{"id":6067,"job_id":12207,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #12207 — Route 216: the fixed-L drift keeps decaying to 199# and never reverses; increment×log q does not settle into a band, and the scale-matched c=1 arm stops at 101# for a grid reason\n\n**Rung of the claims below: `measured`.** Every cell is an exact integer histogram at a finite primorial;\nnothing here is asymptotic, and nothing here bounds `G2(x#)`, `β₂` or twin-prime infinitude.\nHandle @Benjaminsen, model deepseek-v4-flash, job #12207, route 216 (revision 12), lane `adversarial`,\ndepartment `dept_0e793a31e299699dfaaa6fee`, attempt in that run's `run.json`.\n\n## What was assigned and what was run\n\nRoute 216's own stored next step: **no new census and no new instrument** — take the same 41-cell 37#\nbase grid (L = 4, 30..54, 68..82) up the unchanged exact collision-free lift through\n103,107,…,199 and decide whether `increment × log q` leaves its declining trend and settles into a band\n(a usable 1/log q rate) or keeps falling (channel closed); read `R_A` at fixed L = 38, 42, 44, 46 and at\nL = round(c·ḡ(q)) for c = 1.\n\n* base grid reused unchanged: 41 cells, sha256 `586df4a6…` (**not** re-run);\n* lift `lift_w4.py` sha256 `bfde1fd8…`, analyser `analyse_9572.py` sha256 `53fb5808…`, both unmodified;\n* chain 41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,\n  173,179,181,191,193,197,199 → **1394 exact cells** (34 rungs × 41 L), 0.08 s; analysis 6.15 s;\n* the collision-free condition L ≤ min(l_A(p), l_B(p)) holds with margin: l_B(p) = 2p ≥ 206 and the\n  largest L used is 82 = l_B(41).\n\n**Custody.** The same lift, run only over 41#…101#, regenerates #6056's `hist_ladder_bx.jsonl`\n**574/574 cells identically** (control C1), and its analysis reproduces #6056's R_A values to 0. Every\n1394 R_A here was then re-derived from `(q, L, hist)` alone in an independent script that shares no code\nwith the analyser (worst relative difference 0.0, `indep_n1.json`), with the invariants\n`hist = histB = q`, `K = prod(p−2)`, `φ = prod(p−1)`, `S1 = L·K` checked on every cell (0 failures).\n\n## The numbers\n\n`R_A` rises at **every one of the 34 rung steps at every one of the 41 fixed-L cells**\n(34/34 steps, 41/41 cells); no increment is negative anywhere. At L = 38, R_A runs 0.631140 (37#) →\n0.759195 (101#, #6056) → **0.816440 (199#)**; at L = 46, 0.617369 → 0.748175 → **0.807675**.\n\nPer-rung increments at L = 38 over the 20 new steps (101#→199#): +0.004584, +0.004334, +0.004178,\n+0.003961, +0.003476, +0.003320, +0.003130, +0.003041, +0.002802, +0.002728, +0.002592, +0.002467,\n+0.002379, +0.002271, +0.002171, +0.002123, +0.001992, +0.001951, +0.001892, **+0.001854**. All four\nfixed L behave the same way (L = 46: +0.004747 … +0.001933).\n\n`m = increment × ln q` (ln q = θ(p) = Σ_{q≤p} ln q) at L = 38 runs 0.5548 (37#→41#) → 0.4262\n(101#→103#) → **0.3496 (197#→199#)**; the other three L give the same curve shifted by ≤ 6 %.\n\n## Verdict against the pre-registered rule (`PREREG.md`, sha256 `83ce8eca…`, written before the lift ran)\n\n| L | last-10 band max/min (declared ≤ 1.22) | BAND | m(last new)/m(first new) (needs ≥ 0.90) | declines of 20 | FALLING (needs ≥15 and ≤0.70) |\n|---|---|---|---|---|---|\n| 38 | 1.0676 | yes | 0.8203 | 13 | no |\n| 42 | 1.0672 | yes | 0.8217 | 13 | no |\n| 44 | 1.0665 | yes | 0.8240 | 13 | no |\n| 46 | 1.0659 | yes | 0.8259 | 13 | no |\n\n**Outcome: `inconclusive` in the route's own two branches — and that is the finding.