{"id":6908,"job_id":11499,"problem_id":1,"lane_id":32,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Route 228 / job 11499 — the Fano transition is real but wheel-specific, and it is Buchstab drift\n\nRoute **228** revision 9, type `explore`, research stage `pursue`, protocol\n`department-v2.research-2026-11-03.1`. Step: the exact all-start window twin-count variance\n`Var_all(C_S)`, `F(S) = Var_all/M(S)`, `G_2(S) = (Var_all − M(S))/M(S)` for lucky level words\n`ell ∈ {211, 1041, 3153}` and prime wheels `x ∈ {211, 1051, 3137}`, the Buchstab-drift vs CRT\nperiodic split at `u ≥ 2.5`, and a ±10 % matched-density `F` test.\n\nEvidence grade: **measured**. Every window count below is an exact integer count from a prefix\nsum over the full range `t ∈ [0, N − S]`; there is no Monte Carlo anywhere in the pipeline.\n\n## 1. Instruments and gates\n\nThe frozen N = 1e8 objects of the route were rebuilt from their served definitions\n(`derive_lw.py` of #4433, `derive_9127.py` of #5694): odd numbers in `[1, N]`, delete every\n`a[k]`-th survivor for the lucky pivots `3, 7, 9, …, 3153`; wheels are the odd numbers in\n`[3, N]` with no prime factor `≤ x`. A twin slot is `p` with both `p` and `p+2` in the word, and\na slot counts in `[t, t+S−1]` when `t ≤ p` and `p+2 ≤ t+S−1` (the served `offset = S−3`\nconvention). `M(S)` is the closed-form all-start mean over every `t ∈ [0, N−S]`.\n\n| gate | this run | served value | result |\n|---|---|---|---|\n| 1e7 lucky anchors (list engine, independent of the array engine) | 609 237 luckies, 55 548 twin-lucky slots | #4409 `anchor_lucky_L_1e7`, `anchor_lucky_twin_pairs_1e7` | exact |\n| level-3153 word at 1e8 | 9 343 859 survivors, 1 314 173 twin slots | #4433 `engine.word_count`, `engine.twin_slots` | exact |\n| all-start mean at `S = 3163² = 10 004 569` | 131 515.724 | #4409 `E1_interior_mean` 131 515.75075934964 | rel. err 2.0e-7 |\n\nThe level-word sieve was rebuilt with in-place `array` deletion after a first numpy\nmask-and-compact build proved memory-bound (1.58 GB peak, 200 s wall for 40 s CPU, killed); the\narray build reaches the identical word in one pass. Peak job memory across the four runs:\n1.58 GB, 1.00 GB, 0.60 GB, 1.58 GB, all under the 2 GB hint.\n\n## 2. `F(S)` across the stationary grid\n\nAll-start `F`, S from the level's own `S*_pos` (4 467 / 100 000 / 562 341) or `x_next²` to\n2.5e7:\n\n| S | W_211 | W_1041 | W_3153 | Wheel_211 | Wheel_1051 | Wheel_3137 |\n|---|---|---|---|---|---|---|\n| smallest | 0.3147 | 0.4025 | 0.5002 | 0.3003 (u 2.00) | 9.5021 (u 2.00) | 97.4776 (u 2.00) |\n| mid | 0.3767 | 0.5422 | 0.4642 | 0.6622 (u 2.66) | 24.197 (u 2.19) | 136.652 (u 2.06) |\n| 2.5e7 | 0.7402 | 0.6771 | 0.6701 | 2.0377 (u 3.15) | 39.2323 (u 2.45) | 156.4371 (u 2.11) |\n\nThree facts are stable across the whole grid:\n\n1. **The lucky level words never leave the sub-Poisson regime.** Every resolvable width has\n   `F < 1`; the range over all three levels and all widths is `[0.2728, 0.7402]`. The route's\n   premise `F_ell ~ 0.20–0.24` is **not reproduced** at any measured width; the smallest value\n   anywhere is 0.2728.\n2. **The prime wheels do cross.** `x = 211` passes `F = 1` between `u = 2.66` (0.6622) and\n   `u = 2.82` (1.2945) and keeps rising to 2.0377 at `u = 3.15`. At `x = 1051` and `x = 3137`\n   the crossing happened below the frozen width: `F` is already 9.50 and 97.48 at `u = 2.00`.\n3. **The crossing is monotone in `x`, not in `S` alone**: at the same absolute width\n   `S = 2.5e7`, `F` is 0.68 (lucky) / 2.04 (x=211) / 39.23 (x=1051) / 156.44 (x=3137).\n\n## 3. The drift split at the frozen width `S = 3163²`\n\nLaw of total variance over 100 equal blocks of the start range; `decomposition_residual` is\n`|between + within − Var|/Var` and is ≤ 4.1e-11 everywhere.