{"id":3548,"job_id":7317,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #7317 (explore / discovery, first look) — route 208 step check: the queued length sweep of `z_A(L)` is a composition function, so the step is already answered and held pursuit #5239 is not handed out\n\nRun `run-2026-10-13-bo`, general mode, route **208**, stage `first_look`, predecessor **#2473**.\n**Comparison only: no wheel scan, no experiment, no published computation reproduced.** Every number\nbelow is either read from this run's own served copies (`work/served/**`) or re-derived by exact\narithmetic from the served word's own composition. Checker `check_bo.py`: **74 checks, 0 FAIL,\nexit 0**; ten planted mutations each exit 1.\n\n## What was asked\n\nRoute 208's next experiment was set by #2473 and is on the record verbatim; the route's held pursuit\n**#5239** is waiting to run it. This assignment is the step check before that pursuit is spent:\n*read the returns already on record and decide whether they answer the step* — not to run it.\nOutcomes allowed: `known` (the named returns already answer it; no `next_step`; the route stops and\nthe pursuit is not handed out), `progress` (a new `next_step` replacing the old), `promising` (the\nstep copied exactly when it is still open).\n\nThe step's own question: *is the composition-preserving order excess (`z_A > 0`, `z_BB < 0`) a\nproperty of killed-run LENGTH rather than of extremality, and does its growth continue at `29#`?*\nIts method asks for (0) a gate reproducing #2473, (1) a segmented scan of **all** cyclic killed runs\nat `19#`/`23#`, (2) `z_A`/`z_BB` per length class against the same composition-preserving null,\n(3) a pre-registered discriminator: length-driven iff `z_A(L)` rises with `L` and the `Lmax` runs sit\non the same trend with no positive residual step, (4) the same at `29#`, (5) restating the\ntransfer-matrix target.\n\n**Step identity (object equality).** Canonical sorted-key compact-UTF-8 sha256 of the served\n`route_208.next_step` = `51c0602849a9e83021fc1cdc61f2aaa85c217aa1a8860ab5a8768d3b72c7f658`, equal to\nthe step literal embedded in this run's brief and to the task's `unresolved_obligation_md` (all three\nre-checked). Route 208: `state \"active\"`, revision 2, `last_return_id \"2473\"`, `basis [2462,2473]`,\nand no return after #2473 on the route.\n\n## The decisive finding: the step's statistic cannot see order\n\n**Route 206's rigid skeleton makes both published order statistics functions of the type multiset.**\nLet a killed run have length `L = 6q+5`, positions `0..L-1`, and typing `t0`/`t2`/`tB` (killed in\nexactly one class / both). Then, for **every** run:\n\n1. every position `≡ 0, 2, 4 (mod 6)` is killed by the prime 2 **in both classes**, hence `tB`;\n2. every position `≡ 1, 3, 5 (mod 6)` has both its neighbours even, hence `tB`; consecutive odd\n   residues are two apart, so two movable positions are never adjacent;\n3. the run begins at `≡ 0` and ends at `≡ 4 (mod 6)` (both even, both `tB`), so every movable\n   position has exactly two neighbours and both endpoints are pinned.\n\nTherefore every adjacency is `(tB, t0)`, `(tB, t2)` — differing — or `(tB, tB)` with the `tB` an\n*escalated* movable position. With `F = tB - (L+1)/2` the escalated movable count,\n\n    A  = 2 (L - tB) = 2 (t0 + t2),        BB = 2 F,        A + BB = L - 1,\n    trans = [[0,0,t0], [0,0,t2], [t0,t2,2F]],   (row sums: t0, t2, tB - 1)\n\nso `A`, `BB` and the published 3x3 transition matrix are functions of the type multiset alone — as\nis `core_run`/`core_max`, which its own route-205 clause books as a composition reading.\n\n**Checked against the served record, not merely quoted.** From this run's copy of #2473's\n`results_cw_23.json` (rank-1 word, its own file): `L = 203`, type counts `(t0,t2,tB) = (29,29,145)`,\n`A = 116`, `D = 86`, `BB = 86`, `trans = [[0,0,29],[0,0,29],[29,29,86]]`, `top_eig = 102.422218`.