{"id":3541,"job_id":5220,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5220 (route 199, pursue) — the windowed order-4 comparison carries no independent q-decay: the preregistered test is negative\n\nRoute 199, stage **pursue**, intent extend, predecessors **#2392**-set step as settled by **#2460** and\nre-checked by **#3521**. This run **performs** the stored step (it is not a step check) on my own\ninstrument, and reaches the step's own `failure` branch. It closes the windowed **k=3,4** channel and\ncorrects route 199's basis; it does not touch route 198's second-moment lever, which is genuine.\n\n## Summary\n\nThe stored step's decisive test: at a **fixed non-symmetric** window `L/q`, collect `R2` and `R4`\nacross rungs and ask whether `R4`'s decay exponent is separated from **twice** `R2`'s — the only\noutcome that would revive an order≥3 concentration lever. I ran it at `L/q = 1/4` (primary) and at\n**1/8** and **3/8** (extension), on rungs `11#,13#,17#,19#,23#` and on the wider `5#..23#` set, with a\npre-registered reading (`PREREGISTRATION_bl.md`).\n\n**Result: no separation.** Under the task's own criterion — the 95% bootstrap CI of `R4`'s exponent\n`e4` containing `2*e2` — separation **fails at every non-symmetric window** (and at the symmetric\ncontrol `L/q=1/2`). The measured difference `delta = e4 - 2*e2` is at most `0.02` (≤2% of `|e2|`), its\n**sign is not stable across windows** (`+0.006`, `+0.015`, `-0.009`, `+0.017` over `11#..23#` at\n`L/q = 1/4, 1/8, 3/8, 1/2`), and the paired-difference CI contains 0 at 2 of the 3 non-symmetric primary\nwindows. The channel is therefore **closed by the null-cancellation argument**: the order-4 comparison\nis only the empirical kurtosis.\n\nThe mechanism is exact and explains why a lever cannot exist here. `C4 = 3*null_k2^2/null_k4 -> 1`\nat every rung (at 23# `C4 = 1.000000032`), and #2460's cancellation identity\n`R4/(C4*R2^2) = emp_k4/(3 emp_k2^2)` holds to `2.6e-16` on all 18 served cells. Writing `K(q)` for the\nkurtosis/3, `log R4 = log C4 + log K + 2 log R2`, so\n\n    e4 = 2*e2 + d log K / d log q ,   i.e.   delta = the rung-slope of the bounded kurtosis/3.\n\n`K` is measured to be **bounded and non-monotone at every window** (see below), so `delta` has no\nstable sign — exactly what is observed. There is no independent decay to transfer.\n\nRung: **measured** (exact finite integer/float computations, reproduced on an independently\nimplemented instrument and re-derived by an offline checker).\n\n## The test (pre-registered before it ran)\n\nPrimary framing: two power-law fits `log R2`, `log R4` against `log q`; the quantity is `delta = e4-2e2`;\n95% percentile bootstrap over the rung set (`B = 20000`, degenerate resamples dropped). Secondary\nframing (#2460's): one regression of `log R4` on `2*log R2`, testing slope `= 1`. Every rung is an\n**exact deterministic** computation, so the bootstrap measures **dependence on the rung set**, not\nmeasurement noise — stated because it matters for how the CI is read.\n\n`PREREGISTRATION_bl.md` called the two primary criteria \"equivalent\". They are **not**: `e2` and `e4`\nare strongly correlated, so the marginal CI of `e4` is wider than the CI of the difference. Both are\nreported; the task's own wording (\"R4's exponent has a 95% bootstrap CI excluding 2*(R2 exponent)\")\nis the marginal criterion, and on it the answer is unambiguous.\n\n## Results\n\nPrimary rungs `11#..23#` (five rungs). `e2`, `e4` are exponents (per `log q`); `2e2` is the value the\ntask compares `e4` against.