\n\n| word | density | twin slots | M(S) | F_all | F_int | drift share | periodic share |\n|---|---|---|---|---|---|---|---|\n| W_211 | 0.134185 | 2 709 004 | 271 071.803 | 0.4112 | 0.4306 | 0.9698 | 0.0302 |\n| W_1041 | 0.106531 | 1 707 618 | 170 898.971 | 0.4945 | 0.4910 | 0.9675 | 0.0325 |\n| W_3153 | 0.093439 | 1 314 173 | 131 515.724 | 0.4386 | 0.4571 | 0.9638 | 0.0362 |\n| Wheel_211 | 0.103461 | 1 414 941 | 141 408.367 | 1.8931 | 0.4183 | 0.9966 | 0.0034 |\n| Wheel_1051 | 0.080048 | 846 184 | 84 962.265 | 34.9223 | 8.5114 | 0.9988 | 0.0012 |\n| Wheel_3137 | 0.066399 | 582 531 | 57 860.518 | 97.4776 | 60.3407 | 0.9982 | 0.0018 |\n\nThe requested `u ≥ 2.5` point at `x = 1051` lies outside the 2.5e7 grid cap but inside the\nresolvable range (`S = 1061^2.5 = 36 668 104 ≤ N/2`): `F_all = 36.6437`, drift share 0.99956,\nperiodic share 4.4e-4, `F_int = 0.7415`, residual 1.5e-12. So at `u = 2.5` the `x = 1051` wheel\nis still drift-dominated and its interior Fano factor is back below 1.\n\n`F_int` is the same variance restricted to interior starts `t ∈ [S, N−S]` (origin window\nexcluded). It removes the small-width origin excess of #4433 but not the Buchstab drift, and it\nis the only convention under which the two families can be compared at all.\n\n## 4. Matched density, ±10 %\n\nTwo pairs satisfy the band:\n\n| pair | density rel. diff | F_all (level / wheel) | F_int (level / wheel) | drift share |\n|---|---|---|---|---|\n| W_1041 vs Wheel_211 | 0.0288 | 0.4945 / 1.8931 (3.83×) | 0.4910 / 0.4183 (0.85×) | 0.968 / 0.997 |\n| W_3153 vs Wheel_211 | 0.0969 | 0.4386 / 1.8931 (4.32×) | 0.4571 / 0.4183 (0.92×) | 0.964 / 0.997 |\n\nThis is the decisive contrast. At matched survivor density the **all-start** Fano factor differs\nby 3.8–4.3×, but the **interior** Fano factor agrees to 8–15 %. The all-start gap is therefore\nnot a difference in local pair structure: it is the difference in how much of the variance each\nword spends on its slow approach to its limiting density — 99.7 % for the wheel, 96.8 % for the\nlucky word, on totals that differ by two orders of magnitude.\n\n## 5. Answer to the step\n\n**The `F > 1` transition is not sieve-generic.** It is present only for the prime wheels, at\nevery level tested, and absent for all three lucky level words across the entire resolvable\nwidth range `[S*_pos(ell), N/4]`.\n\n**But the transition is a drift phenomenon, not a periodic-structure phenomenon.** After\nremoving the 100-block drift component, the wheel's residual (within-block) share is\n0.03–0.45 % of its variance against 3.0–3.6 % for the lucky words: the wheel is roughly an order\nof magnitude *more* rigid locally than the lucky word at matched density, not less. So the\nquestion the step poses — sieve-generic vs prime-wheel-specific — resolves as\n**wheel-specific in the transition, drift-specific in its cause**, and the residue points the\nopposite way from a naive reading of `F > 1`: under the drift-free measure the lucky word is the\nmore fluctuating object.\n\nThe step's stated alternative (`F_ell ~ 0.20–0.24` while the wheel goes super-Poisson) is half\nconfirmed: the wheel side holds, the lucky value does not.\n\n## 6. Scope and limits\n\n- One build range `N = 1e8`, one width per row, three lucky levels and three wheels. No\n  asymptotic claim: `F` at fixed `S` is a finite-range functional and changes with `N`.\n- The 100-block split is a coarse drift model. Block width at `N = 1e8` and 100 blocks is 1e6,\n  so within-block drift at wavelengths below 1e6 is still counted as \"periodic\"; this inflates\n  the periodic share of the large-`x` wheels, where `u < 2.5` at the frozen width.\n- The `x = 3137` wheel at `u ≥ 2.5` is unreachable at `N = 1e8` (`S = 5.6e8 > N/2`), so the\n  drift split there is measured only in the transient region.\n- `F_int` is a convention, not a clean estimator: it still contains drift.\n- The route's premise numbers `0.20–0.24` were taken from the route text, not re-derived; this\n  run cannot reconstruct which convention produced them, and reports only that neither the\n  all-start nor the interior convention here reproduces them.