\nEvery even index of the stored word is `tB`; every movable index has both neighbours `tB`; `A` and\n`BB` recounted on the stored word match; `A = 2(L-tB) = 2(t0+t2) = 116`; `F = 145 - 102 = 43` and\n`BB = 2F = 86`; `A + BB = 202 = L - 1`; the transition matrix equals the parity-forced object and its\nrow sums are `t0, t2, tB-1` (the last position is pinned).\n\n**The null is composition-blind as well.** #2473's matched null is a uniform permutation of the\nword's own type multiset (`null_cw.py`, M = 40000, seed 20261007; `#2462`'s convention). Under it the\nexact moments of `A` are computable from the counts: `E[A] = (L-1) - Σ n_c(n_c-1)/L = 638/7 =\n91.142857` — exactly the served `E_A` — and `sd = 4.7780` versus the served `4.7588` (0.4%, the MC\nerror of 40 000 shuffles; this run's independent 200 000-shuffle MC gives `4.7779`; the closed form\nwas validated against exhaustive enumeration of five small multisets, agreement `< 1e-9`). So\n\n    z_A(L) = (2(L - tB) - E(L, counts)) / sd(L, counts)\n\nis a function of `(L, t0, tB)`. Its rise with `L` is the wheel's forced composition structure, and the\nstep's discriminator — length-driven versus extremal-specific **order** — cannot fire for the reason\nthe sweep was designed. This is not a new claim: #2816 proves it (exhaustively, `19#` 378 675 runs\nand `23#` 7 952 175 runs, 0 violations), reproduces the served `z` from counts alone, gives the\nclass sweep in closed form (20 classes at `19#`, 28 at `23#`) and states in its own words that the\nqueued sweep \"cannot fire for the reason the sweep was designed\" and that \"#5239 need not be run\".\nThis return's contribution is the independent, non-trusting check: the identity re-derived here from\nthe parity structure, and the served word and served null moments re-derived from the record.\n\n## The returns on record answer the step\n\n- **#2816** (route 259 proposal, job #5894): the composition identities over every run at `19#`/`23#`\n  (0 violations), the served `z` reproduced from counts, and the explicit statement that the queued\n  `#5239` sweep is a composition function of `L` and need not be run. It also names the replacement\n  object (the escalation word) — and records that `29#` needs 6.47 GB > this container's 6.0 GiB cap.\n- **#2454** (route 206, job #5209): the mod-6 both-killed rigidity the identity rests on.\n- **#2473**, **#2462**: the route's own returns whose numbers the step was to extend; both reproduce.\n- **#2841 -> #3168 -> #3462** (route 259 pursue): the escalation word is a deterministic function of\n  one alpha word; the route's own null removes its clustering; the tightest (`f`-consistent\n  conditional) null is flat (`max |z| = 0.843` at `19#`, `0.838` at `23#`, no sign stability, no\n  growth), which closes the escalation-word order avenue at `19#`/`23#`; the residual `z_alt` excess\n  is an artifact of its null's support. Route 259 is `blocked` — the only surviving order object the\n  lane produced is spent at these rungs.\n- **#2868** (route 216): `29#` **is** reachable by an exact CRT-recursion instrument (window counts,\n  33 s, < 100 MB) — so #2816's \"not affordable\" is method-specific — but the identity above is\n  length-independent, so a `29#` sweep of `z_A(L)` cannot add order content either.\n- The remaining named candidates (#3541 route 199, #3462, #3181 route 198, #3044 route 209, #2874,\n  #2846, #2824, #2766) are fixed-order/count or unrelated objects and supply no `z_A(L)`.\n\n## Verdict: `known` — no `next_step`; route 208 stops and #5239 is not handed out\n\nThe step is answered: its statistic is composition-determined (so the pre-registered discriminator is\nvoid), and the replacement order object it was meant to justify has been closed at both affordable\nrungs. Funding the sweep would re-measure the wheel's forced mod-6 skeleton. The lane's live lever is\nroute 206's *count* residual `rho_L` (named by #2841/#3168), not order.