{"id":6879,"job_id":13621,"problem_id":1,"lane_id":32,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #13621 (route 228 first look / step check): the sieve-genericity Fano-gate step set by #5694 is still open — outcome `promising`, step returned unchanged\n\n**Scope.** Comparison only, per the brief (\"Read and compare; do not run the experiment and do not reproduce a computation a return already made\"). cpu_hours 0; no experiment run, no computation reproduced, no files attached.\n\n**Custody.** Served route 228 (authenticated helper read, saved-bytes sha256 `f47d335268b6056e7d3f4dd77597aab18b5f7dd9f369345528b5d7ec46f30d14`): `state` `active`, revision **8**, `origin_return_id` 2547, `last_return_id` **5694** (no route-228 return after it), obstacle unset, updated 2026-10-24T15:28:00.531Z. The served `next_step` has canonical SHA-256 **`0a1e584d0b601f0a5ba58f90f6baf8e85c96a46a85edbd28e39b8f75694172ad`** (canonical JSON: sorted keys, no whitespace); this brief's step object reproduces it exactly, so the step is unchanged since #5694 set it. Dependencies [2547, 2554, 2624, 4388, 4409, 4433, 5685] are all `recorded`.\n\n**Decisive-token census** (method of the route's own step check #5685, applied fresh): each compared return's complete served record was fetched by authenticated helper read and searched as a literal case-sensitive substring for the exact token list executed: `Fano`, `Var_all`, `Var(C`, `all-start`, `all start`, `G_2`, `G2`, `2.5e7`, `25000000`, `3137`, `1051`, `Buchstab`, `periodic`, `stationar`, `matched`, `F_stat`, `twin-count variance`, `window twin`, `interior window`, `u >= 2.5`, `density-drift`, `density drift`, `translation-invariant`, `±10`/`+-10`, `lucky`, `wheel`. Note `G_2`/`G2` are step-adjacent but also match the route-227 dial constant `G_2(x#)` and #5760's own disclaimer; under the stricter step reading `G_2(S)`/`G2(S)` there are zero hits in all five records.\n\n| return | route / job | status | distinct tokens / occurrences |\n|---|---|---|---|\n| #6806 | 307 / 11452 | pending | **0 / 0** |\n| #5967 | 255 / 11651 | accepted, proven | **0 / 0** |\n| #5760 | 255 / 9386 | accepted, measured | 3 / 10 (`G2` 1, `matched` 7, `wheel` 2) |\n| #5706 | 227 / 9025 | accepted, measured | 4 / 12 (`G_2` 8 = dial constant, `matched` 1, `window twin` 1, `wheel` 2) |\n| #5757 (cited evidence, after #5694) | 255 / 11632 | recorded | 3 / 7 (`stationar` 1, `lucky` 1, `wheel` 5) |\n\nThe lane's own state-of-the-art text (dir-558 version 46, as served in this brief) contains **zero** occurrences of `Fano`, `Var_all`, `all-start`, or `Buchstab` outside the route-228 description and step itself — no result on the lane has ever measured the step's objects.\n\n**What the later returns settle.**\n\n- **#6806** (route 307, job 11452, pending, gpt-6.1-sol): completes route 307's finite experiment on the `A+` twin-admissible packing construction — 33,208 constant-`A+` plateaus covering every integer in [46,000, 9,895,453], 2,060,345 residual-prime/plateau certificates, exact minimum of `g(x)=2|A+(x)|−π2(x)` equal to 34 on [53,281, 53,365], measured residual tail empty through 10^7. Its object is a construction's admissibility gain, not window statistics: no window twin-count variance, no lucky level word, no prime wheel, no Fano factor. Not an answer.\n- **#5967** (route 255, job 11651, accepted proven, gpt-6-astra): analytic repair of route 255's two-rung decision rule — explicit counterexamples (`R(X)=b/(log X)^2` gives `c20/c27=27/20` while `R20/R27=(27/20)^2`; a two-point interpolation agreeing with `c/log X` at both rungs without being `c/log X`), the 0.037 pp uncertainty identified as a same-height cross-pair contrast, and corrected contrast-variance formulas. Purely analytic on route 255's recorded ladder; no measurement, no lucky/wheel object. Not an answer.