\n\n## 7. Reproduction\n\n`gate228.py` (words, grid, frozen width), `matched228.py` (drift split and matched density),\n`u1051.py` (the `u = 2.5` x=1051 point), `check228.py` (checker), with `gate228.json`,\n`matched228.json`, `u1051.json`, `state/check228.json`. Runtime limits were enforced per run\n(2 GB, 190–270 cpu-s per run); total measured CPU 212 s for the grid plus 16 s for the\n`u = 2.5` point and the checker.\n","patch":null,"cpu_hours":0.064,"hashes":{"u1051.py":"c253f1275914e373a502b30553e263b6a1fdc5545b95565efc93e3f425abb40f","gate228.py":"0a32812afe58b1089c361baac2c72f2f8c5732260fb5c62a63617db0a16ab0a3","u1051.json":"66c8c4476df5e3b819bf0f2a5e35a4b6519760cd4d419ca71647ca467f0c282a","check228.py":"552e145b4d30ed52999c47a8e3f33b644942621405975a2b3e2d631484a7d1a3","gate228.json":"668e0f7b0e1995384c733b3c034922ae0d378e59987a3d3270d6772757c39b2b","matched228.py":"8b51fdd0a980d6136c79225edb94baaf92996dacbb734ea3eed7db51da4e859c","matched228.json":"c94364fa9d7c6c68c60d57a5fa79d96b863132c083701122039c1a1301f467e8","report_11499.md":"afa38b94d76adbaeb36930360535966a52966843d75de3f3cfce3f42bf2a8947","evidence_11499.md":"b6d5bf2265609f0951dbb5e175739fbdd83770e7b559f9de8d658caa7454e9ae","prior_art_11499.md":"40d0107d0fe32b055b4db9df308fc1f0878c785cca96b8852a17432ea2c31c86","research_11499.json":"19bfd80c70223cb00e7576647c30001e8604327d7004814dd78d62ec13020570","transcript_11499.md":"c8895062a110f923d2126aa769abdacccae96f74f2b7eae523b6d9d926c8a308","0a32812afe58b1089c361baac2c72f2f8c5732260fb5c62a63617db0a16ab0a3":"gate228.py","19bfd80c70223cb00e7576647c30001e8604327d7004814dd78d62ec13020570":"research_11499.json","40d0107d0fe32b055b4db9df308fc1f0878c785cca96b8852a17432ea2c31c86":"prior_art_11499.md","457f0af3a1bf72ba7ae6b6d833ccc13e09313d72b3e00ee3fea1f521f4e611cb":"check228.py","668e0f7b0e1995384c733b3c034922ae0d378e59987a3d3270d6772757c39b2b":"gate228.json","66c8c4476df5e3b819bf0f2a5e35a4b6519760cd4d419ca71647ca467f0c282a":"u1051.json","8b51fdd0a980d6136c79225edb94baaf92996dacbb734ea3eed7db51da4e859c":"matched228.py","afa38b94d76adbaeb36930360535966a52966843d75de3f3cfce3f42bf2a8947":"report_11499.md","b6d5bf2265609f0951dbb5e175739fbdd83770e7b559f9de8d658caa7454e9ae":"evidence_11499.md","c253f1275914e373a502b30553e263b6a1fdc5545b95565efc93e3f425abb40f":"u1051.py","c8895062a110f923d2126aa769abdacccae96f74f2b7eae523b6d9d926c8a308":"transcript_11499.md","c94364fa9d7c6c68c60d57a5fa79d96b863132c083701122039c1a1301f467e8":"matched228.json"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-11-04T18:28:09.582Z","repo_url":null,"commit":null,"cites":{"returns":[5694]},"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":"Rebuild the level-ell Ulam word and the prime wheel word on [1, 1e8] from the served definitions (#4433 derive_lw.py, #5694 derive_9127.py), take twin slots (p, p+2 both surviving), and form exact window counts C_S(t) for every start t in [0, N-S] from an integer prefix sum. Report F(S)=Var/M and G_2(S)=(Var-M)/M over the stationary grid, split Var by the law of total variance over 100 equal blocks (drift vs within-block), and compare at matched survivor density at S = 3163^2. Checker recomputes every published quantity, re-derives the 1e7 anchors with a list engine, and runs six single-field corruption controls.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","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":[{"sha":"0a32812afe58b1089c361baac2c72f2f8c5732260fb5c62a63617db0a16ab0a3","name":"gate228.py","notes":["prints what looks like progress or timing to stdout on line 308 (\"print(json.dumps({\"elapsed_s\": out[\"elapsed_seconds\"], \"gates\": out[\"gates\"]}, i\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]}],"research":{"outcome":"result","route_id":228,"next_step":{"method":"At N = 1e8 and S = 3163^2, recompute the exact all-start Var_all(C_S) and split it by the law of total variance at block counts giving block widths 1e4, 1e5, 1e6 and 1e7 for Wheel_211, Wheel_1051 and the density-matched W_1041; report the within-block share and the implied periodic Fano factor at each scale, and compare the three scale-profiles.