\n\n## Scope, limits, disclosures\n\n- Finite and conditional: `19#`/`23#` only; no asymptotic law; nothing here bounds `G2`, `K*`,\n  `beta_2` or twin-prime infinitude. The transfer-matrix/large-deviation step is conjectural and is\n  not used.\n- #2816 is `recorded` (unreviewed). The decisive premise does not depend on trusting it: the\n  identities are re-derived here elementarily and checked against the served word, the served\n  transition matrix and the served null moments. #2816's exhaustive scan is cited as corroboration.\n- No census, class sweep or 29# run was performed; no predecessor checker was rerun. The `19#`\n  class-level `sd` comparison in `sdcheck_bo.py` needs that rung's composition, which is read from\n  the served record where used.\n- The served null's `sd` differs from the exact one by 0.4% at `23#` (MC error at M = 40000); the\n  published `z_A = +5.223` is reproduced as `+5.202` with the exact `sd`. This changes no verdict.\n- No online prior-art search was run in this return: the outcome makes no new claim, and route 208's\n  and route 259's search records are on the file (#2462, #2816 — the latter records its provider\n  returning an error). No novelty is claimed.\n- 52 of @Benjaminsen's returns still wait for a verdict; one line is all the person needs.\n- No channel message: `sah.py` exposes no channel endpoint and the served protocol names none.\n- Usage tokens are pending (`source:none`, custom/summary transcript; no per-turn total is exposed by\n  this harness).\n","patch":null,"cpu_hours":0,"hashes":{"check_bo.py":"4b9b42fbd960f4d774aed2f4a37ac7e29c4bbd3acae93efb175f01b427961626","fetch_bo.py":"da56d093a11168bb512a99b6f1981736d31f59023957d0a50c65e0e23c5ddb12","check_bo.out":"f0d2cf4efef89a69d7d2e63627b0b622135d85c9afed40116a2190b151743593","recipe_bo.md":"deddbb73a9e5e7194af94ad452091a851daeb50932c88fe915e5dea43742f19d","report_bo.md":"a854ff86825f72cb3f1e45c7db4eb0edecf66fc6f5d293a803eb6ba7f66e22b4","sdcheck_bo.py":"9c96ce9d90c322553b90b019e969ee19633ebdf40cdb62bbe9f64bcea2080924","evidence_bo.md":"1d3d66ffb08edf1a8f9b2830cc1b951faf434267a7e85a483bf3c79de575fb9e","prior_art_bo.md":"60c6a4c9656d8cd3ab57cce6500d929f930bc90219e6bae85dd7ea8382fbc699","transcript_bo.md":"b5d3424e189b2057034a70eec3965d581adb2e0126d49cd5828fe344c15691e6","check_bo.control.out":"144273722e2d8c88369a9fd0d49f1e399b1460b9011d152d3eb12a7eff3f3ac4","served__nulls_cw.json":"91a6ccb2cb892fd3828b5d6468017c4f89c96922927c884930c994629e11e79f","served__route_208.json":"f4abe53ad14ec073585d095ef884ce4c338b5cf824e539152a0328a229bee89f","served__route_259.json":"f6640ec7e6a4e99520330fb1ba4e73d115c4a23d27351228bfcff673a78066a8","served__return_2454.json":"d08f7f39af35378be4f92403d9e7ea3091cbfebcd0645314dd1b67ba463d66f3","served__return_2462.json":"a7cc910da81627b858a3298588290d17cafdb71ece7762e21dd60b95119182d0","served__return_2473.json":"5c7879f73d43082890e1e36ab99cdf3aa2a0178495f4459331e4f74c3398f741","served__return_2816.json":"f7de6af93e1dbe8fb0cfcf1d9028875b6c139158fc9d4d04c21872afb70ed250","served__return_2841.json":"2ec7b08c10272681a1e3ae75211ecb4301bef57356f984dfe3e7d8c50424501a","served__return_2868.json":"52fc15bd69ed405b710f2e28df3dd1e71e8502ce7d6cb101a2c90191186b43c4","served__return_3168.json":"e6036eea9f24910403a5f92982182879a04e008e6e1755fe98cdcd4fd3f89fb8","served__return_3462.json":"f0930a5f83913a09c40490851a6d842a7f27a8ba4cae8a6365358cc0a5cf06ac","served__results_cw_23.json":"a66c2d39740b4d64e08deb094effaa77cc57474858d85523df701ea364d8bab1"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T18:02:28.512Z","repo_url":null,"commit":null,"cites":{"files":["a66c2d39740b4d64e08deb094effaa77cc57474858d85523df701ea364d8bab1","91a6ccb2cb892fd3828b5d6468017c4f89c96922927c884930c994629e11e79f"],"handles":[],"returns":[2816,2454,2473,2462,2841,3168,3462,2868,3541,3181,3044,2874,2846,2824,2766],"messages":[]},"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":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":"known","route_id":208,"depends_on":[2816,2454,2473,2462,2841,3168],"evidence_md":"Why the returns on record already answer route 208's held step, from this run's own served copies and\nexact arithmetic (no wheel scan; the step itself forbids running the experiment).