\n- **#5760** (route 255, job 9386, accepted measured, deepseek-v4-flash): recorded-data-only analysis showing the −0.53793% shared offset is one log⁴-normalisation correction shared with route 248's ladder (the two normalisation changes move it +0.00132 pp; window mass ≤1.49e-3 of the band; Euler tail deficit 1.772e-7; float32 noise ≤1.46e-11), with the 0.08 pp pair spread inside block error (2.17σ bootstrap, 95% interval contains zero). Its three token hits are its own disclaimer (\"Nothing here bears on the twin-prime conjecture, on `G2`, `beta_2` or `pi2`\"), route 255's \"20 matched lags\" ladder table, and route 255's step vocabulary (\"the FFT instrument and the wheel model\"). Not an answer.\n- **#5706** (route 227, job 9025, accepted measured, glm-5.3-flash): exact full-period bridge test at `x ∈ {11,13,17,19}`, κ ∈ {1,2}: the empty-window count `E(h)` is bounded by the gap-law tail (B2 ratio `E(h)/(q·P(D>h))` ∈ [0.199, 0.784] at all 19 deciding cells; identity `E(h)=Σ_j max(D_j−h,0)` exact at all 48 cells), and the certificate `min_{k≤64} M_2k(h) < mu^{2k}` at `h=x²` matches #1457's served `at_x2.k_true` 8/8; new side-A κ=2 gap moments (`Var/mu²` 0.30–0.45, kurtosis 2.87–6.42). This is the closest recorded statistic in spirit, but it is a different object: the **cyclic gap-length dispersion of the twin-site word at full period** `q=x# ≤ 9.7e6`, not the step's all-start interior-window twin-count variance `Var_all(C_S)` over windows `[S, N−S]`; measured on the wheel word only (no lucky word `W_ell`), with no Buchstab-drift/CRT split and no matched-density cross-set comparison. Its four token hits are the route-227 dial constant `G_2(x#) = 42, 66, 108, 150`, \"at matched rungs\", a prior-art screen naming #5665's route-307 single-window construction, and route 232's wheel-scale `K(h)` step. Not an answer.\n- **#5757** (route 255 step check, job 11632, recorded, gemini-4-argon): custody/decision check of #5760's evidence for route 255's step. Its `lucky`/`wheel` occurrences quote route 228's #5694 bug-fix note and route 255's own step text. Not an answer.\n\n**Why the step survives.** None of its three components is on record anywhere: (1) `Var_all(C_S)`, `F(S)=Var_all(C_S) over M(S)` and `G_2(S)` across the stationary grid `S ∈ [S*_pos(ell), 2.5e7]` for `ell ∈ {211, 1041, 3153}` and wheels `x ∈ {211, 1051, 3137}` — never computed (the route's own returns measured single-origin-window ratios `rho(S)`, not all-start window variance); (2) the Buchstab density-drift vs translation-invariant CRT periodic decomposition at `u ≥ 2.5`, `x=211/1051` — never attempted; (3) the matched-survivor-density ±10% `F_stat` test between `W_ell` and `W_wheel(x)` — never attempted. The step's success and failure clauses are both undecided.\n\n**In-flight coordination.** The queued jobs named in the brief (#13506 audit, #13471, #13466, #13435 route 232, #13409, #13408) are on other routes/topics; none is the route-228 Fano experiment. No duplication.\n\n**Outcome.** `promising`: the step is still open; it is returned unchanged (canonical sha `0a1e584d…`) and the held pursuit goes out with this note. One reusable observation for the successor, at the same rung as its source: #5706's exact big-integer moment instrument (`bridge227.py`, value-histogram central moments of a cyclic word) is a candidate building block for the wheel side's exact variance work, but the step needs the frozen N=1e8 engine (#4409/#4433/#9127) all-start window variance — the instrument does not transfer as-is.\n\n## Sources\n\n- Served route 228 via `sah.py read` (saved sha256 `f47d335268b6056e7d3f4dd77597aab18b5f7dd9f369345528b5d7ec46f30d14`).\n- Returns #6806 (`2abace5e1a1094bb2a74c9c2742db6ddeca6393954c0e4be0d4e4d1ff1d17c94`), #5967 (`ca5e098ef8814fccb4484ad0a4f739e712e26e214ef2b22ecc32dd733b40048b`), #5760 (`4ebb7a765703dc8990f30b2c3c3f5d7bc7afbf648dfcff763563eb33556b6799`), #5706 (`60674438b41ea13a4ac87ee811b31b0f869b9c530329140776f8bc280acf03ab`), #5757 (`4e290a988a90427276ed2b712214bd7400292ea726402fd45baaca70c9fef829`) via `sah.py read` (saved-bytes sha256 in parentheses).\n- The brief's served state-of-the-art (dir-558 v46) and route-228 description; department protocol department-v2.research-2026-11-03.1 saved locally with versions.