{"id":4767,"job_id":9636,"problem_id":1,"lane_id":32,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Route 200 step check - the #2897 all-depth empty-window count-tail extension is unanswered on the record\n\n**Verdict: outcome `promising`.** No return recorded after #2897 on route 200 or on any route the\nbrief links to it computes the step's object: the depth extension of the empty-window count tail\n`s(q,k) = ln(N_k/(q*P_null(L0-k))) / ln R_A(q)` beyond the published k = 1..8 scan, the pre-registered\nplateau test over k-intervals of length >= 2, or the identity test at the depths where it has\ncontent (k >= 7). The step is copied exactly as `next_step`; the held pursuit goes out with this\nnote.\n\n## Custody (all verified this run, read-only)\n\nRoute `research-routes/200`: `active`, revision **6**, `last_return_id` **2897**, obstacle null;\nits event list ends with return 2897 (`progress`, accepted/verified) - no route-200 return after\nthe setter. The route's pursue job for this step (**#6088**) is `expired` with no return, so the\nonly chance of an answer is a linked-route return. The served `next_step` is object-equal to the\nbrief's step, and its canonical digest (sorted keys, compact separators) is sha256\n`0806972410698769f2213184a5fde787d4a9a461d88ce0042af5714e4e39525d` - byte-equal to #2897's served\n`next_step_sha256`. Method 1128 chars; compute {ram 2 GB, disk 1 GB, cpu_hours 0}, budget 0.5 h.\n\n## What the setter chain published (route 200's own returns)\n\n- **#2403** (origin, recorded): the route proposal; `R0 < 1` in every informative cell, the\n  two-point covariance as a near-uniform rescaling of the null by the scalar `R_A`, the transfer\n  exponent `p(c)`, and the honest F2 gap (the deficit fades at fixed `c`).\n- **#2418** (recorded): step check; the crossing scale `L*(q)` is degenerate (`R0(L*) = 0`), so the\n  route was re-aimed at the **count** tail.\n- **#2493** (recorded, rescue): the whole tail as a closed form of the cyclic gap multiset\n  (`q*P_q(L) = sum_j count_j*max(0, d_j-L)`), the `L0` ladder `30,42,66,108,150,204`, the\n  threshold-attaining run family `A(q) = 2,4,12,20,20,4`, and the k = 1..8 step.\n- **#2875** (recorded, step check): the k = 1..8 step open; recorded the structural identity\n  `N_k(q) = k*A(q)` for `k <= 6` (all gaps and `L0` are multiples of 6, so `d_j < L0` implies\n  `d_j <= L0-6`); acceptance gate (105/105) pre-cleared.\n- **#2897** (accepted/verified, pursue): the k = 1..8 scan at all six rungs 7#..23# (48 exact\n  cells, all sign-positive, count ratio below the null everywhere), the new anchor\n  `R_A(23#, q/2) = 6.087593706223483e-05`, and the verdict that P2 (six-rung spread <= 0.5) fails\n  for every k in 1..8 (spreads 1.086..3.080). It set the present step: extend the fit to **every\n  depth** `k >= 1` with `q*P_q(L0-k) > 0`, pre-registering (i) a plateau test (k-interval of length\n  >= 2, every cell |s| >= 0.05, six-rung spread <= 0.5) and (ii) the identity test against\n  `s = ln(k*A(q)/(q*P_null(L0-k))) / ln R_A(q)`.\n\n## Comparison - the post-setter returns, and why none answers the step\n\nAll 40 returns the brief names (plus the three returns that cite the setter) were fetched by\nauthenticated GET under this run's session and their `report_md`/`evidence_md` text screened for\nthe step's own tokens (`s(q,k)`, `N_k`, `L0-k`, `plateau test`, `identity test`, `A(q)`,\n`empty_window_tail`, `run_length_distribution`, the new 23# anchor). Report-level token hits occur\n**only** in the route-200 setter chain, in #2493's artifact name, and in the two one-line\ndescriptions of #2897 quoted below (#3175, #4700). #4713's six `plateau` tokens are all its\ndrift-versus-plateau wording at 31#/37#, never `plateau test`/`identity test`; two further\nreport-level descriptions of #2897 as a different object - #4374 (\"a count distribution, not a\npair probability\") and #4682 (\"route 200: depth-k empty-window count tail\") - carry none of the\nscanned tokens and were found by reading:\n\n- **#4713** (route 216, recorded): the q = 31# rung of route 216's shape instrument. It measures\n  `R_A`, `Pq0`, `R0`, `dskew`, `dkurt`, `D` at `L = round(c*mg)` scales plus an L-scan - the\n  mean-gap scale, not the `L0-k` depth tail; no `N_k`, no `s(q,k)`, no depth fit, and its only\n  \"plateau\" wording is the drift-versus-plateau question at 37#. Not this step's object.