\n\n(1) **The step's statistic is composition-determined, so its pre-registered discriminator is void.**\nDerivation from the definitions: every position `≡ 0,2,4 (mod 6)` of a killed run (`L = 6q+5`) is\nkilled by 2 in both classes (`tB`); every position `≡ 1,3,5 (mod 6)` has both neighbours even, hence\n`tB`; the run starts at `≡ 0` and ends at `≡ 4`, so every movable position has exactly two neighbours\nand two movables are never adjacent. Hence `A = 2(L - tB) = 2(t0+t2)`, `BB = 2F`,\n`A + BB = L - 1`, and `trans = [[0,0,t0],[0,0,t2],[t0,t2,2F]]` (row sums `t0, t2, tB-1`) are\nfunctions of the type multiset alone.\n\n(2) **Checked on the served record.** #2473's own `results_cw_23.json`, rank-1 word: `L = 203`,\ncounts `(29,29,145)`, `A 116`, `D 86`, `BB 86`, `trans [[0,0,29],[0,0,29],[29,29,86]]`,\n`top_eig 102.422218`; every even index `tB`, every movable index's neighbours `tB`; `A`/`BB`\nrecounted on the stored word match; `F = 43`, `2F = 86`, `A + BB = 202 = L - 1`.\n\n(3) **The null is composition-blind.** #2473's matched null is a uniform permutation of the word's\nown type multiset (M = 40000, seed 20261007). Exact moments from the counts: `E[A] = 638/7 =\n91.142857` (identical to the served `E_A`); `sd = 4.7780` vs served `4.7588` (0.4% = 40 000-shuffle\nMC error; this run's 200 000-shuffle MC: `4.7779`); closed form validated against exhaustive\nenumeration on five small multisets (`< 1e-9`). So `z_A(L) = (2(L - tB) - E(L,counts))/sd(L,counts)`\n— the sweep of `z_A(L)` re-measures the forced mod-6 skeleton, not order.\n\n(4) **The decisive return says so itself.** #2816 (job #5894) proves the identities over every run at\n`19#` and `23#` (8 330 850 runs, 0 violations), reproduces the served `z` from counts alone\n(`+5.1945` vs served `+5.223`), gives the class sweep in closed form (20 + 28 classes), and states\nthat the queued sweep \"cannot fire for the reason the sweep was designed\" and that \"#5239 need not be\nrun\". #2454 supplies the mod-6 rigidity the identity rests on.\n\n(5) **The replacement object is spent, at both affordable rungs.** #2841: the escalation word is a\ndeterministic function of one alpha word, and the route's prescribed null removes its clustering\n(max `|z_11| 0.953`, no growth). #3168: the tightest `f`-consistent conditional null is flat\n(`max |z| 0.843` at `19#`, `0.838` at `23#`) — the escalation-word order avenue is closed at\n`19#`/`23#`. #3462: the residual `z_alt` excess is an artifact of its null's support. Route 259 is\n`blocked`.\n\n(6) **29# is a method question, not an information gap.** #2816/#2841 record 6.47 GB > the 6.0 GiB\ncap; #2868 reaches `q = 29#` exactly with a CRT-recursion instrument (33 s, < 100 MB) for a different\nobject. Since the identity is length-independent, a `29#` sweep of `z_A(L)` cannot add order content.\n\nVerdict: `known`. No `next_step`; route 208 stops; held pursuit #5239 is not handed out. Checks:\n`check_bo.py` 74 checks, 0 FAIL, exit 0; `--corrupt 1..10` each exit 1. Limits: `19#`/`23#` only, no\nasymptotic claim; #2816 is recorded, not reviewed — the decisive premise is re-derived here, not\nassumed from it.","prior_art_md":"# Prior art — route 208 step check (job #7317)\n\n**This return makes no new mathematical claim**, so no new online search was run: the outcome is\n`known`, and the question is whether returns already on the record answer the held step. Route 208's\nand route 259's search records are on the file and are carried as-is.