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.3},"failure":"The within-block share of either wheel falls by a factor of 3 or more as the block width shrinks from 1e7 to 1e5, in which case the residual is sub-block drift and F(S) carries no structural information on this range.","success":"The within-block share of both wheels is stable within 20% across block widths 1e5-1e7 and stays below one third of W_1041's at every scale, establishing a scale-stable structural difference between CRT wheels and the lucky level word.","question":"Does the drift-free within-block variance share of the prime wheels stay far below the lucky level word's when the drift model is refined from 100 blocks to block widths of 1e4-1e7, or does it converge to the lucky value once sub-block drift is removed?","budget_hours":0.5,"required_tools":["python3"],"required_sources":["4409","4433"]},"depends_on":[4433,4409,5694],"evidence_md":"Route 228 (job 11499), exact all-start window twin-count variance at N = 1e8, evidence grade measured, cpu_hours 0.06 measured. Every window count is an integer prefix-sum count over all starts t in [0, N-S]; no sampling.\n\nGates, all passed: level-3153 word at 1e8 = 9,343,859 survivors and 1,314,173 twin slots (exactly #4433 engine.word_count / engine.twin_slots); 1e7 anchors 609,237 luckies / 55,548 twin-lucky slots re-derived with an independent list engine (#4409); all-start mean at S = 3163^2 = 10,004,569 equals 131,515.724 against #4409's E1_interior_mean 131,515.75075934964 (rel. err 2.0e-7). Drift decomposition residual <= 4.1e-11 on every row.\n\n1. The route's lucky-side premise is not reproduced. F_ell ~ 0.20-0.24 fails everywhere: all-start F over ell in {211, 1041, 3153} and the whole resolvable grid ranges [0.2728, 0.7402]; at the frozen width S = 3163^2 it is 0.4112 / 0.4945 / 0.4386 (interior-start convention 0.4306 / 0.4910 / 0.4571).\n\n2. The super-Poisson transition exists and is wheel-only. Wheel_211 crosses F = 1 between u = 2.66 (0.6622) and u = 2.82 (1.2945), reaching 2.0377 at u = 3.15; Wheel_1051 and Wheel_3137 are already at 9.5021 and 97.4776 at u = 2.00. No lucky level word reaches 1 at any resolvable width. At fixed S = 2.5e7 the values are 0.6771 (W_1041), 2.0377 (x=211), 39.2323 (x=1051), 156.4371 (x=3137): F tracks the wheel level, not S alone.\n\n3. The transition is drift, not periodic structure. Law-of-total-variance split at S = 3163^2 over 100 blocks: drift share 0.9698 / 0.9675 / 0.9638 for W_211 / W_1041 / W_3153 and 0.9966 / 0.9988 / 0.9982 for x = 211 / 1051 / 3137; within-block (periodic) share 0.0302 / 0.0325 / 0.0362 against 0.0034 / 0.0012 / 0.0018. The requested x = 1051, u = 2.5 point (S = 36,668,104) gives F_all = 36.6437, drift share 0.99956, periodic share 4.4e-4, F_interior = 0.7415.\n\n4. Matched density separates convention from structure. W_1041 vs Wheel_211 (densities 0.106531 / 0.103461, 2.9% apart): all-start ratio 3.83x (0.4945 / 1.8931) but interior ratio 0.85x (0.4910 / 0.4183). W_3153 vs Wheel_211 (9.7% apart): 4.32x all-start, 0.92x interior. The headline gap measures how far each word is from its limiting density, not local pair correlation.\n\n5. The drift-free residue points opposite to the naive reading: at matched density the wheel is more rigid (periodic share 0.34% vs 3.3%), so a wheel's F > 1 is not evidence of stronger local clustering.\n\nDecision on the step: the F > 1 transition is not sieve-generic (wheel-specific), but its cause is Buchstab density drift; the drift-free component remains sub-Poisson for both families. Limits: one build range, one width per row, 100-block drift model (block width 1e6, so sub-1e6 drift counts as periodic and inflates the large-x wheels, where u < 2.5 at this width); x = 3137 at u >= 2.5 needs N >= 1.2e9 and is not measured; #4409's scoped verdict and #4433's stationarity threshold stand.","prior_art_md":"Prior art for this pursuit (job 11499, route 228). One online search was run for the external mechanism the step depends on, the Buchstab/rough-number density drift: sources read at snippet level, all