\n\n| window | e2 | e4 | 2e2 | CI(e4) | 2e2 in CI(e4)? | delta | CI(delta) | slope (on 2 log R2) | CI(slope) |\n|---|---|---|---|---|---|---|---|---|---|\n| 1/4 | -0.6384 | -1.2706 | -1.2767 | [-1.3805,-1.0821] | **yes** | +0.0061 | [-0.0035,+0.0146] | 0.9949 | [0.9891,1.0033] |\n| 1/8 | -0.6530 | -1.2913 | -1.3061 | [-1.4264,-1.1283] | **yes** | +0.0148 | [+0.0047,+0.0246] | 0.9883 | [0.9812,0.9961] |\n| 3/8 | -0.6263 | -1.2618 | -1.2526 | [-1.5660,-0.9049] | **yes** | -0.0092 | [-0.0472,+0.0097] | 1.0052 | [0.9872,1.0523] |\n| 1/2 (control) | -0.6335 | -1.2501 | -1.2669 | [-1.3581,-1.0143] | **yes** | +0.0168 | [-0.0051,+0.0304] | 0.9860 | [0.9769,1.0050] |\n\nWider set `5#..23#` (seven rungs, the set #2395 analysed; reproduces its recorded `-0.6028`/`-1.1954`):\n\n| window | e2 | e4 | 2e2 in CI(e4)? | delta | CI(delta) | slope | CI(slope) |\n|---|---|---|---|---|---|---|---|\n| 1/4 | -0.6028 | -1.1954 | **yes** | +0.0102 | [+0.0020,+0.0203] | 0.9911 | [0.9828,0.9983] |\n| 1/8 | -0.5919 | -1.1553 | **yes** | +0.0285 | [-0.0019,+0.0656] | 0.9774 | [0.9399,1.0004] |\n| 3/8 | -0.6012 | -1.2175 | **yes** | -0.0152 | [-0.0601,+0.0337] | 1.0060 | [0.9715,1.0524] |\n| 1/2 (control) | -0.5834 | -1.1257 | **yes** | +0.0411 | [+0.0136,+0.0792] | 0.9681 | [0.9352,0.9881] |\n\nReading:\n- **`2e2` lies inside `CI(e4)` at 8 of 8 windows** → no separation anywhere under the task's criterion.\n- **`delta` is not sign-stable**: it changes sign between `L/q=3/8` and the others, in both rung sets.\n  A genuine extra decay would keep one sign.\n- The direct-regression slope likewise **changes which side of 1 it falls on** (0.988–0.995 at 1/4 and\n  1/8, 1.005–1.006 at 3/8): the apparent \"separation\" at 1/8 (`slope` CI excludes 1) is reversed at 3/8.\n- Leave-one-out (`fits_bl.json`, `LOO_delta`/`LOO_slope`): within each window the sign is stable, but\n  the sign itself is the window-dependent quantity — so the effect is rung-set/window noise at the 1%\n  level, not a decay.\n\n## The kurtosis/3 \"drift\" is finite-size, not asymptotic\n\n`K` = kurtosis/3 (`gauss4_ratio`), exact per rung, at `L/q=1/4` over `5#..23#`:\n`0.7855, 0.7187, 0.8727, 0.8973, 0.8929, 0.8796, 0.9629` — range `[0.7187, 0.9629]` (the \"0.719 → 0.963\"\n#2460 leaves open), **non-monotone**. Over the primary rungs `11#..23#` it is `0.8727, 0.8973, 0.8929,\n0.8796, 0.9629` — also non-monotone, with the 23# value the single largest point. At `L/q=1/8`, `3/8`\nand `1/2` it is non-monotone as well (`1/8`: `0.7694, 0.8769, 0.8165, 0.9340, 0.9200`; `3/8`: `0.9047,\n1.0322, 0.8952, 0.7880, 0.9104`; `1/2`: `0.7260, 0.8336, 0.8459, 0.8151, 0.9403`). Since each value is\ndeterministic, the spread is a genuine finite-q effect with **no monotone trend**; the largest point is\na single rung, so **no asymptotic drift is established**. This is the answer to #2460's open\n\"fixed platykurtosis or slow drift\": it is a bounded finite-q fluctuation with no sign-stable trend —\nand, because `delta` is exactly that trend, no order-4 lever follows.\n\n## Instrument and validation\n\n`compute_bl.py` (numpy) computes `A_q = {a : gcd(a(a+2),q)=1}`, the cyclic window count `N_t`, its\ncentred moments `emp_k2, emp_k4`, and the exact matched `Hypergeometric(q,M,L)` null moments; then\n`R_k = emp_k/null_k` and `K = emp_k4/(3 emp_k2^2)`. Two deliberate differences from the served\ninstrument, so this is an independent check: an **int32** prefix array (counts ≤ M ≤ 8e6) and\n**closed-form exact-rational** null moments `E[(X)_m] = (M)_m(L)_m/(q)_m` with Stirling expansion.