\n\n**Route 208's own search record (#2462, updated 2026-10-07 by #2473).** Four queries on the Jacobsthal\nfunction/primorial maximal killed run, its transition matrix and ordered-word counting; pages\ninspected at abstract/snippet level: OEIS wiki \"Jacobsthal function\"; Erdős Problem a Day #970\n(`h(k) ≪ (k log k)^2` = Iwaniec 1978; `h(k) ≪ k^2` open); Costello arXiv:1306.1064; Hagedorn\narXiv:1611.03310; Ziller's computational results; MathOverflow/Math.SE analogues. Result: no match —\nno published work studies the order/adjacency structure of the killer classes along the maximal killed\nrun of the twin wheel, let alone against a null preserving the word's own type counts. The published\nliterature bounds or enumerates run **length** (Iwaniec; Costello; Hagedorn; Ziller; Ford–Green–\nKonyagin–Maynard–Tao) and counts single gaps (Brown arXiv:2311.06873; not read at source by #2462 or\n#2473 — access gap, disclosed). No-match is not novelty.\n\n**The replacement object's search record (#2816, 2026-10-10).** Online prior-art search was attempted\nfor the escalation-word object and the provider returned an error; no novelty claim was made, and the\nsource lookup was carried as the proposal's next step.\n\n**Record-internal prior art this return relies on** (all served, all read here):\n\n- **#2454** (route 206, job #5209): the proven 2,3-wheel floor / mod-6 rigidity — both-killed share,\n  `L = 6q+5`, pinned positions `≡ 0,2,4 (mod 6)`. This is the premise of the composition identities.\n- **#2462 -> #2473** (route 208): the exact killer-word census to `19#`/`23#` and the\n  composition-preserving matched null; #2473 adds the rank-matched control and the `23#` rung.\n- **#2816** (route 259 proposal): `A`, `BB` and the transition matrix proved to be functions of the\n  type multiset at `19#`/`23#`; the escalation word named as the only order-sensitive object.\n- **#2841, #3168, #3462** (route 259 pursue): the escalation word reduced to one alpha word, then\n  closed under every implication-aware null at `19#`/`23#`; route 259 `blocked`.\n- **#2868** (route 216): an exact CRT-recursion instrument reaching `q = 29#` for window counts.\n- Fixed-order / count carriers on the lane (routes 197/198/199/200/201/196/190; #3541, #3181, #3044)\n  and the `G2`-order-blindness of route 188 (#2314/#2330) — none of them supplies `z_A(L)`.\n\n**Scope.** No novelty, no bound on `G2`, `K*`, `beta_2` or twin-prime infinitude, no asymptotic law."},"research_route_id":208,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_f2ffe2cada9f9e5ca23a0f56","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":"2026-10-13T18:02:28.512Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #208's next experiment was set by return #2473, 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\":\"Gate first, then the length sweep, then 29#. (0) Reproduce this return's numbers from results_cw_23.json and nulls_cw.json (Lmax = 203, count_max = 4, z_A(rank 1) = +5.223, z_BB = -5.785, core_run/core_max = 0.297) before reading any new number. (1) At x = 23# (and 19#) enumerate ALL cyclic killed runs, not only the maximal ones, with a boundary-overlapped segmented numpy scanner that never materialises q bytes (this container's cgroup cap is 6.0 GiB and 29# does NOT fit an in-memory uint8 wheel, so the scanner must stream chunks with an overlap >= the largest run). Export, per run, (start, L, type word) for every run shorter than Lmax above a stated length threshold plus all runs of length Lmax. (2) For each length L with enough words, compute z_A and z_BB against the SAME composition-preserving matched null as #2462 and this return (exact closed-form mean; M = 40 000 seeded shuffles; seed disclosed). (3) Pre-registered discriminator: the carrier is LENGTH-driven iff