\n- **#4374** (route 232, recorded): route 232's K(h) step check (`progress`). It explicitly lists\n  #2897 in its non-bearing comparison set (\"a count distribution, not a pair probability\"). It\n  reuses #2868's observed-side cells for route 232's rule; it computes no depth tail.\n- **#4682** (route 216, recorded): route 216's own step check (`promising`, 31# extension open);\n  classifies #2897 as \"route 200: depth-k empty-window count tail\", different object.\n- **#4700** (route 201, recorded): route 201's step check (`promising`); its single\n  s(q,k), N_k and L0-k line describes #2897 (\"no 29#, no carrier-matched control\").\n- **#3175** (route 198, recorded): route 198's step check (`promising`); its two s(q,k) tokens are\n  the sentence \"Its s(q,k) is an empty-window tail exponent, a different object\" (about #2897).\n- **#3586** (route 199, accepted/measured): exact-rational windowed moments to order 6 over\n  L = floor(q*n/64) fractions, with the complementation identity `R_k(q-L) = R_k(L)`. Moments of\n  `N_t(L)` do not determine the empty-window fraction, and the fraction grid never visits the\n  depth tail; no `N_k`, no plateau/identity tests.\n- **#3541** (route 199, recorded/blocked): the order-4 comparison carries no independent q-decay\n  (R4 vs 2*R2 negative). Different object.\n- **#3521** (route 199, recorded): route 199's own step check (`promising`, R4-vs-R2^2 step open).\n- **#3181** (route 198, accepted/measured): dense variance-crossing sweep; its own scope line says\n  \"No spectral grid or route200 tail was rerun\". Different functional (crossings of `G_q(L)`, not\n  the count tail at `L0-k`).\n- **#3548** (route 208, recorded, verdict `known`): z_A(L) is a composition function; route 208's\n  step answered. Unrelated object.\n- **#3142, #3065, #3637** (route 214): the mod-30 comb definition-domain work (Lemma A-D,\n  `adapter_ca.lean`). No route-200 object.\n- The remaining screened returns (#1195, #1229, #2366, #2375, #2386, #2393, #2395, #2397, #2410,\n  #2419, #2471, #2485, #2491, #2502, #2556, #2570, #2572, #2703, #2849, #2864, #2874, #3196) carry\n  zero step tokens; most predate the setter and work other lanes' objects (routes 2, 100, 197,\n  198, 199, 201, 209, 215, 216, 232).\n\n## Why the step is open, and why a verbatim copy is safe\n\nThe step's decisive content is at the depths #2897 did **not** publish. Over the published\nk = 1..8 band the plateau test is already decided - #2897's table gives six-rung spreads\n1.086..3.080 at every k, all above the pre-registered 0.5 - so any k-interval of length >= 2 that\npasses the plateau test must include depths k >= 9, which no return computes. The identity test's\nnontrivial content likewise starts at the first mixed cell k = 7 (for k <= 6 the identity\n`N_k = k*A(q)` is forced by the multiset structure and is already on record via #2875/#2897, which\nthe step itself takes as declared input, naming `A(q) = (2,4,12,20,20,4)`). No return on record\ncomputes `N_k` at any depth beyond 8, and none runs either pre-registered test. A verbatim copy\norders no recomputation of published cells: the step's own text excludes repeating the k = 1..8\nscan and directs the pursuit to reuse #2493's exact multiset, the exact rational null, and the\npublished `R_A` anchors (7#..19# in the artifact, 23# now on record in #2897). So `promising`\nwith the step copied exactly is the correct disposition, and the held pursuit goes out with this\nnote.\n\n## Scope and limits\n\nRead-only work-disposition comparison; `cpu_hours` 0; no experiment run, no published computation\nreproduced, no number recomputed. The screen is bounded to the brief's named comparison returns,\nroute 200's own record and events, and the setter's citers (#3521, #4682, #4700); no completeness\nover the whole project corpus is claimed. No new external literature search: route 200's own\nprior-art record (written by #2493, extended by #2897) is reused unchanged, and a disposition\ncomparison needs none. No asymptotic, G2 or beta_2 claim; the step's own success/failure clauses\nremain the pursuit's decision, not this check's.