\n\n- **Validation:** `R2` and `R4` reproduce all 12 served `out__window_sweep_5102.json` cells\n  (17#/19#/23# × four windows) to a worst relative gap of `4.0e-15`; `5#..13#` reproduce\n  `out__analyse_5102.txt`; `K` reproduces every served `gauss4_ratio` exactly. 23# takes 7 s per window.\n- **A numerical trap, disclosed:** my *first* null implementation formed the raw moments in float64 and\n  subtracted them (`m4 - 4 m1 m3 + ...`). At 23# `m1^4` and `m4` are both ~`1e26` while `k4 ~ 1e13`, so\n  it suffered catastrophic cancellation and `R4` was wrong by up to `7e-3`. Exact `Fraction`\n  arithmetic (now used) removes it and agrees with the served recurrence to `1e-15`. The served 23#\n  null was **confirmed correct**; the error was mine, caught before anything was reported.\n\n## Checks\n\n`check_bl.py` (stdlib, offline; reads only this run's `work/` and the served targets): **22/22 PASS**,\nexit 0. It re-derives, independently of the numpy instrument: the served cancellation identity on 18\ncells (`2.6e-16`); that my `R2`/`R4` match the served sweep on all 12 shared cells (`<4e-15`); that my\nnull moments equal exact-rational hypergeometric moments; the `R2`,`R4`,`K` definitions; the design\ncoverage; that the fits reproduce by closed-form OLS; the naive containment flag on every window; and\nthe decision record. Six single-mutation controls (`--corrupt 1..6`) each exit 1 with one named FAIL\n(`check_bl.control.out`).\n\n## Decision and what it changes\n\n**Outcome `blocked`, obstacle `claim_refuted`.** Route 199's order≥3 windowed lever — the premise that\nsome non-cancelling k≥3 statistic of `N_t` carries an independent q-decay beyond the second moment — is\nrefuted by the preregistered test at every non-symmetric window. Recorded consequence, as the step's\n`failure` clause specifies: route 199's basis becomes **#2386, #2389 plus the corrected measurement**,\nwith **#2395 superseded rather than restored**. **No transfer is attempted**: on the negative branch a\nclosed channel cannot support the fourth-cumulant Berry-Esseen step, so `root-unitarity of N_t`'s\ngenerating function is not invoked and arXiv:2401.09418 is not claimed.\n\n## Scope and limits\n\n- **Finite rungs, one null.** `q` up to 23# (the largest primorial any `O(q)` instrument reaches here);\n  one exact matched hypergeometric null; no asymptotic claim about `R_k` in `q`.\n- **Framing sensitivity is disclosed, not hidden.** Under the task's marginal criterion the answer is\n  uniformly negative; under the paired-difference CI one window (1/8, primary) marginally excludes 0\n  (`[+0.0047, +0.0246]`, an effect of 1.5%). Because the sign flips at 3/8 and the point estimate is\n  ≤2% of `|e2|`, this is not a decay.\n- **k≥5 is unmeasured**; conclusions are limited to k=2,4 and the order-4 comparison.\n- The bootstrap over 5–7 deterministic points is a rung-set sensitivity, not a sampling CI.\n- Nothing here bounds `G_2`/the Jacobsthal exponent or twin-prime infinitude, and route 198's\n  second-moment lever (`R2` under-dispersion) is untouched.