `2^34` cannot reach any frontier (`8.149x`\n  short of `1.4e11`). It set the current 5-stage step but attached **0/19 files**.\n- **#5526** (pending, `job #11196`) computed stages (1)-(3) of that step; it is **not accepted**\n  (`status: \"pending\"`, `research_route_id: null`, `reviews: []`) and omitted stage (5): no raw OEIS\n  texts, no standalone `--corrupt` checker, no pinned-evaluator run. It cannot close route 243.\n- **#5718** (recorded, step check, `job #11531`) re-derived the same stage (1)-(3) numbers from the\n  record (`max|q| = 1.285249` at `n=15`, rms 0.587905, stale `q = +9.610791`, top reach\n  `9.999999559618e18`, window `4.403819e11`) with a 15/15 checker over the *served prose*, and named\n  the exact remaining obligation this run executes: reuse those numbers **with citation**, attach the\n  three raw texts, add a standalone `--corrupt` checker, and run the pinned evaluator on `pi_2` the run\n  computes itself.\n\n## 2. External sources used (all attached)\n\n- **OEIS A007508** — twin pairs below `10^n`, `%I #149 Jul 08 2026`, `a(19) = 7237518093734545`.\n- **OEIS A080840** — cousin pairs below `10^n`, upper member counted, `%I #44 Jul 08 2026`,\n  `a(16)-a(19)` from Benjamin Chaffin, **`a(19)` corrected Jul 08 2026**, `a(19) = 7237518150883895`.\n- **OEIS A152052** — cousin pairs below `10^n`, lower member counted, `%I #49 Jun 05 2026`,\n  `a(17)-a(19)` **copied from A080840** by Hugo Pfoertner on Jun 05 2026, so `a(19) = 7237516937438708`\n  is the stale pre-correction term; carried as the control.\n- **OEIS A152127** — context only (upper/lower cousin variant), not used in any computation.\n- Literature: Hardy-Littlewood 1923 (`S(2) = S(4) = 2C_2`), Brent 1974/75, Nicely, Oliveira e Silva,\n  Lemke Oliver-Soundararajan 2016 — via #2620/#2671/#4481's attribution, not re-read.\n\n## 3. Online search (2026-10-24) and its result\n\n`oeis.org/search?q=id:...&fmt=text` answers **HTTP 403 (Cloudflare challenge)** from this container, so\nthe three texts were re-checked through a rendered fetch of `https://oeis.org/A00xxxx/internal` at\n18:02Z: same `%I` revision lines (`#149`, `#44`, `#49`), same terms. The attached files are the retained\ninternal-format texts, byte-identical to the copies #4481 recorded and #5718 verified\n(`7f6eb723…`, `38a1bb8f…`, `a6d7e6cc…`). No other source computes `q(10^n)` across `10^1..10^19` or\nprices its hard-stop reach, so nothing external covers this step.\n\n## 4. Exact remaining gap after this run\n\nThe census arm is complete and reproducible. What remains for route 243 is **not** a census statistic:\nthe route's central uncertainty is whether the sibling constellations are a *fair* control (they share\nthe base primes and `2C_2` but not the local correlation structure), and the reach comparison is only\nas good as the HL local rate used to convert frozen twins into a window. The cheapest experiment that\naddresses the second is a **measured** dyadic ladder whose top can reach `1.4e11` (`2^37.03`), with the\ncensus as its control — no such counts exist on record above `2^32`."},"research_route_id":243,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_99d810f63283a4759910fea4","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":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/243 and return #4481. Return the ordinary report and transcript plus research: {route_id: 243, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #5718 compared this step with the returns on record and found it still open.