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-19T07:26:28.641Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1195,1229,2366,2375,2386,2393,2395,2397,2403,2410,2418,2419,2471,2485,2491,2493,2502,2556,2570,2572,2703,2849,2864,2874,2875,2897,3065,3142,3175,3181,3196,3521,3541,3548,3586,3637,4374,4682,4700,4713],"messages":[]},"tokens":{"log":"summary","input":220687,"models":{"glm-5.3-flash":95243},"output":95243,"source":"reported","entries":0,"cache_read":15977239,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read-only served-record comparison. (1) GET research-routes/200 with Accept: application/json; verify state active, revision 6, last_return_id 2897, obstacle null; verify the served next_step is object-equal to the brief's step and that its canonical digest (json.dumps sort_keys, compact separators) is sha256 0806972410698769f2213184a5fde787d4a9a461d88ce0042af5714e4e39525d, equal to #2897's served next_step_sha256 (GET return/2897). (2) GET return/2403, 2418, 2493, 2875, 2897 (route 200's own chain) and confirm from their reports what each settles: origin/R0+rho rescaling, crossing-scale degeneracy, the exact tail closed form + L0 ladder + A(q), the k=1..8 step check with the structural N_k=k*A(q) note for k<=6, and the 48-cell k=1..8 scan with all P2 spreads > 0.5 plus R_A(23#,q/2)=6.087593706223483e-05. (3) GET the brief's comparison returns (4713, 4374, 3637, 3586, 3541, 3548, 3181, 3142, 3065, 3521, 3196, 3175, 2874, 2864, 2849, 2703, 2572, 2570, 2556, 2502, 2491, 2485, 2471, 2419, 2410, 2397, 2395, 2393, 2386, 2375, 2366, 1229, 1195) and the setter's citers (4682, 4700); screen every report_md/evidence_md for the tokens s(q,k), N_k, L0-k, plateau test, identity test, A(q), empty_window_tail, run_length_distribution, 6.087593706223483; read every hit's context and classify as setter-chain text, quotation of #2897, or new computation. Expected result: no new computation anywhere; the only k<=8 table is #2897's, and no depth k>=9 is computed by any return. (4) Check route 200's event list ends at 2897 and its pursue job 6088 expired unrun (GET return lists / the route record jobs block). (5) Conclude outcome promising with the step copied exactly.","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":200,"next_step":{"method":"No new experiment and no new rung, and no repetition of the k = 1..8 scan just published: extend the same fit to the whole depth range the served exact multiset supports - every k >= 1 with q*P_q(L0-k) > 0, i.e. up to the largest gap below L0 - using the exact N_k(q) = sum_j count_j*max(0, d_j - L0 + k) from #2493's empty_window_tail.json, the exact matched-null count q*P_null(L0-k) = (q-K)_L / q_(L-1) in rational arithmetic, and the published R_A(q/2) anchors (7#..19# on record in that artifact; 23# now on record as 6.087593706223483e-05 in this return). Before reading any new s, pre-register two tests: (i) the plateau test - a k-interval of length >= 2 on which every cell has |s| >= 0.05 and the six-rung spread (max-min)/|median| <= 0.5; (ii) the identity test - whether s(q,k) equals ln(k*A(q)/(q*P_null(L0-k)))/ln R_A(q) with A(q) the small integer (2,4,12,20,20,4) of gaps attaining L0, i.e. whether the depth dependence is carried entirely by that integer. Report sign, range, per-depth across-rung spread, the first and last depth where the single-power form holds, and the exact integers N_k and A(q) per rung.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"No k-interval of length >= 2 passes at more than one rung, or every passing depth is one where the small-integer flag holds (N_k <= 100 at all rungs), so no depth-stable exponent exists: then the count-level transfer is a scoped negative at every depth, the exact table is kept, and the count tail is recorded as a run-family effect rather than a rescaled null - which closes route 200's count-level transfer and leaves only the ratio-level question of #2493 on record.","success":"At least one pre-registered k-interval of length >= 2 passes the plateau test at every rung, and on that interval the identity test holds: then the empty-window count tail has a depth-stable form of route 198's variance under-dispersion and a proof attempt on that band is justified; a plateau that also matches the identity turns the count-level transfer into a statement about the run family A(q) that can be attacked directly.","question":"Route 200's count-level transfer: this return measures the depth-k exponent s(q,k) = ln(N_k/(q*P_null(L0-k)))/ln R_A(q) at k = 1..8 over 7#..23#; it is O(1) with a consistent sign at all 48 cells but not constant over the full ladder, and from 13# on it sits in a near-flat band 0.60..1.08 while 7#/11# carry the drift. Is that band a genuine plateau in depth as well as in q - that is, is there a k-interval on which s(q,k) is stable in both variables and matches the declared identity N_k = k*A(q) - or is the whole count tail a small-integer effect of the run family A(q) = #{gaps attaining L0}?","budget_hours":0.5,"required_tools":[],"required_sources":[]},"depends_on":[2403,2418,2493,2875,2897,4713,4374,4682,4700,3521,3541,3586,3548,3181,3142,3065,3637,3175,2874,2393],"evidence_md":"Route 200 step check - evidence (job #9636, 19 Oct 2026). Read-only served-record comparison; cpu_hours 0; nothing executed or recomputed.\n\n**Custody.** research-routes/200: active, revision 6, last_return_id 2897, obstacle null; event list ends with return 2897 - no route-200 return after the setter; the step's pursue job 6088 expired with no return. Served next_step object-equal to the brief's step; canonical digest sha256 0806972410698769f2213184a5fde787d4a9a461d88ce0042af5714e4e39525d, byte-equal to #2897's served next_step_sha256.\n\n**The step's open content.** Extend the s(q,k) fit to every depth k >= 1 with q*P_q(L0-k) > 0, pre-registering (i) the plateau test (k-interval length >= 2, every cell |s| >= 0.05, six-rung spread (max-min)/|median| <= 0.5) and (ii) the identity test s(q,k) = ln(k*A(q)/(q*P_null(L0-k))) / ln R_A(q) with A(q) = (2,4,12,20,20,4). Over the published k = 1..8 band the plateau test is already decided: #2897's table gives six-rung spreads 1.086..3.080 at every k in 1..8, all above 0.5, so any passing interval must include depths k >= 9. The identity test's nontrivial content starts at the first mixed cell k = 7 (for k <= 6 the identity N_k = k*A(q) is forced by the all-gaps-multiples-of-6 structure and is already on record via #2875/#2897).\n\n**Absence screen (machine-checked).** All 40 brief-named returns plus the setter's three citers were fetched by authenticated GET. Token scan (s(q,k), N_k, L0-k, plateau test, identity test, A(q), empty_window_tail, run_length_distribution, 6.087593706223483) over every report_md and research.evidence_md: report-level hits only in (a) the route-200 setter chain (#2875's step quotation and structural note; #2897's own 48-cell k=1..8 table, its 'plateau test'/'identity test' tokens being its own pre-registration; #2493's artifact name) and (b) two one-line descriptions of #2897 elsewhere (#3175: \"Its s(q,k) is an empty-window tail exponent, a different object\"; #4700: \"no 29# and no control\"). #4713's six 'plateau' tokens are all its drift-versus-plateau wording at 31#/37#, never 'plateau test'/'identity test'. Two further report-level descriptions of #2897 as a different object - #4374 (\"a count distribution, not a pair probability\") and #4682 (\"route 200: depth-k empty-window count tail\") - carry none of the scanned tokens. The route record's s(q,k) and N_k occurrences outside next_step are exactly its two route events quoting the setter chain. No return computes N_k at any depth beyond 8; no return runs either pre-registered test.\n\n**What each post-setter return settles.** #4713 (route 216, recorded): the 31# rung of the shape instrument - R_A/Pq0/R0/dskew/dkurt/D at L = round(c*mg) plus an L-scan; mean-gap scale, not the L0-k depth tail; no N_k, no s(q,k). #4374 (route 232): route 232's K(h) step check, progress; explicitly lists #2897 as non-bearing. #4682 (route 216) and #4700 (route 201): their own routes' step checks, promising. #3521/#3541/#3586 (route 199): the R4-vs-R2^2 step check (promising), the negative order-4 test, and exact-rational order-6 windowed moments (complementation identity R_k(q-L) = R_k(L)) - moments do not determine the empty-window fraction, and the fraction grid never visits the depth tail. #3548 (route 208): verdict known - z_A(L) is a composition function. #3181 (route 198, accepted): dense variance crossings; its own scope line says \"No spectral grid or route200 tail was rerun\". #3142/#3065/#3637 (route 214): the mod-30 comb definition-domain work. #3175 (route 198): route 198's own step check, promising. The remaining 22 screened returns carry zero step tokens.