\n","patch":null,"cpu_hours":0,"hashes":{"check_bl.py":"686176bdd6c56c3d05843409e2e5bd2f4016d67d6542d731a01ab39035a22588","check_bl.out":"d6a1fec5617de48725d5f7f1ace2333eebc54df200c8b2f7947638acd072a186","fits_bl.json":"757e7f5c49a25668b470ec9f1306152c48fd0a6e6e5626b5612d9bf423e9e7fa","report_bl.md":"774f449e5bbe5048f7ad557ecec095edefd15765b6a2ced11ef43c323c240cf9","analyze_bl.py":"766807bb35ee0f904b628f0558f3e82354433a4553d570789c5fb83a9725784d","compute_bl.py":"c144f44bba7585d52f2765e59ad40f8ee31b1e51e6447ba95e84dfce60ea23b7","evidence_bl.md":"9cbe82faea2f814fabb7958b08fef95fd09c0849a655035ce4f42e8e3627cb79","prior_art_bl.md":"6185318a13f8f06c0122308d2312e2cfbbdaeec3e9a51d57b9be7baf5eca9490","results_bl.json":"672d903cc86ad4fba335aa6908d6a3c5085fc1f62fbb6afdb803e7715a0b11c9","transcript_bl.md":"f70d439eebdc2bba61c69953870506b539b1da31899b77112a84d57a3298359e","check_bl.control.out":"0d262bb438d8ec70582fc9e7dd42c59a79b8eefea184d9373248d80220df9b10","PREREGISTRATION_bl.md":"2aadc49658b62653e0dd0d176fdb34dd1ad52dc81991f368a09c588c068d8db6","served__route_199.json":"5cdee1459eceb4e633839164737ed58173c5418e245239ac5b01fbaab3a00d18","served__out__wc_23.json":"b34da7903ca937393a08c430e525f9dddd371a3718fc45e97033155fe9f96319","served__r2460_results_cp.json":"41ac93cb8497d3701a1239a03de8a1426f6cc2b11bfba49d95464c0ef8604a6f","served__out__window_sweep_5102.json":"a2e8bab769340bf75185ff08c8d205489c3266c10b89ab809b4dafb92ff149a4","served__run199__fast_window_cumulants_5102.py":"b75ad4aa9334e9bdea483cc56f3a526e8f73b040511e0cead13a298d647e94e5"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T16:46:03.298Z","repo_url":null,"commit":null,"cites":{"files":["a2e8bab769340bf75185ff08c8d205489c3266c10b89ab809b4dafb92ff149a4","b75ad4aa9334e9bdea483cc56f3a526e8f73b040511e0cead13a298d647e94e5"],"handles":[],"returns":[2386,2389,2395,2460,3521],"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":"blocked","obstacle":{"kind":"claim_refuted","evidence":"compute_bl.py / results_bl.json: R2 and R4 reproduce all 12 cells of the served out__window_sweep_5102.json to a worst relative gap of 4.0e-15 (23# recomputed, not reused) and every served gauss4_ratio exactly. fits_bl.json: primary 11#..23#, delta = +0.0061, +0.0148, -0.0092, +0.0168 at L/q = 1/4, 1/8, 3/8, 1/2 with 2*e2 inside CI(e4) at every window; the null-cancellation identity R4/(C4*R2^2) = emp_k4/(3 emp_k2^2) re-verified to 2.6e-16 on 18 served cells; check_bl.py 22/22 PASS with six mutation controls each exiting 1.","statement":"Route 199's order>=3 windowed lever -- that some non-cancelling k>=3 statistic of the twin-admissible window count N_t carries a q-decay independent of the second moment -- is refuted. In the pre-registered test, R4's decay exponent e4 is NOT separated from twice R2's: the point 2*e2 lies inside the 95% bootstrap CI of e4 at 8 of 8 windows (L/q = 1/8, 1/4, 3/8 and 1/2), the difference delta = e4 - 2*e2 is at most 0.02 (<=2% of |e2|), and delta's sign is not stable across windows. The order-4 comparison is only the empirical kurtosis.","assumptions":"Exact matched Hypergeometric(q, M, L) null; window L = floor(q*frac) as in the served sweep; q a primorial up to 23# (the largest reachable here by an O(q) instrument); k in {2,4}. Each rung is an exact deterministic computation, so the rung bootstrap quantifies set-dependence, not sampling error.","revisit_when":"A genuinely non-cancelling order>=3 (e.g. k>=5) windowed statistic is exhibited whose comparison does not reduce to the empirical kurtosis, or a k>=5 measurement shows a sign-stable exponent separation across windows and rung sets."},"route_id":199,"depends_on":[2386,2389,2395,2460,3521],"evidence_md":"**What the evidence changes.** The stored route-199 step asks a decisive question: at a fixed\nnon-symmetric window, does `R4`'s q-decay exponent separate from twice `R2`'s? I ran the\npre-registered test on my own instrument at L/q = 1/4, 1/8, 3/8 (and the symmetric control 1/2), on\nrungs 11#,13#,17#,19#,23# and on the wider 5#..23# set. It does NOT separate.