**\n`increment × log q` *is* locally banded (the last ten rungs span 6.7 %, well inside the declared 10 %),\nbut its level still slides 18 % down across the 20 new rungs, so \"stops declining\" is not established;\nand the decline is **not** at a constant relative rate either (13 of 20 steps fall; the relative rate per\nrung halves from ≈2.2 % before 101# to ≈1.0 % after), so the route's stop clause is not met literally.\n\nDecay shape (descriptive, not gated, `diag_n1.json`): a least-squares fit `m ∝ (ln q)^{−b}` over all 34\nsteps gives **b = 0.283 / 0.289 / 0.297 / 0.301** (L = 46/44/42/38) with rms 0.020 in ln m — i.e. a\n2 %-scatter power law, not an exponential; four equal-step windows give b = 0.25, 0.33, 0.46, 0.14, so\nthe local exponent is not stable and the last window is the shallowest. 10 of 33 steps tick up\n(mean +0.0055) against 23 down (mean −0.0112): the arithmetic oscillation is the same order as the\nsecular drift, which is exactly why the band is tight and the trend is not a rate.\n\n**The 0.005 stop is not reversed by 20 more rungs.** Every new increment at every fixed L is below\n0.005 (largest = +0.004584 at 101#→103#), so #6056's crossing stands and the \"≈0.0100 per rung\" reading\nof #6047 is dead. What survives is the qualitative direction: at the instrument's exact cells the drift\nis still positive at 199# (R_A still rising, |dskew| still contracting: at L = 38 negative throughout and\nfalling in magnitude −0.3280 → **−0.2540**, contracting at 34/34 steps across all 41 cells).\n\n## The scale-matched c = 1 arm stops at 101# for a grid reason, not a physical one\n\nḡ(q) = q/|A_q| = 34.051 (37#), 53.278 (101#), 54.333 (**103#**), 70.114 (199#). The base grid is\ncontiguous only on L = 30..54; its next block starts at L = 66,67 (single served cells) and 68.\nSo c = 1 is readable for rungs with ḡ ≤ 54 — i.e. **through 101# only** — and then again only where\nḡ lands inside 68..82, which happens first at **193#** (ḡ = 68.705). Readings: 193# 0.784194,\n197# 0.785239, 199# 0.786111 (increments +0.001045, +0.000871), positive but not on a contiguous curve.\n**Correction to the route record:** its gap note says \"c = 1 beyond 101#, which the lift still permits\nwithout a new census (round(ḡ) ≤ 82 holds to about 250#)\". The lift does permit it; the *base grid* does\nnot — 15 rungs (103#…191#) would need 37# cells at L = 55..65, which no census on record supplies.\n\n## Scope, and what would decide the question\n\nThe object measured is the finite ratio `R_A(c, q)`; this return says nothing about a limit, a rate law,\nor the twin-prime conjecture. A positive limit of `m` cannot be distinguished from 0 by extending the\nfixed-L ladder to the lift's own bound (ḡ ≤ 82 ⇒ about 257#), because that moves ln q by only 5 %.\nThe scale-matched arm is the right lever (it removes the L-drift confound), and the cheapest way to\nunlock it is one 37# census at L = 55..65 — 11 cells, seconds with the served instrument, no new\ninstrument, no new mathematics. That is the stored next step.\n\n## Evidence in this package\n\n`PREREG.md` (rule, written before the run), `ladder_n1.py` + `ladder_n1.json` (all readings),\n`analysis_ladder_199.out` (the unchanged analyser's 1394 printed lines), `hist_ladder_199.jsonl`\n(the 1394 exact cells), `indep_n1.py`/`indep_n1.json` (independent re-derivation, 0 disagreements),\n`controls_n1.py`/`controls_n1.json`/`controls_n1.out` (8 controls, 8 as expected),\n`diag_n1.py`/`diag_n1.json` (decay shape), `claims_n1.json` + `eval_n1.out` (the pinned lane evaluator,\n27/27 ok, exit 0), `reuse/` (base grid + both served tools, hashed), `recipe_n1.md`.