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-11-04T07:51:29.230Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5757,6806,5967,5760,5706,5694],"messages":[]},"tokens":{"log":"summary","input":156934,"models":{"glm-5.3-flash":59627},"output":59627,"source":"reported","entries":0,"cache_read":10123354,"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":"xhigh","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"promising","route_id":228,"next_step":{"method":"Using the frozen N = 1e8 engine from #4409, #4433, and #9127: (1) Across the stationary grid S in [S*_pos(ell), 2.5e7] for lucky levels ell in {211, 1041, 3153} and prime wheels x in {211, 1051, 3137}, compute the exact all-start window twin-count variance Var_all(C_S) over all interior windows t in [S, N - S] and form F(S) = Var_all(C_S)/M(S) and G_2(S) = (Var_all(C_S) - M(S))/M(S). (2) Decompose the prime wheel variance into its deterministic Buchstab density-drift component and its translation-invariant CRT periodic fluctuation component on post-trough windows u >= 2.5 at x = 211 and x = 1051. (3) Test whether the translation-invariant Fano factor F_stat(S) at matched survivor density agrees between W_ell and W_wheel(x) within +/-10%.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.5},"failure":"Finite-range Buchstab drift at N = 1e8 prevents isolating a stationary interior variance on the prime wheel even at shallow levels x = 211 and x = 1051, requiring exact periodic tile-Fourier evaluation rather than finite-N window sampling.","success":"Exact all-start and translation-stationary Fano curves F(S) and G_2(S) are measured across ell in {211, 1041, 3153} and x in {211, 1051, 3137} on S in [S*_pos(ell), 2.5e7], deciding whether window twin-count variance suppression (F < 1) on the stationary domain is sieve-generic or prime-wheel-specific once Buchstab drift is separated.","question":"Within the established stationary width domain S in [S*_pos(ell), N/2], is the window twin-count Fano factor F(S) = Var(C_S)/M(S) sieve-generic across lucky level words W_ell (ell in {211, 1041, 3153}) and prime wheel words W_wheel(x) (x in {211, 1051, 3137}), or does the prime wheel transition from sub-Poisson to super-Poisson across the Buchstab trough while W_ell stays sub-Poisson (F_ell ~ 0.20-0.24)?","budget_hours":1,"required_tools":["python3"],"required_sources":["4433","4409"]},"depends_on":[5757,6806,5967,5760,5706],"evidence_md":"## Custody (served records only; no experiment run, cpu_hours 0)\n\nRoute 228 served record (saved sha `f47d3352…`): `active`, rev **8**, `last_return_id` **5694**, obstacle unset, updated 2026-10-24T15:28:00.531Z. Served `next_step` canonical sha **`0a1e584d…`**; the brief's step object reproduces it byte-exactly — unchanged since #5694.\n\n## Census (method of #5685, fresh)\n\nFull served records of #5757, #6806, #5967, #5760, #5706 fetched fresh; each literal case-sensitive substring-searched with the exact executed token list: Fano, Var_all, Var(C, all-start, all start, G_2, G2, 2.5e7, 25000000, 3137, 1051, Buchstab, periodic, stationar, matched, F_stat, twin-count variance, window twin, interior window, u >= 2.5, density-drift, density drift, translation-invariant, +-10, ±10, lucky, wheel. Note the G_2 and G2 tokens also match the route-227 dial constant G_2(x#) and #5760's own disclaimer; under the stricter step reading G_2(S) or G2(S) there are zero hits in all five records. Every hit resolved in context.\n\n| return | route/job | decision | distinct tokens / occurrences | resolution |\n|---|---|---|---|---|\n| #6806 | 307/11452 | pending | 0 / 0 | — |\n| #5967 | 255/11651 | accepted proven | 0 / 0 | — |\n| #5760 | 255/9386 | accepted measured | 3 / 10 (G2 1, matched 7, wheel 2) | own disclaimer \"Nothing here bears on … G2, beta_2 or pi2\"; 20-matched-lags ladder table; route 255 step text (\"wheel model\") |\n| #5706 | 227/9025 | accepted measured | 4 / 12 (G_2 8 = dial constant, matched 1, window twin 1, wheel 2) | dial constant G_2(x#)=42,66,108,150; \"matched rungs\"; prior-art screen naming #5665; route 232 wheel-scale K(h) |\n| #5757 | 255/11632 | recorded | 3 / 7 (stationar 1, lucky 1, wheel 5) | quotations of route 228's #5694 note and route 255's step text |\n\nLane state-of-the-art (dir-558 v46, as served): **0** occurrences of Fano/Var_all/all-start/Buchstab outside route 228's own description.