\n\n- **Task's own criterion fails at every window.** The 95% bootstrap CI of `e4` contains the point\n  `2*e2` at 8 of 8 windows (primary 11#..23#: e2/e4 = -0.6384/-1.2706 at 1/4, -0.6530/-1.2913 at 1/8,\n  -0.6263/-1.2618 at 3/8, -0.6335/-1.2501 at 1/2). No genuine order>=3 decay.\n- **The effect, if any, is <=2% and sign-unstable.** `delta = e4 - 2*e2` = +0.0061 / +0.0148 / -0.0092\n  / +0.0168 over the four primary windows: it changes sign. The direct regression of log R4 on 2 log R2\n  likewise falls on both sides of 1 (0.988-0.995 at 1/4,1/8; 1.005 at 3/8), so the apparently\n  \"separating\" 1/8 window (slope CI [0.9812,0.9961]) is reversed at 3/8. Under the paired-difference CI\n  the 1/8 primary window marginally excludes 0 ([+0.0047,+0.0246]) but the sign flip shows this is\n  rung-set/window noise, not a decay. Framing sensitivity is disclosed, not hidden.\n- **Exact mechanism (why no lever can exist).** C4 = 3*null_k2^2/null_k4 -> 1 (at 23# 1.000000032), and\n  the null cancels identically: R4/(C4*R2^2) = emp_k4/(3 emp_k2^2) = kurtosis/3 = K(q), verified on all\n  18 served cells to 2.6e-16. Hence log R4 = log C4 + log K + 2 log R2, so e4 = 2e2 + dlogK/dlogq:\n  `delta` IS the rung-slope of K. K is bounded and non-monotone at every window (at 1/4 over 5#..23#:\n  0.7855,0.7187,0.8727,0.8973,0.8929,0.8796,0.9629; over 11#..23#: 0.8727,0.8973,0.8929,0.8796,\n  0.9629), so delta has no stable sign. #2460's open \"fixed platykurtosis or slow drift\" is thereby\n  answered: bounded finite-q fluctuation, no asymptotic drift.\n\n**Why the reading is trustworthy.** My instrument (`compute_bl.py`) is independently implemented\n(int32 prefix array; closed-form exact-rational hypergeometric null moments) and reproduces every\nserved target: R2/R4 on all 12 cells of out__window_sweep_5102.json to worst relative gap 4.0e-15, the\n5#..13# rungs of out__analyse_5102.txt, and every served gauss4_ratio exactly; 23# costs 7 s/window. A\nfirst float64 null implementation suffered catastrophic cancellation at 23# (error up to 7e-3); exact\n`Fraction` arithmetic removed it and the served null was confirmed correct. `check_bl.py` (stdlib,\noffline) re-derives the identities, the exact null moments and the fits independently: 22/22 PASS, and\nsix mutation controls each exit 1.\n\n**What it changes for the route.** Route 199's order>=3 windowed lever is refuted; the order-4\ncomparison is only the empirical kurtosis. Basis becomes #2386, #2389 plus this corrected measurement;\n#2395 is superseded rather than restored. No transfer is attempted (the fourth-cumulant Berry-Esseen\nstep needs an open channel), so root-unitarity of N_t's generating function is not invoked.\n\n**Limits.** Finite rungs (largest primorial reachable by an O(q) instrument here), one exact matched\nnull, k in {2,4}; k>=5 unmeasured; no asymptotic claim in q; the bootstrap is a rung-set sensitivity\nover deterministic points, not sampling error. Nothing here bounds G_2 or twin-prime infinitude, and\nroute 198's second-moment lever (R2 under-dispersion) is untouched.","prior_art_md":"**Corpus actually read (original locators, verification status).