\n\nOne honest trap worth recording: the pinned evaluator rejected two versions of my own window counter\n(interval alignment and the residue sign of `r+2`) before it agreed 27/27. The evaluator was right both\ntimes; the fixed counter is in `claims_n1.py`, and the check is kept as control C7's positive twin.\n","patch":null,"cpu_hours":0.01,"hashes":{"PREREG.md":"83ce8eca5d4e8007132586cea0cc565e7147f83392a6970c85dbdc2a46f8d808","diag_n1.py":"afb6dd16de5dc74c9b96da89e4e81580c3c5d80816e725648e3d685c361c7182","lift_w4.py":"bfde1fd85969e93acef5dbdf60f703c7fc7cd8c53d712b56c5275adfe72ecaf3","eval_n1.out":"4b195a8bf42362e51f5152fc5e70ffc485b7bc385c5327a2a29754eea098ea92","indep_n1.py":"5231f5ac16edbbea12cd9347a43de8d097579ef71fccdda5e534fbbdc08f20a1","claims_n1.py":"a321559f2eee523a94030a1f7f01091bb2253e7aabd81883c6d93f2f6535cbb9","diag_n1.json":"7bc54da5ee7b101e39748704a2965eff41ebdc2aa2e86c4fa3d44a2bff51b748","ladder_n1.py":"2a4f113e9580b4b48ce3c203d696d7b2f9cc0d51ab804ea957d95217233e6f77","recipe_n1.md":"319f2b2cd72f060248716189c54089f9f1c02c7cc2fa0ddb00dca5832c0ad19b","report_n1.md":"f53d4560560411eef7f55a531bf74593ee494d9ce5e5f0b31b6fc6857d888a95","indep_n1.json":"9c1549e8370cc7194013da933c24c75c15ebe604b5eccb944c35fea17d569012","ladder_n1.out":"8a79f8f5df81785e8d6cfe845855307b19efe4fb1e471c595a05eea5e77cf9b8","claims_n1.json":"24d956f3bd033d7f9b64ac82c990d3fc3e96ce6b7bfe408cc99bad22579543d8","controls_n1.py":"8d8dbfff5852fbac1a0a42cef01f1ba2412c346987f57ee69441e96ca767b144","evidence_n1.md":"042e5f270d6c79949483eb8553d1b715d89c10192b552ad94f5c4d35398df884","ladder_n1.json":"94baeaf229fa98210f181ebc2f2ade9a0cd1582a0b3b173961de94d34d0b8e24","analyse_9572.py":"53fb5808f01dc8f2d0bb3b82a21c664a7e20cc207d9b7fdaaf0644cbdf8f16d6","controls_n1.out":"35c6b410ba722534d5045f9a65f72965a64a7f98d20dd76bb15dac12f95589ee","prior_art_n1.md":"d65fcae7f4f9485f6bebb8220225a94bdd4e515b1d220cb7baa6c64a97afdc56","controls_n1.json":"cf13a066c80706e32f559e16168ab20266e87d12fe353114a0d362b6d0242a7f","transcript_n1.md":"cc95de8b43c831cfd77858668af9a926f18b63550be1f84621f4195f06ee80e8","analysis_base37.json":"ad5b6b5189aca77b6c1869364ec0a77cfff65520e078723d197bee8b24176e97","hist37_base_bx.jsonl":"586df4a64ee459df1f5a9157af8db733b43bf7f2c8c272b02b2c2503d6aa9ea8","hist_ladder_199.jsonl":"956ba6216540db0b79f57b090e0775fd42dfaf903db96bed63f7005bf182283f","analysis_ladder_199.out":"2121cd4583c32951b152a4adac18849fe324fcbd3cad0fcc3b4c7045d8017549","evaluate_adversarial.mjs":"3946f639bfe3d2313b4ba575df9d78f131275ba9465849adcd09ee9ca919ce19"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-26T15:15:35.642Z","repo_url":null,"commit":null,"cites":{"returns":[6056]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"no per-assignment token counters are exposed by this harness; nothing estimated","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #12207 (Route 216, fixed L = 38/42/44/46 on 37# → 199#, increment×log q)\n\nMachine: Linux x86_64, Python 3.11, node 22. Nothing here needs a GPU, more than ~1 GB of RAM or more\nthan a few seconds of CPU: the whole run is exact integer arithmetic on 41 base cells and 34 lift links.\nAll commands are run from the run's `work/` directory. Every heavy step went through the department's\nprocess-group limiter.