\n\n## What each return settles\n\n- #6806: route 307's finite A+ construction — 33,208 plateaus over [46,000, 9,895,453], exact min gain 34 on [53,281, 53,365]. Object: admissibility gain, not window variance.\n- #5967: analytic repair of route 255's two-rung rule (c20/c27=27/20 vs R20/R27=(27/20)^2 counterexample; two-point interpolation). No measurement.\n- #5760: −0.53793% = one log⁴-normalisation correction shared with route 248's ladder (identical to 8.1e-14); window/tail/float32 excluded (+0.00132 pp, ≤1.49e-3, 1.772e-7, ≤1.46e-11); pair spread 2.17σ, 95% CI contains 0. Recorded 4-tuple data only.\n- #5706: route 227 bridge test at x ≤ 19: B2 ratio ∈ [0.199, 0.784] at 19/19 deciding cells; identity exact 48/48; certificate at h=x² matches #1457 8/8; side-A κ=2 gap moments Var/mu² 0.30–0.45. Closest statistic in spirit but a different object: cyclic gap-length dispersion at full period q ≤ 9.7e6, wheel word only, no Buchstab/CRT split, no matched-density cross-set test; its exact big-integer cyclic-moment instrument is a candidate building block for the wheel side but does not transfer as-is (the step needs the frozen N=1e8 engine's all-start window variance).\n- #5757: route 255 step check verifying #5760; no route-228 content.\n\n## Step components not on record\n\n1. Var_all(C_S), F(S), G_2(S) across S ∈ [S*_pos(ell), 2.5e7], ell ∈ {211,1041,3153}, x ∈ {211,1051,3137}: never computed (the route's own returns measured single-origin ratios rho(S), not all-start variance).\n2. Buchstab drift vs CRT periodic decomposition at u ≥ 2.5, x=211/1051: never attempted.\n3. Matched-density ±10% F_stat test W_ell vs W_wheel(x): never attempted.\n\nBoth step clauses undecided → step open, returned unchanged (sha `0a1e584d…`). Queued jobs #13506, #13471, #13466, #13435, #13409, #13408 are on other routes; none duplicates the step.","prior_art_md":"Step check on the route's own served step (set by #5694, job 9127; canonical sha `0a1e584d0b601f0a5ba58f90f6baf8e85c96a46a85edbd28e39b8f75694172ad`). No new route or method is proposed, so no new online search was run and none is required by the brief; the route's served prior art (Gardiner–Lazarus–Metropolis–Ulam 1956 lucky-number sieve; Hawkins; Buchstab 1937; Hildebrand–Tenenbaum 1993; Montgomery–Soundararajan 2004; the route's returns #2547–#5694 and its declared dependencies) stands unchanged. The comparison is against served returns #5757, #6806, #5967, #5760, #5706 only; no external literature is relied on."},"research_route_id":228,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_af2bf113c60c560d67e005a5","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":"malaiwah","job_brief":"Step check before pursuit. Route #228's next experiment was set by return #5694, 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\":\"Using the frozen N = 1e8 engine from #4409, #4433, and #9127: (1) Across the stationary grid S in [S*_pos(ell), 2.5e7] for lucky levels ell in {211, 1041, 3153} and prime wheels x in {211, 1051, 3137}, compute the exact all-start window twin-count variance Var_all(C_S) over all interior windows t in [S, N - S] and form F(S) = Var_all(C_S)/M(S) and G_2(S) = (Var_all(C_S) - M(S))/M(S). (2) Decompose the prime wheel variance into its deterministic Buchstab density-drift component and its translation-invariant CRT periodic fluctuation component on post-trough windows u >= 2.5 at x = 211 and x = 1051. (3) Test whether the translation-invariant Fano factor F_stat(S) at matched survivor density agrees between W_ell and W_wheel(x) within +/-10%.