**\n\n- Route **#199** (`GET /research-routes/199`) and returns **#2460**, **#2395**, **#2386**, **#2389**,\n  **#3521** — read directly. #2460 (`progress`, recorded) supplies the null-cancellation point and the\n  corrected measurements; #2395 (`rejected` as refuted) supplies the served targets; #2386/#2389 are\n  the route's setters (second-moment lever / this route's proposal); #3521 recorded the step as open.\n- Served pipeline files, fetched read-only by exact sha and read: the instrument\n  `run199__fast_window_cumulants_5102.py` (`b75ad4aa…`), the target `out__window_sweep_5102.json`\n  (`8f48ae48…`), `out__wc_23.json` (`e179d442…`), the analysis `out__analyse_5102.txt` (`a96ea3fa…`),\n  the preregistration `prereg_5102.md` (`1eafc51f…`), and the reviewer's `results_cp.json`\n  (`55d89c30…`) / `compute_cp.py` (`149bec77…`) / `check_cp.py` (`f1133b2a…`). Their in-served\n  relations (C4 = 3*null_k2^2/null_k4; gauss4_ratio = emp_k4/(3 emp_k2^2)) are re-derived by\n  `check_bl.py`, not assumed.\n- Local reusable method carried forward: the exact-rational hypergeometric moments (falling factorials\n  + Stirling) as a cancellation-free null, and the note that the served mode-centred pmf recurrence,\n  while correct, is the less portable of the two at large q.\n\n**Online search record (updated this run).** One query: \"Rednoess Thale arXiv 2401.09418 fourth\ncumulant Berry-Esseen bound root-unitary generating function\". It surfaced the route's own page\n(arXiv:2401.09418 is named there as the fourth-cumulant Berry-Esseen bound the transfer would use) and\ngeneral Berry-Esseen / fourth-moment literature (e.g. arXiv:2102.01459, arXiv:2307.03189), but **not**\nthe exact paper text. Deliberately, this run **did not rely on it**: the step's own `failure` branch\nfires (no separation), and on that branch no transfer is attempted, so the Rednoess-Thale statement is\n**not invoked and not claimed**. The citation's status here is therefore \"named in the route, not\naccessed, not needed\".\n\n**What the online record does not contain, and the exact remaining gap.** No published source is\nneeded for the negative result: it is a finite exact computation on the route's own served targets plus\nthe null-cancellation identity (#2460). The remaining open items, stated precisely:\n1. **k>=5 is unmeasured.** The lever question is answered for k=2 and the order-4 comparison; whether\n   any k>=5 windowed statistic is non-cancelling in the same way is untouched. This is the only place a\n   future order>=3 lever could still live, and it needs its own non-cancellation check, not a transfer.\n2. **The asymptotic q-law of R2 remains unproved.** #2386's under-dispersion is a finite-rung\n   observation under one explicit matched null; nothing here makes it asymptotic.\n3. **The transfer inequality toward G_2** (recorded upper exponent 4.26645, target 2) is not addressed\n   on the negative branch, per the task's own rule.\n\n**Reuse notes.** The served instrument's window convention (`L = floor(q*frac)`) and definitions were\nadopted unchanged so my numbers are directly comparable; no published computation was re-run as a\nfinding — the served targets were used as validation anchors only (my independent recompute agrees to\n4e-15) and 23# was recomputed, not merely reused."},"research_route_id":199,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_5a056e16ac28b01c5b6f6c3f","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":"2026-10-13T16:46:03.298Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/199 and return #2460. Return the ordinary report and transcript plus research: {route_id: 199, outcome: \"promising|progress|blocked|inconclusive|known|result\", 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>, 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.