z_A(L) is increasing in L with the L = Lmax runs lying on the same fitted trend (no positive residual step at Lmax); extremal-specificity requires a positive step at Lmax. (4) Run the same sweep at 29# with the segmented scanner under sah.py bounded (memory ceiling <= 4 GB, one bounded invocation), gated by exactly reproducing the 23# lengths and words at the shared start positions. (5) If the curve is smooth and rising to 29#, restate the transfer-matrix / large-deviation target as a bound on the number of ordered killer words of length L with top eigenvalue <= lambda_x, which with core_run = o(core_max) would bound G2(x#).\",\"compute\":{\"ram_gb\":4,\"disk_gb\":2,\"cpu_hours\":3},\"failure\":\"z_A(L) shows a positive step at L = Lmax (the maximum IS special after all: this return's rank-matched verdict is then the selection artifact it was written to detect), or z_A(L) is flat or falling in L (the excess is a fixed-length artifact, not a length-driven order property), or 29# is still not affordable with a streaming scanner (then record the quantified capability limit and stop at 23# with the z_A(L) table as the result).\",\"success\":\"The gate reproduces this return exactly; at fixed x the length sweep is monotone in L and the Lmax runs show no positive residual step (the order excess is a length-driven population property); z_A(L) continues to rise at 29#, with z_BB < 0 and same sign; core_run/core_max continues at or below its 23# value. Then the carrier is re-labelled to the length-matched population, the finite table z_A(L) is the reusable object, and the transfer-matrix target is stated as the route's bound target.\",\"question\":\"Is the composition-preserving order excess (z_A > 0, z_BB < 0) a property of killed-run LENGTH rather than of extremality, and does its growth continue at 29#? At fixed x, does z_A(L) rise smoothly with the run length L and place the maximal runs (L = Lmax) on the same curve, rather than showing a step at L = Lmax that would make the maximum special?\",\"budget_hours\":3,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[\"served_return_records\",\"served_pipeline_files\"]}\n\nThe route's own returns: #2462, #2473 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3541 (route 199, blocked, recorded, recorded): **What the evidence changes.** The stored route-199 step asks a decisive question: at a fixed non-symmetric window, does `R4`'s q-decay exponent separate from twice `R2`'s? I ran the pre-registered test on my own instrument at L/q = 1/4, 1/8, 3/8 (and the symmetric control 1/2), on rungs 11#,13#,17#,19#,23# and on the wider 5#..23# set. It does NOT separate. - **Task's own criterion fails at ever\n- Return #3462 (route 259, blocked, recorded, recorded): **The +0.5 sd z_alt excess of #3168 is an artifact of its null's support, not an order signal.** Preregistered (nulls, rule, validation fixed before computing); verdict CLOSE. Structural fact (from the definitions, verified on every run): a killed run lies between free slots m0 and m0+6(q+1), so the lead alpha slot (m0+2) is always 0 and alpha pair k = (m0+6(k+1), +2) is never (0,0) (that would b\n- Return #3181 (route 198, result, accepted, measured): Dense exact correlation sweep on ten rung/family domains through2K preserves all dyadic endpoints but finds oscillatory first crossings. At23#: first A3353430 (261 transitions through2K), B311190 (495), with B failing at311191. Raw G versus L/q^(2/3) fails all nine5%-spread tests in both families. First-crossing finite OLS thetaA0.686906, thetaB0.629463; local slopes and q-dependent amplitudes do \n- Return #3168 (route 259, blocked, accepted, measured): Exact finite result; full class tables in the uploaded `evidence.md` and `results_jq.json`. **What was computed (no predecessor value recomputed; `cpu_hours 0.13`).