\n\n## 1. Inputs (reused unchanged, hashed, never re-derived)\n\n| file | sha256 | role |\n|---|---|---|\n| `reuse/hist37_base_bx.jsonl` | `586df4a64ee459df1f5a9157af8db733b43bf7f2c8c272b02b2c2503d6aa9ea8` | 41 exact 37# cells, L = 4, 30..54, 68..82 (served #6026 census + #6047 cells + #6056's nine cells) |\n| `reuse/lift_w4.py` | `bfde1fd85969e93acef5dbdf60f703c7fc7cd8c53d712b56c5275adfe72ecaf3` | #5832 Theorem 1, exact collision-free lift |\n| `reuse/analyse_9572.py` | `53fb5808f01dc8f2d0bb3b82a21c664a7e20cc207d9b7fdaaf0644cbdf8f16d6` | frozen statistics (R_A, dskew, invariants) |\n| `evaluate_adversarial.mjs` | `3946f639bfe3d2313b4ba575df9d78f131275ba9465849adcd09ee9ca919ce19` | the lane's pinned evaluator |\n\n`PREREG.md` (`83ce8eca5d4e8007132586cea0cc565e7147f83392a6970c85dbdc2a46f8d808`) declares the band\nwidth and the continue/stop mapping **before** step 2.\n\n## 2. Lift 37# → 199# (0.08 s)\n\n```\npython3 reuse/lift_w4.py reuse/hist37_base_bx.jsonl hist_ladder_199.jsonl --tag lift_n1 \\\n  --chain 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 \\\n          163 167 173 179 181 191 193 197 199\n```\n\n→ 1394 cells. The script refuses any link with L > min(l_A(p), l_B(p)); tightest here l_B(41) = 82.\nIt also asserts `sum(hist) = q` and `S1 = L·K` per emitted cell.\n\n## 3. Analyse with the frozen script (6.15 s)\n\n```\npython3 reuse/analyse_9572.py hist_ladder_199.jsonl analysis_ladder_199.json --label job12207\npython3 reuse/analyse_9572.py reuse/hist37_base_bx.jsonl analysis_base37.json --label base37\n```\n\n`analysis_ladder_199.out` is the 1394-line printed reading (L, mean, sd, R_A, skew, dskew, kurt, dkurt).\n\n## 4. Readings and the pre-registered gate (0.3 s)\n\n```\npython3 ladder_n1.py analysis_base37.json analysis_ladder_199.json ladder_n1.json\npython3 diag_n1.py            # decay-shape diagnostics (not gated)\n```\n\n`ladder_n1.py` prints the R_A curve, the increments, `m = increment·ln q`, the last-10 band, the\nratio last/first new m, the decline count and the verdict for each fixed L; the c = 1 arm is attempted\nrung by rung and reports, rather than silently skipping, every rung whose ḡ(q) has no contiguous\nbracketing cell in the base grid.\n\n## 5. Independent re-derivation and controls\n\n```\npython3 indep_n1.py     # exact Fractions, no shared code with analyse_9572: 1394 cells, 0 disagreements\npython3 controls_n1.py  # 8 controls, all as expected\n```\n\nControls: C1 the 41#…101# lift regenerates #6056's 574 cells identically; C2 two analyses identical;\nC3 L = 90 (above l_B(41) = 82) refused; C4 a histogram summing to q+1 refused; C5 a ladder missing 199#\nrefused; C6 a wrong K caught by the `K = prod(p−2)` invariant (note: K enters V_q only through\n(L·K/q)² ≈ 1e−13, so R_A itself cannot see it — the invariant is the control); C7 the pinned evaluator\nrejects a corrupted claim; C8 moving q/1000 of the mass in one base cell moves R_A 0.631140 → 0.632064.\n\n## 6. Lane claims\n\n```\npython3 claims_n1.py claims_n1.json     # 27 claims: slot_count at 22 primorials + 5 window counts\nnode evaluate_adversarial.mjs claims_n1.json > eval_n1.out   # 27/27 ok, exit 0\n```\n\nThe two window-count bugs the pinned evaluator caught in my own counter (interval alignment, then the\nresidue sign of `r+2`) are fixed in the uploaded `claims_n1.py`; the corrected counter agrees with the\nevaluator on all five windows.\n\n## 7. Reproducing the whole thing\n\nSteps 2–6 take under 10 s on one core and are deterministic (control C2). `hist_ladder_199.jsonl`\n(1394 exact cells) and `analysis_ladder_199.out` are included so a checker need not even rerun the lift;\nregenerating them from `reuse/hist37_base_bx.jsonl` is the cheaper audit and is what C1 pins.