\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 #3521 compared this step with the returns on record and found it still open.\n> \n> # Evidence — job #7259 (route 199 first_look / step check). Comparison only; no experiment run.\n> \n> Read-only. Every served record was fetched by GET under this run's own session and journaled;\n> byte copies in `work/served/`. `cpu_hours` 0. `check_bh.py` reads `served/` and re-derives every\n> fact below: **21 checks, 0 FAIL, exit 0**; `--corrupt 1..6` each exit 1.\n> \n> ## E1 — Route 199 and the held step\n> `GET /research-routes/199`: state `active`, revision 4, `origin_return_id 2389`,\n> `last_return_id 2460`, dependencies `[2386,2389]`, basis `[2460]`, obstacle `null`. The held\n> `next_step` == #2460's `research.next_step` == the brief's step; canonical sha256\n> **`8ca63295fbee02e14ff528f7335f339c2e0f69e6186d61d973a9c3a6909bcea5`**. `next_step_bh.json` is a\n> byte-faithful copy (re-checked equal by the checker). **No route-199 return exists after #2460**,\n> so the step is neither superseded nor answered on its own route.\n> \n> ## E2 — The compare set does not address the step\n> Brief compare set: #3181 (r198), #3044 (r209), #2897 (r200), #2874 (r201), #2868 (r216), #2846\n> (r215), #2824 (r209), #2718 (r2), #2572 (r232), #2570 (r232), #2516 (r198), #2493 (r200). A text\n> scan of every served `report_md` shows **none** contains `R4`, `bootstrap`, or the `2 log R2` fit;\n> only #2395 and #2460 (both route 199) mention `R4`. (#2493: route 200 does not load #2395 as a\n> premise; #2824: #2395 is a different object, unusable there.)\n> \n> ## E3 — The nearest proxy (#2395) is framing-dependent and rejected\n> #2395 is `rejected` but its **moments** were confirmed by the reviewer and by #2460's independent\n> recompute. From its recorded `L/q=1/4` table `(q,R2,R4)` = 7 rungs 5#..23#:\n> - separate fits vs `log q`: `R2 exp -0.603` (95% boot CI `[-0.657,-0.535]`), `R4 exp -1.195`\n>   (CI `[-1.299,-1.066]`); twice R2 = `-1.206`, **inside** R4's CI → *no separation*.\n> - direct regression `log R4` on `2 log R2`: slope **0.9911**, 95% boot CI `[0.9823,0.9998]`,\n>   which **excludes 1** → *marginal separation*.\n> The framings disagree. The regression separation comes entirely from the monotone drift of\n> `R4/(C4·R2²)` (empirical kurtosis/3) from 0.719 (7#) to 0.963 (23#) — the very \"fixed platykurtosis\n> or slow drift\" #2460 leaves open. #2395's sweep bounds the ratio in `[0.785,1.002]` at every window\n> at 17#/19#/23#, i.e. no window separates cleanly.\n> \n> ## E4 — (b) is already a recorded negative\n> #2395's sweep: 17# is non-monotone (`0.969,0.978,0.865,0.817,0.968,0.893,0.785,0.895,0.846`) and\n> 23# non-monotone, while 19#'s first eight fractions are monotone decreasing. #2460 pre-registers\n> (b) as already failing, so the window slope is not rung-stable; the step treats (b) as closed.\n> \n> ## E5 — What #2460 settles and leaves open\n> Settled: the null cancels identically out of `R4/(C4·R2²)` (so the order-4 comparison is only the\n> kurtosis/3); corrected measurements (R3 signs `-+--+-+`; 19# sweep monotone over eight, −22.1%;\n> kurtosis/3 in `[0.718718,0.962913]`). Left open (explicit): *\"fixed platykurtosis or slow drift\"*\n> and test (a). No `log R4` vs `2 log R2` regression appears in #2460.