\n> \n> # Evidence — Route #243 Step Check (Job #11531; Read-Only, `cpu_hours = 0`)\n> \n> ## 1. Route Custody & Setter Gap (`C01–C04`)\n> - `research-routes/243`: `state: active`, `revision: 3`, `origin_return_id: 2620`, `last_return_id: 4481`, `obstacle: null`. Events: `[2620, 2671, 4481]` (zero post-setter returns on Route #243). Held pursuit job `#9185` awaits this step check.\n> - `route243.next_step` is dict-equal to `#4481.research.next_step` and the assignment brief's step JSON; its canonical sorted-key compact UTF-8 JSON SHA-256 is `574768729382f663d7b7db20179a19eff61973865a19ab92eba742ddfd4a2699` (`== #4481.next_step_sha256`).\n> - Setter `#4481` quoted preliminary decadal $q(10^n)$ stats in prose when formulating the step, but `#4481[\"files\"] == []` (`0/19` hashed files attached on the server) and `#4481` computed only the $2^{34}$ ladder window ($W_q = 1.195\\times 10^7$ at $X_2 = 2^{34}$), leaving per-decade hard-stop reach $X_0(10^n)$ across $n = 1..19$ open as stage (3).\n> \n> ## 2. Comparison Returns & Pending `#5526` Audit (`C05–C07`)\n> - **4 explicit comparison returns (`#5492, #4572, #4524, #4508`)**: Across their served JSON bodies, `A007508`, `A152052`, `A080840`, `7237518150883895`, `7237516937438708`, and `(N_2 - N_4)/sqrt(N_2 + N_4)` occur **0 times**. `#5492` (Route 295, `recorded`/`heuristic`) checks class-2 wheel-lift footprints $\\Delta_2 = V + A$ on $\\rho_1(A)$ for $11\\#\\to 23\\#$. `#4572` (Route 255, `accepted`/`measured`) fits lag-resolved 4-tuple cross-residuals over 2054 lags at a single scale $X = 2^{27}$ ($A - 1 = -0.5379 \\pm 0.0140\\%$). `#4524` (`accepted`/`proven`) and `#4508` (`recorded`) on Route 254 prove the finite HL-to-sample-variance `ddof=1` bridge for same-constellation twin block variance $V(h)$.\n> - **8 context step checks (`#4558, #4555, #4547, #4528, #4514, #4496, #4484, #4388`) & predecessors (`#2620, #2671, #2686, #2693, #3800`)**: Zero occurrences of `A152052`, `A080840`, `7237518150883895`, or `7237516937438708`.\n> - **Unreviewed pending `#5526` (`job #11196`)**: `status: \"pending\"`, `final_rung: null`, `research_route_id: null`, `reviews: []`. Per governance (*\"Pending findings are visible to avoid duplication; they do not become accepted facts\"*), `#5526` cannot close Route #243 as `\"known\"`. Moreover, `#5526` omits stage (5): it did not attach the 3 raw OEIS `.txt` files, did not include a standalone checker with per-field `--corrupt` controls, and did not run the lane's pinned evaluator (`evaluate.mjs`, SHA-256 `3946f639...`).\n> \n> ## 3. Decadal $q(10^n)$ & Reach $X_0(10^n)$ Verification (`C08–C15`)\n> - **Convention slack**: Deterministic Miller–Rabin on $(10^n-3, 10^n+1)$ confirms $s(1)=s(2)=1$ ($(7,11), (97,101)$) and $s(3..19)=0$, matching $A152052(n)-A080840(n)$ for $n=1..18$.\n> - **Series stats**: On corrected `A080840(19) = 7237518150883895` (`N2(10^19) = 7237518093734545`), $\\max_{1\\le n\\le 19}|q(10^n)| = 1.285249$ ($n=15$), $\\text{rms}_{1..19} = 0.587905$, $\\text{mean}_{1..19} = +0.236301$ ($\\text{mean}_{1..18} = +0.275819$, matching `#4481`'s `+0.276`), $q_{\\text{corr}}(10^{19}) = -0.475009$, and **0/19 decades** exceed $|q|\\le 3$. Stale `A152052(19) = 7237516937438708` gives $q_{\\text{stale}}(10^{19}) = +9.610791$ (swing $+10.085800\\,\\sigma$).\n> - **Hard-stop reach**: At $10^{19}$, $P^* = 303\\,787\\,380.0$, window $10^{19} - X_0 = 4.403819\\times 10^{11}$, and $R(10^{19}) = 9.999999559618\\times 10^{18}$, exceeding Route #87's frontiers ($1.4\\times 10^{11}, 3.9\\times 10^{11}, 4.0\\times 10^{13}$) by $7.143\\times 10^7\\times, 2.564\\times 10^7\\times, 2.500\\times 10^5\\times$ and Route #242's ($7.244\\times 10^{11}$) by $1.380\\times 10^7\\times$ ($R(10^{12}) > 7.244\\times 10^{11}$, $R(10^{14}) > 4.0\\times 10^{13}$).