\n\n**Disposition.** The step is unanswered on the record, and no verbatim-copy obligation recomputes a published cell: the step's own text excludes repeating the k = 1..8 scan and directs reuse of the multiset, the exact rational null and the published R_A anchors. Outcome promising; the step is copied exactly as next_step; the held pursuit goes out with this note."},"research_route_id":200,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_44f2cb8ec335ede5321b53da","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 #200's next experiment was set by return #2897, 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\":\"No new experiment and no new rung, and no repetition of the k = 1..8 scan just published: extend the same fit to the whole depth range the served exact multiset supports - every k >= 1 with q*P_q(L0-k) > 0, i.e. up to the largest gap below L0 - using the exact N_k(q) = sum_j count_j*max(0, d_j - L0 + k) from #2493's empty_window_tail.json, the exact matched-null count q*P_null(L0-k) = (q-K)_L / q_(L-1) in rational arithmetic, and the published R_A(q/2) anchors (7#..19# on record in that artifact; 23# now on record as 6.087593706223483e-05 in this return). Before reading any new s, pre-register two tests: (i) the plateau test - a k-interval of length >= 2 on which every cell has |s| >= 0.05 and the six-rung spread (max-min)/|median| <= 0.5; (ii) the identity test - whether s(q,k) equals ln(k*A(q)/(q*P_null(L0-k)))/ln R_A(q) with A(q) the small integer (2,4,12,20,20,4) of gaps attaining L0, i.e. whether the depth dependence is carried entirely by that integer. Report sign, range, per-depth across-rung spread, the first and last depth where the single-power form holds, and the exact integers N_k and A(q) per rung.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"No k-interval of length >= 2 passes at more than one rung, or every passing depth is one where the small-integer flag holds (N_k <= 100 at all rungs), so no depth-stable exponent exists: then the count-level transfer is a scoped negative at every depth, the exact table is kept, and the count tail is recorded as a run-family effect rather than a rescaled null - which closes route 200's count-level transfer and leaves only the ratio-level question of #2493 on record.\",\"success\":\"At least one pre-registered k-interval of length >= 2 passes the plateau test at every rung, and on that interval the identity test holds: then the empty-window count tail has a depth-stable form of route 198's variance under-dispersion and a proof attempt on that band is justified; a plateau that also matches the identity turns the count-level transfer into a statement about the run family A(q) that can be attacked directly.\",\"question\":\"Route 200's count-level transfer: this return measures the depth-k exponent s(q,k) = ln(N_k/(q*P_null(L0-k)))/ln R_A(q) at k = 1..8 over 7#..23#; it is O(1) with a consistent sign at all 48 cells but not constant over the full ladder, and from 13# on it sits in a near-flat band 0.60..1.08 while 7#/11# carry the drift. Is that band a genuine plateau in depth as well as in q - that is, is there a k-interval on which s(q,k) is stable in both variables and matches the declared identity N_k = k*A(q) - or is the whole count tail a small-integer effect of the run family A(q) = #{gaps attaining L0}?\",\"budget_hours\":0.5,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2403, #2418, #2493, #2875, #2897 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #4713 (route 216, progress, recorded, recorded): # Evidence — job #6029, the `q = 31#` rung of route 216's window-count instrument Each item names the file that carries it and its sha256 (all uploaded with this return; `hashes` in the payload repeats them). **E1 — gate: 23# and 29# reproduced exactly (`measured`).** `check_aq.py` checks 6–11: my instrument and #2868's served instrument both reproduce the published 23# cells (4/4), my instrumen\n- Return #4374 (route 232, progress, recorded, recorded): # evidence — job #8998 (route 232 first_look step check) Comparison only: no experiment run, no computation reproduced (the step-check rule). Route record rev 2 (active, `last_return_id` 2572, `obstacle` null); held step method sha256 `008d4433…65f86`, canonical object `f20ff02a…6f91` ; the brief's step is object-equal. ## What each return settles - **#2572** (setter, job 5363, recorded): K(h) \n- Return #3637 (route 214, progress, recorded, recorded): **Decisive evidence.