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0.5},\"failure\":\"Finite-range Buchstab drift at N = 1e8 prevents isolating a stationary interior variance on the prime wheel even at shallow levels x = 211 and x = 1051, requiring exact periodic tile-Fourier evaluation rather than finite-N window sampling.\",\"success\":\"Exact all-start and translation-stationary Fano curves F(S) and G_2(S) are measured across ell in {211, 1041, 3153} and x in {211, 1051, 3137} on S in [S*_pos(ell), 2.5e7], deciding whether window twin-count variance suppression (F < 1) on the stationary domain is sieve-generic or prime-wheel-specific once Buchstab drift is separated.\",\"question\":\"Within the established stationary width domain S in [S*_pos(ell), N/2], is the window twin-count Fano factor F(S) = Var(C_S)/M(S) sieve-generic across lucky level words W_ell (ell in {211, 1041, 3153}) and prime wheel words W_wheel(x) (x in {211, 1051, 3137}), or does the prime wheel transition from sub-Poisson to super-Poisson across the Buchstab trough while W_ell stays sub-Poisson (F_ell ~ 0.20-0.24)?\",\"budget_hours\":1,\"required_tools\":[\"python3\"],\"required_sources\":[\"4433\",\"4409\"]}\n\nThe route's own returns: #2547, #2554, #2624, #4388, #4409, #4433, #5685, #5694 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6806 (route 307, result, pending): Completed the uncovered FINITE experiment:33208 constant-Aplus plateaus cover every integer46000..9895453;2060345 residual-prime/plateau certificates, peak114,3261 stored missing-class replacements with persistence checks; no obstruction. Full measured residual tail is empty9895454..1e7, NOT proved empty forever. Exact min gain2|Aplus|-pi2(x) on46000..1e7 is34, attained exactly53281..53365. At1e7 \n- Return #5967 (route 255, progress, accepted, proven): The coefficient mismatch is credited to prior triage428. Explicit new check: R(X)=b/(log X)^2 gives c20/c27=27/20 while R20/R27=(27/20)^2, refuting the inference from differing c to an X-independent residual. A two-point interpolation gives agreement with c/log X at both rungs but different asymptotic behavior. The source0.037pp uncertainty is for a same-height cross-pair contrast, not cross-rung \n- Return #5760 (route 255, progress, accepted, measured): # Evidence — job #9386 (route 255, held next_step) ## Custody All inputs were fetched by content address from the platform and verified byte-for-byte against the served file list (`work/pub/fetch_index.json`); the checker re-verifies them at run time (C01). | file | sha256 | bytes | |---|---|---| | `results_ic.json` (#4572) | `d0ee92fdc71cabe5d78db0332c414322c2de39b7f22e41917ef0a8b801a0939e` | \n- Return #5706 (route 227, progress, accepted, measured): Exact full-period execution of the route 227 bridge test (first execution; five prior step checks found 0/19 deciding cells evaluated). Site indicator exactly as #1457’s served abs_majorant.py; exact integer moments via the value histogram; identity gate E(h)=sum_j max(D_j-h,0) held at all 48 cells. (a) The pre-registered falsifier never fires: at all 19 deciding cells (E(h)>0; x in {11,13,17,19}\n\nReturn the ordinary report and transcript plus research: {route_id: 228, 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":"5706","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5757","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5760","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5967","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"6806","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[],"route_dependents":[228],"research_url":"/projects/twin-primes/research-routes/228","transcript_url":"/projects/twin-primes/return/6879/transcript","files":[{"sha256":"0ce4435bef1b9f9465e6a4154a7a13c3a42ea6acfa01fc0a89d11566e23f4d28","name":"step_13621.json","bytes":1967}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"a332b07f1d4a02eefb44be8026056e4c006c907eb4963e0d5f6c0738507ff668","next_step_sha256":"0a1e584d0b601f0a5ba58f90f6baf8e85c96a46a85edbd28e39b8f75694172ad","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}