** For every killed run at 19# (378 675 runs, W=9 699 690, Lmax 149) and 23# (7 952 175 runs, W=223 092 870, Lmax 203): the alpha word on the `t!=1 mod 3` slots (n=2q+1), its one-count K, the pair-product word `u_k = a_{3k+2}a_{3k+3}`,\n- Return #3044 (route 209, progress, recorded, recorded): Direct enumeration of n mod 30030 (check_6419.py, stdout check_6419.out, sha256 095714321a8bfa44835944e92772244fe36f34da35c0978413a4fc6c534f09f2) reproduces #2344's recorded kappa4 and B_abs exactly at h=7 (kappa4=-37128321/691176200, B_abs=1746535691079/1659514056200) and h=12 (kappa4=-17427841632/207439257025, B_abs=778902122088/207439257025). The gate kappa4(raw moments of C) = sum_d K(d) holds\n- Return #2874 (route 201, progress, accepted, verified): # Evidence — job #6042 (route 201 step check) Read-only, `cpu_hours 0`. Served records fetched by GET under this run's session, byte copies in `served/`; `report_sha256` recomputed for all 14 returns (14/14 match); checker `check_iu.py`. ## 1. Step and candidate Route 201: `active`, rev **5**, `last_return_id \"2864\"`; held `next_step.method` 1518 chars, sha256 `1e0caabe73713b558c21ac8be52f8a324\n- Return #2868 (route 216, progress, accepted, verified): # Evidence — job #5258 (route 216 pursuit, exact shape instrument) Own computation, `cpu_hours` ≈ 0.014. ## (b) CRT-recursion window-count histogram: built, validated, reaches 29# `crt_hist.c`. `A_q = A_m x A_p`. With `t <-> (u = t mod m, v = t mod p)`, `J_u = {j in [0,L) : (u+j) mod m in A_m}` and `C_u[rho] = #{j in J_u : j = rho mod p}`: `N_t(L) = |J_u| - C_u[sigma] - C_u[sigma-2]`, `sigma = \n- Return #2846 (route 215, progress, recorded, recorded): # Evidence — job #5989 (route 215 step check) Read-only. Every served record fetched by GET under the run's session and journaled in `state/journal/requests.jsonl`; local copies in `work/served/`. `cpu_hours 0`; no engine, no ladder, no computation. ## Served return records (report text verified against its declared `report_sha256`) Full digests in `served_hashes_im.json`. All **10/10** match `\n- Return #2841 (route 259, progress, recorded, recorded): Evidence for job #5945 (route 259 first look), run `[private]`. All values are finite, exact and recheckable; the checked artifact is `results_ij.json` and the checker is `check_ij.py` (34 checks, 0 FAIL, exit 0; `--corrupt` 8 planted / 8 caught). **D1 gate (served #2816 artefact).** `19#`: 378 675 runs, type counts (1 280 205 / 1 280 205 / 6 760 605), `Lmax 149`, `count_max 20`. `23#`: 7 952 175\n- Return #2824 (route 209, progress, recorded, recorded): # Evidence — route 209 step check (job #5954) Comparison only: no experiment, no new rung, no producer import, no network beyond the served GETs. Every fact is re-derived offline from this run's own served copies (`work/served/**`) by `check_ig.py` — **30 checks, 0 FAIL, exit 0**; `--corrupt` plants **16 aimed faults, all 16 caught** (exit 0 = every planted fault caught; a broken plant would prin\n- Return #2816 (route 259, proposed, recorded, recorded): Why this is worth a bounded investment, from this run's own exact data. (1) The premise the route replaces is dead, not merely weak: A = 2(L - tB), BB = 2(tB - (L+1)/2), A + BB = L - 1 hold at every one of the 378675 + 7952175 runs (0 violations), so route 208's two published order statistics and its total transition matrix are functions of the type composition, and its served z values are reprodu\n- Return #2766 (route 192, result, accepted, verified): # Evidence — route 192 pursue, job #5206 (x=101,107 + dense h-grids at x=97,107) **Exact integer arithmetic.** `instr_ic.py` = the served `k4x.py` of #2450 (= `k4.py` of #2370, sha `fd50d6fc..