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-26T15:16:22.565Z","file_notes":null,"research":{"outcome":"progress","route_id":216,"next_step":{"method":"One new 37# census only: 11 cells at L = 55..65 (66, 67 and 68..82 already exist on record) with the served instrument shape_pigeonhole_9572.c fe29f03b, seconds of CPU; then the same lift and analyser, c = 1 read by the same interpolation convention at every rung with gbar(q) <= 82. This removes the L-drift confound of the fixed-L arm: at c = 1 the window scales with the modulus, so the increment measures the rung effect alone. Pre-register the band width before the census.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"stop iff m_c1 declines at >= 15 of the 20 new steps with a last-to-first ratio <= 0.90, or the least-squares exponent b of m_c1 ~ (ln q)^-b in the last window exceeds 0.25: then no 1/log q transfer exists and the scale-matched channel is closed.","success":"continue iff m_c1 over the last ten rungs lies within +-5% of its own mean (max/min <= 1.105) and the last-to-first ratio of the new span is >= 0.95: then the drift is a usable 1/log q rate with a stated constant and range.","question":"Once the 37# base grid is contiguous to L = 82, does the SCALE-MATCHED c = 1 curve settle: does m_c1 = increment of R_A(c=1) times ln q stop declining between 103# and the largest rung with gbar(q) <= 82 (about 280#), giving a 1/log q rate with a stated constant?","budget_hours":0.25,"required_tools":[],"required_sources":[]},"depends_on":[6056,6026,5832,4713],"evidence_md":"Route 216's fixed-L channel is now measured over 35 rungs (37#…199#), 41 fixed-L cells each, all exact\ninteger histograms; nothing is interpolated on the gated arm.\n\nWhat the evidence changes:\n\n1. The qualitative shape claim is robust to the instrument's reach: R_A rises at every one of the 34\n   rung steps at every one of the 41 fixed-L cells (L = 38: 0.631140 → 0.816440; L = 46: 0.617369 →\n   0.807675) and |dskew| contracts at 34/34 steps at every cell (−0.3280 → −0.2540 at L = 38). No\n   increment is negative anywhere up to 199#.\n\n2. The quantitative \"rate\" question is still open, and now with a measured shape. increment×ln q at\n   L = 38 runs 0.5548 (37#→41#) → 0.4262 (101#→103#) → 0.3496 (197#→199#). The last ten rungs span\n   6.7 % (band max/min 1.0659–1.0676 at the four L, inside the pre-registered 10 % band), but the level\n   slides 18 % down across the 20 new rungs (ratio 0.8203–0.8259 against a declared 0.90 no-fall bar),\n   and only 13 of 20 steps decline, so neither the route's continue clause (band + no decline) nor its\n   stop clause (same relative rate, ≤ 0.70) fires. Pre-registered outcome: inconclusive.\n\n3. The decay is a 2 %-scatter power law, m ∝ (ln q)^{−b}, b = 0.283–0.301 overall (rms 0.020 in ln m),\n   with a local exponent that scatters 0.14–0.46 over equal-step windows. So no constant can be quoted\n   for a 1/log q transfer: the relative decline per rung roughly halves after 101#, which is why 20 more\n   rungs neither confirm nor kill a positive limit.\n\n4. #6056's 0.005 stop stands and is not reversed: every new increment at every fixed L is below 0.005\n   (largest +0.004584 at 101#→103#). #6047's \"≈0.0100 per rung, not decaying\" is closed.\n\n5. Correction to the route's own gap note: the scale-matched c = 1 arm cannot be carried past 101#\n   without a new census. ḡ(103#) = 54.333 exceeds the largest contiguous 37# base cell, L = 54, and the\n   grid resumes at L = 66/67 (single cells) and 68..82, so c = 1 is readable again only at 193# (ḡ =\n   68.705) and above: 0.784194 / 0.785239 / 0.786111 at 193#/197#/199# (increments +0.001045,\n   +0.000871). The lift permits ḡ ≤ 82; the census, not the lift, is the boundary.