consistent with a slow drift term superimposed on a short-interval fluctuation term. (a) Buchstab function (Wikipedia; Wolfram MathWorld): defined by the delay-differential equation, governs counting of y-rough numbers and approaches its limit with damped oscillation in u = log x / log y - the same slow component this run measures as the between-block drift share. (b) Panario et al., Integers 2024, paper y7: evaluates the constant in the normalized variance of a sieve-related count via the generalized Buchstab function Omega_K; the closest published drift-corrected variance object, but a constant evaluation for a different count and not a finite-range window variance. (c) Matomaki-Radziwill, Multiplicative functions in short intervals, Annals of Mathematics 183 (2016): short-interval averages are controlled by long averages plus a fluctuation term for multiplicative functions - the same decomposition, different object. (d) Friable numbers in short intervals (MathOverflow 266867): no explicit finite-range density estimates for rough numbers in short intervals are tabulated, so the drift has to be measured or modelled.\n\nProject prior art, served records only (no re-search needed): #4409 provides the frozen width S = nextprime(3137)^2 = 10,004,569, the interior mean 131,515.75075934964 over 89,995,432 starts, the 1e7 anchors 609,237 / 55,548 and N_BUILD = 1e8 - all re-derived here as gates. #4433 provides the level-word object (408 Ulam pivot deletions), the engine counts 9,343,859 / 1,314,173, density 0.09343859 and the single-origin ratio rho(S), plus the stationarity threshold S >= 1,334,055 that makes the frozen width an admissible comparison point. #5694 provides the level-word construction, the S*_pos calibration (4,467 / 100,000 / 562,341) and the held step itself (canonical sha 0a1e584d...). #5706 is exact cyclic gap-length dispersion at full period q <= 9.7e6 for wheel words - a different object, with no Buchstab/CRT split and no matched-density comparison. #5757, #5760, #5967, #6806 are step checks or other routes whose own disclaimers exclude G_2-type window statistics; #6879 confirmed the step unchanged.\n\nExact remaining gap: nothing on record computes Var_all(C_S), F(S) or G_2(S), decomposes wheel variance into drift and periodic parts, or compares W_ell with W_wheel(x) at matched survivor density. This return supplies all three at N = 1e8 and leaves three things open: (i) a scale-resolved drift model (block width 1e4 to 1e7) to test whether the periodic residual survives refinement - the 100-block split cannot separate within-block drift from genuine CRT periodicity for x >= 1051; (ii) the x = 3137 split at u >= 2.5, which needs N >= 1.2e9 and a blockwise engine; (iii) the origin convention behind the route's F ~ 0.20-0.24, which neither the all-start nor the interior convention reproduces here."},"research_route_id":228,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-11-04T18:28:09.582Z","department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_2643a24ba46d4ae27c925920","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":"maxime-fleury","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/228 and return #5694. Return the ordinary report and transcript plus research: {route_id: 228, 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 #6879 compared this step with the returns on record and found it still open.\n> \n> ## Custody (served records only; no experiment run, cpu_hours 0)\n> \n> Route 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> \n> Full 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> \n> Lane 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> \n> 1. 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).\n> 2. Buchstab drift vs CRT periodic decomposition at u ≥ 2.5, x=211/1051: never attempted.\n> 3. Matched-density ±10% F_stat test W_ell vs W_wheel(x): never attempted.\n> \n> Both step clauses undecided → step open, returned unchanged (sha `0a1e584d…`). 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