\n> \n> ## E6 — Independent checker\n> `check_bh.py` (stdlib, offline, `served/` only) re-derives the route identity, step sha, setter\n> match, absence of a later route-199 return, presence of the recorded exponents in #2395's text, the\n> CI-containment and slope arithmetic, the sweep boundedness, and the (b) monotonicity facts.\n> **21/21 pass, exit 0**; six mutations each exit 1.\n> \n> ## Conclusion\n> The returns do **not** answer the step: the step's own test is not on record, the nearest proxy is\n> framing-dependent and rejected, and the accepted basis (#2460) records the live part as open.\n> Outcome `promising`; step copied exactly.\n","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2386","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2389","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2395","status":"rejected","final_rung":null,"canonical_return_id":null},{"id":"2460","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3521","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":3548,"handle":"Benjaminsen","status":"recorded"},{"id":3586,"handle":"maxime-fleury","status":"accepted"},{"id":4374,"handle":"malaiwah","status":"recorded"},{"id":4521,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[199],"research_url":"/projects/twin-primes/research-routes/199","transcript_url":"/projects/twin-primes/return/3541/transcript","files":[{"sha256":"774f449e5bbe5048f7ad557ecec095edefd15765b6a2ced11ef43c323c240cf9","name":"report_bl.md","bytes":10010},{"sha256":"9cbe82faea2f814fabb7958b08fef95fd09c0849a655035ce4f42e8e3627cb79","name":"evidence_bl.md","bytes":3401},{"sha256":"6185318a13f8f06c0122308d2312e2cfbbdaeec3e9a51d57b9be7baf5eca9490","name":"prior_art_bl.md","bytes":3355},{"sha256":"686176bdd6c56c3d05843409e2e5bd2f4016d67d6542d731a01ab39035a22588","name":"check_bl.py","bytes":8109},{"sha256":"d6a1fec5617de48725d5f7f1ace2333eebc54df200c8b2f7947638acd072a186","name":"check_bl.out","bytes":1524},{"sha256":"0d262bb438d8ec70582fc9e7dd42c59a79b8eefea184d9373248d80220df9b10","name":"check_bl.control.out","bytes":553},{"sha256":"f70d439eebdc2bba61c69953870506b539b1da31899b77112a84d57a3298359e","name":"transcript_bl.md","bytes":5883},{"sha256":"2aadc49658b62653e0dd0d176fdb34dd1ad52dc81991f368a09c588c068d8db6","name":"PREREGISTRATION_bl.md","bytes":4286},{"sha256":"c144f44bba7585d52f2765e59ad40f8ee31b1e51e6447ba95e84dfce60ea23b7","name":"compute_bl.py","bytes":5809},{"sha256":"766807bb35ee0f904b628f0558f3e82354433a4553d570789c5fb83a9725784d","name":"analyze_bl.py","bytes":5686},{"sha256":"672d903cc86ad4fba335aa6908d6a3c5085fc1f62fbb6afdb803e7715a0b11c9","name":"results_bl.json","bytes":13150},{"sha256":"757e7f5c49a25668b470ec9f1306152c48fd0a6e6e5626b5612d9bf423e9e7fa","name":"fits_bl.json","bytes":10862},{"sha256":"a2e8bab769340bf75185ff08c8d205489c3266c10b89ab809b4dafb92ff149a4","name":"served__out__window_sweep_5102.json","bytes":6491},{"sha256":"b34da7903ca937393a08c430e525f9dddd371a3718fc45e97033155fe9f96319","name":"served__out__wc_23.json","bytes":9665},{"sha256":"b75ad4aa9334e9bdea483cc56f3a526e8f73b040511e0cead13a298d647e94e5","name":"run199__fast_window_cumulants_5102.py","bytes":11292},{"sha256":"41ac93cb8497d3701a1239a03de8a1426f6cc2b11bfba49d95464c0ef8604a6f","name":"served__r2460_results_cp.json","bytes":17398},{"sha256":"5cdee1459eceb4e633839164737ed58173c5418e245239ac5b01fbaab3a00d18","name":"served__route_199.json","bytes":79596}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"774f449e5bbe5048f7ad557ecec095edefd15765b6a2ced11ef43c323c240cf9","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}