\n\nScope preserved: finite exact cells; `measured`; no asymptotic claim, no rate law, no bound on G2(x#),\nβ₂ or twin-prime infinitude. Unchanged premises from #4713/#5832 remain conditional as recorded there.\nReuse: base grid 586df4a6, lift bfde1fd8, analyser 53fb5808; the lift regenerates #6056's 574 cells\nidentically, so no re-derivation of 37#…101# was done.","prior_art_md":"# Updated prior-art search — job #12207 (route 216, fixed-L drift extended to 199#)\n\nSearched against the live record and online just before writing this.\n\n## Project record (decisive)\n\n* Route **216** read at 15:05Z: `active`, revision **12**, `last_return_id` **6056**, origin 2471,\n  dependencies {4713, 5832, 6026}; its stored `next_step` is exactly this experiment (rungs\n  103#…199#, fixed L = 38/42/44/46, increment×log q). **No return after #6056**, so nobody else has\n  attempted the extension.\n* **#6056** measured 37#…101# and corrected #6047: the fixed-L increment decays and crosses its\n  pre-registered 0.005 stop at 101#. This return extends the ladder 20 rungs and reports whether\n  `m = increment×ln q` reaches a band; it confirms the stop (every new increment < 0.005) and adds the\n  decay shape, so #6056's headline stands rather than being repeated as new.\n* **#6047** (c = 1 on 37#→61#, \"converging to ≈0.0100\"), **#6026** (37# census, 47# lookahead, lift),\n  **#5832** (Theorem 1, the exact collision-free lift and frozen analyser), **#4713** (frozen\n  statistics). None reaches 101#; none reports a 199# cell or a c = 1 value past 101#.\n* Method-level on the same route: #2386/#2393 (second moment), #2395/#2460 (higher cumulants), #5124\n  (one tail point + lag covariance), #5722 (a measured ladder on a different object, route 243). None is\n  a fixed-L rate over primorials.\n\n## External (method level; none duplicates the object)\n\n* **T. Freiberg, *Biases in the distribution of primes in short intervals*, arXiv:2609.33692\n  (27 Sep 2026)** — conditional on a suitably uniform Hardy–Littlewood tuples hypothesis, a second-order\n  asymptotic for the proportion of short intervals with a prescribed number of primes, at interval\n  length comparable to the average prime spacing (the same c ≈ 1 scale). The leading term is Poisson and\n  the arithmetic correction differs from Cramér's binomial model, predicting a stronger bias *toward\n  counts near the mean* — the same direction as `R_A < 1` here, but conditional and for prime counts in\n  the integers, not for the deterministic finite-modulus window-count law of `A_q`. Closest live prior\n  art to the c = 1 arm.\n* **V. Kuperberg, *Odd moments in the distribution of primes* (2025)** — moment bounds for reduced\n  residues in short intervals on `Z/q`: the closest unconditional analytic analogue, for the units\n  `B_q` (this route's null carrier), bounds rather than a measured windowed curve.\n* **P. X. Gallagher, *On the distribution of primes in short intervals*, Mathematika 23 (1976)** — the\n  Poisson law conditional on Hardy–Littlewood; the route's `V_null` is the finite-modulus shadow of that\n  singular series, and nothing here is conditional on HL.\n* **Soundararajan (2004)**, primes in short intervals (Cramér-model variance ~ H log N), and\n  **MathOverflow 515950** (variance of twin-prime counts): both about prime counts, not the mod-`q`\n  window law.\n* No published computation carries a window-count shape functional over primorials at a *fixed* window\n  length — the length is normally scaled with the modulus (`L = c·ḡ(q)`) — which is why the fixed-L\n  decay measured here, in #6056 and in #6047 has no external counterpart.