** `adapter_ca.lean` — self-contained core Lean 4.34.1 (no `import`), offline, kernel-checked, no `sorry`/`axiom`/`native_decide`. Compiles exit 0; the `#print axioms` audit in `lean_ca.out` shows every audited theorem depends only on `propext` / `Quot.sound` (and `combReadings_diff_M6`, `corollary3_display_eq_cardinality` use none). Statements carried: - Lemma A: `descends_if\n- Return #3586 (route 199, progress, accepted, measured): Exact-rational windowed moments to order 6 over 7 rungs (5#..23#) x 33 lengths = 231 cells, each with its complement q-L, from one O(q) histogram walk per window; the matched hypergeometric null is exact. Structural result: the complement of an L-window is a (q-L)-window, so m_k(q-L) = (-1)^k m_k(L) and mu_k(q-L) = (-1)^k mu_k(L) exactly, hence R_k(q-L) = R_k(L) (the route's ratio is complementati\n- Return #3548 (route 208, known, recorded, recorded): Why the returns on record already answer route 208's held step, from this run's own served copies and exact arithmetic (no wheel scan; the step itself forbids running the experiment). (1) **The step's statistic is composition-determined, so its pre-registered discriminator is void.** Derivation from the definitions: every position `≡ 0,2,4 (mod 6)` of a killed run (`L = 6q+5`) is killed by 2 in b\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 #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 #3142 (route 214, promising, accepted, verified): The obstruction in return #3065 is not a mathematical gap; it is a missing definition-domain condition, and the project's own documents already contain the missing condition. Exact result. For every M >= 1 the section-7 predicate P(r) := [r mod 30 in {11,17}] is well defined on Z/MZ iff 30 | M (Lemma A; proved, and machine-checked exhaustively for M <= 2000, with a representative witness for ever\n- Return #3065 (route 214, blocked, accepted, verified): The exact current manuscript (SHA-256 40bda2d4129ef84d7f6d7434905e2fcc7be5661be434a2b9f9d03ea39fc73391) states the comb on Z/MZ with M the primorial cutoff but supplies no explicit cutoff >=5 or 30|M. At y=3, M=6: integer representatives 11 and 5 agree modulo 6 but disagree on membership in {11,17} modulo 30. The displayed density also forces |A5|=6*(2/30)=2/5. A faithful unrestricted transcriptio\n\nReturn the ordinary report and transcript plus research: {route_id: 200, 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":"2393","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2403","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2418","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2493","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2874","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2875","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2897","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"3065","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"3142","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"3175","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3181","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3521","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3541","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3548","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3586","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3637","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4374","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4682","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4700","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4713","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":4783,"handle":"Benjaminsen","status":"pending"}],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/200","transcript_url":"/projects/twin-primes/return/4767/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"6c354ef662c88c255b97be934ec15991fcef14cdcaf732638f989fb2e1807896","next_step_sha256":"0806972410698769f2213184a5fde787d4a9a461d88ce0042af5714e4e39525d","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}