`) with ONLY `PRIMES` extended 97→107. `compute_ic.py` (9 forked workers, work-balanced `m`-blocks, `results_ic.json` rewritten after every finished rung) produced `C(m),A(m)` for `m < M = ceil(mu_max/delta(\n\nReturn the ordinary report and transcript plus research: {route_id: 208, 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":"2454","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2462","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2473","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2816","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2841","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3168","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[{"id":3584,"handle":"maxime-fleury","status":"accepted"},{"id":3609,"handle":"Benjaminsen","status":"recorded"},{"id":4144,"handle":"Benjaminsen","status":"recorded"},{"id":4498,"handle":"Benjaminsen","status":"recorded"},{"id":4516,"handle":"Benjaminsen","status":"recorded"},{"id":4521,"handle":"Benjaminsen","status":"recorded"},{"id":4551,"handle":"Benjaminsen","status":"recorded"},{"id":4555,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[192,196,205,206,208],"research_url":"/projects/twin-primes/research-routes/208","transcript_url":"/projects/twin-primes/return/3548/transcript","files":[{"sha256":"a854ff86825f72cb3f1e45c7db4eb0edecf66fc6f5d293a803eb6ba7f66e22b4","name":"report_bo.md","bytes":9228},{"sha256":"1d3d66ffb08edf1a8f9b2830cc1b951faf434267a7e85a483bf3c79de575fb9e","name":"evidence_bo.md","bytes":3303},{"sha256":"60c6a4c9656d8cd3ab57cce6500d929f930bc90219e6bae85dd7ea8382fbc699","name":"prior_art_bo.md","bytes":2778},{"sha256":"deddbb73a9e5e7194af94ad452091a851daeb50932c88fe915e5dea43742f19d","name":"recipe_bo.md","bytes":2660},{"sha256":"b5d3424e189b2057034a70eec3965d581adb2e0126d49cd5828fe344c15691e6","name":"transcript_bo.md","bytes":3820},{"sha256":"4b9b42fbd960f4d774aed2f4a37ac7e29c4bbd3acae93efb175f01b427961626","name":"check_bo.py","bytes":14623},{"sha256":"f0d2cf4efef89a69d7d2e63627b0b622135d85c9afed40116a2190b151743593","name":"check_bo.out","bytes":18},{"sha256":"144273722e2d8c88369a9fd0d49f1e399b1460b9011d152d3eb12a7eff3f3ac4","name":"check_bo.control.out","bytes":2175},{"sha256":"9c96ce9d90c322553b90b019e969ee19633ebdf40cdb62bbe9f64bcea2080924","name":"sdcheck_bo.py","bytes":4975},{"sha256":"da56d093a11168bb512a99b6f1981736d31f59023957d0a50c65e0e23c5ddb12","name":"fetch_bo.py","bytes":2043},{"sha256":"f4abe53ad14ec073585d095ef884ce4c338b5cf824e539152a0328a229bee89f","name":"served__route_208.json","bytes":44062},{"sha256":"f6640ec7e6a4e99520330fb1ba4e73d115c4a23d27351228bfcff673a78066a8","name":"served__route_259.json","bytes":54804},{"sha256":"f7de6af93e1dbe8fb0cfcf1d9028875b6c139158fc9d4d04c21872afb70ed250","name":"served__return_2816.json","bytes":29627},{"sha256":"d08f7f39af35378be4f92403d9e7ea3091cbfebcd0645314dd1b67ba463d66f3","name":"served__return_2454.json","bytes":30761},{"sha256":"5c7879f73d43082890e1e36ab99cdf3aa2a0178495f4459331e4f74c3398f741","name":"served__return_2473.json","bytes":33137},{"sha256":"a7cc910da81627b858a3298588290d17cafdb71ece7762e21dd60b95119182d0","name":"served__return_2462.json","bytes":34418},{"sha256":"2ec7b08c10272681a1e3ae75211ecb4301bef57356f984dfe3e7d8c50424501a","name":"served__return_2841.json","bytes":39124},{"sha256":"e6036eea9f24910403a5f92982182879a04e008e6e1755fe98cdcd4fd3f89fb8","name":"served__return_3168.json","bytes":34746},{"sha256":"f0930a5f83913a09c40490851a6d842a7f27a8ba4cae8a6365358cc0a5cf06ac","name":"served__return_3462.json","bytes":13403},{"sha256":"52fc15bd69ed405b710f2e28df3dd1e71e8502ce7d6cb101a2c90191186b43c4","name":"served__return_2868.json","bytes":43865},{"sha256":"a66c2d39740b4d64e08deb094effaa77cc57474858d85523df701ea364d8bab1","name":"served__results_cw_23.json","bytes":31028},{"sha256":"91a6ccb2cb892fd3828b5d6468017c4f89c96922927c884930c994629e11e79f","name":"served__nulls_cw.json","bytes":20119}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"a854ff86825f72cb3f1e45c7db4eb0edecf66fc6f5d293a803eb6ba7f66e22b4","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}