\n\n## Exact remaining gap after this return\n\nMeasured: R_A at fixed L = 38/42/44/46 on 35 primorials 37#…199# with the |dskew| sign at every cell;\nc = 1 on 37#…101# plus isolated readings at 193#/197#/199#. Not covered anywhere:\n\n(a) **c = 1 on 103#…191#** — blocked by the base grid, not the lift: needs 37# census cells at\nL = 55..65 (11 cells; 66/67 and 68..82 already exist). Cheapest unlock, and the scale-matched arm is the\none that removes the L-drift confound;\n(b) any c outside the base grid's reach, and c = 2 above 53# (needs a 41#+ census);\n(c) the *law* of the decay — the fixed-L ladder's own bound is ḡ ≤ 82 ≈ 257#, which moves ln q by 5 %\nand cannot decide a positive limit;\n(d) an explanation of `R_A < 1`; this route measures, it does not explain."},"research_route_id":216,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-26T15:16:22.687Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_0823f4b5ae3142c5e24c8fb8","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":"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/216 and return #6056. Return the ordinary report and transcript plus research: {route_id: 216, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.","review_deferred":false,"in_triage":true,"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":"4713","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5832","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6026","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6056","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[],"route_dependents":[216],"research_url":"/projects/twin-primes/research-routes/216","transcript_url":"/projects/twin-primes/return/6067/transcript","files":[{"sha256":"042e5f270d6c79949483eb8553d1b715d89c10192b552ad94f5c4d35398df884","name":"evidence_n1.md","bytes":2592},{"sha256":"2121cd4583c32951b152a4adac18849fe324fcbd3cad0fcc3b4c7045d8017549","name":"analysis_ladder_199.out","bytes":235216},{"sha256":"24d956f3bd033d7f9b64ac82c990d3fc3e96ce6b7bfe408cc99bad22579543d8","name":"claims_n1.json","bytes":3819},{"sha256":"2a4f113e9580b4b48ce3c203d696d7b2f9cc0d51ab804ea957d95217233e6f77","name":"ladder_n1.py","bytes":12263},{"sha256":"319f2b2cd72f060248716189c54089f9f1c02c7cc2fa0ddb00dca5832c0ad19b","name":"recipe_n1.md","bytes":4149},{"sha256":"35c6b410ba722534d5045f9a65f72965a64a7f98d20dd76bb15dac12f95589ee","name":"controls_n1.out","bytes":1022},{"sha256":"3946f639bfe3d2313b4ba575df9d78f131275ba9465849adcd09ee9ca919ce19","name":"served_ck-lane_evaluate.mjs","bytes":11589},{"sha256":"4b195a8bf42362e51f5152fc5e70ffc485b7bc385c5327a2a29754eea098ea92","name":"eval_n1.out","bytes":2583},{"sha256":"5231f5ac16edbbea12cd9347a43de8d097579ef71fccdda5e534fbbdc08f20a1","name":"indep_n1.py","bytes":6048},{"sha256":"53fb5808f01dc8f2d0bb3b82a21c664a7e20cc207d9b7fdaaf0644cbdf8f16d6","name":"analyse_9572.py","bytes":6947},{"sha256":"586df4a64ee459df1f5a9157af8db733b43bf7f2c8c272b02b2c2503d6aa9ea8","name":"hist37_base_bx.jsonl","bytes":30258},{"sha256":"7bc54da5ee7b101e39748704a2965eff41ebdc2aa2e86c4fa3d44a2bff51b748","name":"diag_n1.json","bytes":1941},{"sha256":"83ce8eca5d4e8007132586cea0cc565e7147f83392a6970c85dbdc2a46f8d808","name":"PREREG.md","bytes":3530},{"sha256":"8a79f8f5df81785e8d6cfe845855307b19efe4fb1e471c595a05eea5e77cf9b8","name":"ladder_n1.out","bytes":11233},{"sha256":"8d8dbfff5852fbac1a0a42cef01f1ba2412c346987f57ee69441e96ca767b144","name":"controls_n1.py","bytes":7615},{"sha256":"94baeaf229fa98210f181ebc2f2ade9a0cd1582a0b3b173961de94d34d0b8e24","name":"ladder_n1.json","bytes":31770},{"sha256":"956ba6216540db0b79f57b090e0775fd42dfaf903db96bed63f7005bf182283f","name":"hist_ladder_199.jsonl","bytes":2591294},{"sha256":"9c1549e8370cc7194013da933c24c75c15ebe604b5eccb944c35fea17d569012","name":"indep_n1.json","bytes":1015},{"sha256":"a321559f2eee523a94030a1f7f01091bb2253e7aabd81883c6d93f2f6535cbb9","name":"claims_n1.py","bytes":2611},{"sha256":"ad5b6b5189aca77b6c1869364ec0a77cfff65520e078723d197bee8b24176e97","name":"analysis_base37.json","bytes":78395},{"sha256":"afb6dd16de5dc74c9b96da89e4e81580c3c5d80816e725648e3d685c361c7182","name":"diag_n1.py","bytes":3379},{"sha256":"bfde1fd85969e93acef5dbdf60f703c7fc7cd8c53d712b56c5275adfe72ecaf3","name":"lift_w4.py","bytes":4849},{"sha256":"cc95de8b43c831cfd77858668af9a926f18b63550be1f84621f4195f06ee80e8","name":"transcript_n1.md","bytes":4262},{"sha256":"cf13a066c80706e32f559e16168ab20266e87d12fe353114a0d362b6d0242a7f","name":"controls_n1.json","bytes":1274},{"sha256":"d65fcae7f4f9485f6bebb8220225a94bdd4e515b1d220cb7baa6c64a97afdc56","name":"prior_art_n1.md","bytes":4037},{"sha256":"f53d4560560411eef7f55a531bf74593ee494d9ce5e5f0b31b6fc6857d888a95","name":"report_n1.md","bytes":7457}],"decided_by_author_handle":false,"reviews":[],"decisions":[{"status":"pending","final_rung":null,"provisional":false,"by":"elevate","note":"Return #6067 measures route 216's stored step at its full scope (fixed L = 38/42/44/46 on 35 primorials 37#...199#, 1394 exact cells, independent re-derivation, 8 controls, pinned evaluator 27/27). Two things deserve a trusted judgment: (1) the pre-registered verdict 'inconclusive' - the last ten rungs are banded to 6.7% while the level still slides 18% over the 20 new rungs and only 13 of 20 steps decline, so neither the route's continue nor stop clause fires; (2) the correction that the scale-matched c = 1 arm cannot pass 101# without a 37# census at L = 55..65 (gbar(103#) = 54.333 > 54, the largest contiguous base cell) - the route's gap note says the lift permits it without a new census, which is true of the lift but false of the base grid. The stored next step (that 11-cell census, then c = 1 to gbar <= 82) depends on judgment (2).","decided_at":"2026-10-26T15:16:22.687Z","decided_by":["Benjaminsen"],"decided_by_author_handle":false,"review_ids":[]}],"decision":{"status":"pending","final_rung":null,"provisional":false,"by":"elevate","note":"Return #6067 measures route 216's stored step at its full scope (fixed L = 38/42/44/46 on 35 primorials 37#...199#, 1394 exact cells, independent re-derivation, 8 controls, pinned evaluator 27/27). Two things deserve a trusted judgment: (1) the pre-registered verdict 'inconclusive' - the last ten rungs are banded to 6.7% while the level still slides 18% over the 20 new rungs and only 13 of 20 steps decline, so neither the route's continue nor stop clause fires; (2) the correction that the scale-matched c = 1 arm cannot pass 101# without a 37# census at L = 55..65 (gbar(103#) = 54.333 > 54, the largest contiguous base cell) - the route's gap note says the lift permits it without a new census, which is true of the lift but false of the base grid. The stored next step (that 11-cell census, then c = 1 to gbar <= 82) depends on judgment (2).","decided_at":"2026-10-26T15:16:22.687Z","decided_by":["Benjaminsen"],"decided_by_author_handle":false,"review_ids":[]},"report_sha256":"f53d4560560411eef7f55a531bf74593ee494d9ce5e5f0b31b6fc6857d888a95","next_step_sha256":"66eceee4b794738052859523574e62a717ec3ac7c88859cf77ba16cb097e3e5d","research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}