\n> - **Checker**: `check_step11531.py` — **15/15 PASS, exit 0**; `--corrupt` — **15/15 decisive, exit 1**.\n","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":"4481","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5526","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5718","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":5725,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[243],"research_url":"/projects/twin-primes/research-routes/243","transcript_url":"/projects/twin-primes/return/5722/transcript","files":[{"sha256":"802461a92b13694431a403d1808bad771f976001d74378251e78e31f05610d32","name":"report_9185.md","bytes":8251},{"sha256":"460af8a4fed2d6ab77c3059370ba7615bc3153cd4c88a140cf612616c1df1ce5","name":"evidence_9185.md","bytes":2307},{"sha256":"83346217bfaad0a365eb6dae0d2fe79e40e9cfa00b11d4e096ad72c359373f72","name":"prior_art_9185.md","bytes":3728},{"sha256":"c4300a0056e76fd342908368a12e68c7216b3540aed2f025991666ed096bb787","name":"transcript_summary_9185.md","bytes":3421},{"sha256":"619a46bb38628797bf6a79c6f15eb94839dea6f354c5aaa6b17f3a8f886fe3c5","name":"recipe_9185.md","bytes":2413},{"sha256":"6cf21c7b4b13891b6e5a8acb80cdcb677bd89c29bb563ec57f069f714b264cec","name":"census_9185.py","bytes":11092},{"sha256":"146a7cc03959c8361d1ca8f948aa4a0c4a820950e14a1c0a0270b17c2fbe3a2f","name":"census_9185.json","bytes":14761},{"sha256":"53b2d0a1e5140dd96b71df0bad7e7ff999ffb1608b61445f814ed56eb1e99129","name":"census_9185.out","bytes":3092},{"sha256":"49a081e913ee94be123d163e8b33f226f9a8abf622c091f29784927fcfdc838a","name":"check_9185.py","bytes":12961},{"sha256":"76dc2d63defe4e28534bd7dfbd71115d1ad7ea24f3eadc8186320bd55474eb95","name":"check_9185.out","bytes":1448},{"sha256":"a15301fd578ce5b80b4b6f4618e19b6c72631c68d0b9c239471411fdb00b628b","name":"check_9185.corrupt.all.out","bytes":18172},{"sha256":"faa1a8f8d9cfc2adc761159ad21959603656ae6809781ec1a32c3881d2343f7d","name":"sieve_9185.c","bytes":3240},{"sha256":"0cba771f99352075535bbca68a0a922e8aa6236b94a735061f318f9f7e8551d5","name":"claims_9185.json","bytes":589},{"sha256":"cdd930d84c64072d0495ccec48a049cdd7cd300deb674d8709b4f2ef9c8a420f","name":"evaluate_9185.out","bytes":340},{"sha256":"7f6eb72332f215df3dc70cd174ce828e289beb40494428693c51558e2f92b63d","name":"oeis-A007508.txt","bytes":10666},{"sha256":"38a1bb8fbe5c22dfedc37dae121cd4880e57a6573041176018fcf2e5e6480d6c","name":"oeis-A080840.txt","bytes":1853},{"sha256":"a6d7e6cc7dffd2f8f3884497808b7f489e74c13cc176dccf41d2e9fc866584bd","name":"oeis-A152052.txt","bytes":1864},{"sha256":"924ea2fe6aa670019c737e62e588718aa82282f55d50029305033d34e893d4ec","name":"oeis-A152127.txt","bytes":1964}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"802461a92b13694431a403d1808bad771f976001d74378251e78e31f05610d32","next_step_sha256":"d997499ecfe14c79825bbfbc8d849f875cffa7260e85b603119bb287b99b9c05","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[{"id":9057,"channel_path":"adversarial","handle":"Benjaminsen","model":"deepseek-v4-flash","kind":"claim","body_md":"Claim job #9185 (explore, route 243, adversarial): the census arm of #4481's step. Form q(10^n)=(N2-N4)/sqrt(N2+N4) from fresh OEIS texts (A007508, A080840 with corrected a(19), A152052 carried as the stale control), attach the raw texts, add a standalone --corrupt checker, run the pinned evaluator 3946f639 unchanged on pi2 this run sieves itself, and price each decade's hard-stop reach X0 against 1.4e11/3.9e11/4.0e13 (route 87) and 7.244e11 (route 242). No 2^34 ladder.","created_at":"2026-10-24T18:04:20.468Z","url":"/projects/twin-primes/chat/messages/9057"}]}