{"id":3800,"job_id":4242,"problem_id":1,"lane_id":6,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4242 — route 87: the registered three-seed replication of the LOW R-channel inversion, with the crossing error #1878 omitted\n\nRung: **measured** (a numerical replication of a served instrument, conditional on the fGn model class and on #1122's grid extension, as #1878 was). Scope: route 87, LOW `[1e13,1e15)` and HIGH `[1e15,4e18)`, the served instrument `check-2095.py` unchanged except the three declared parameters of this step.\n\n## What was run\n\n1. **Inputs re-built and hash-checked here.** The seven TOS pi2 tables from `sweet.ua.pt` match #1094's `data-manifest.json` sha256 exactly (2b00 `22ce8e94…`, 2d10 `0c18390f…`, 2d11 `ae14ad8b…`, 2d12 `fdddb964…`, 2d13 `7de6c272…`, 2d14 `72d428e4…`, 2d15 `f0565126…`), and `frontier6.json` is `1a3d24b6…` as #1878 cites. The producer I ran is byte-identical to the served `check-2095.py`, sha256 `44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea`.\n2. **Control first (the cheapest credible check of this environment).** The *unmodified* served producer (N_SUB_LEV = 40, seed 2079) reproduces #1878 on this machine at the printed-digit level: LOW rho1 0.379 +- 0.078, r_dn 0.352 +- 0.046, R 0.490 +- 0.152, R_pool(1.0) 0.488 +- 0.103, R_pool(2.0) 0.490 +- 0.084; HIGH 0.392 / 0.424 / 0.366 / 0.365 / 0.367; `VERDICT: PROMOTE`; promoted H = 0.395 +- 0.060, eps(1e19) = 1.3326e-08. Wall 469 s, one core. (The published log's *bytes* are macOS-arm64/numpy-2.0.2 specific; only the values are portable.)\n3. **The registered step.** The same instrument with exactly **three** declared changes (`rep/check-2095-rep.py`, sha256 `0565ca457d206f974cf3184b953d21dfe577b8f0aee8d1f62cec928b6f7d5759`): `N_SUB_LEV` 40 -> **160**, the RNG seed from the command line, and a seed-named output path. No estimator, anchor, grid, pre-registration or criterion changed. Run once per pre-registered seed **2095 / 2096 / 2097**, three at a time on 10 cores, each in its own enforced process group (`sah.py bounded`, 3600 s limit; all three exit 0, no survivors).\n4. **The crossing error #1878 omits** (`crossing_cq.py`). Its lines 340-351 use `se_H = sd at the first grid point / |end-to-end slope|` — a whole-curve scale, not an inversion scale. Computed here for every channel and seed: (a) the **delta method** on the bracketing family means, `H* = H0 + (H1-H0)(M-m0)/(m1-m0)` with `se_delta^2 = (gM sM)^2 + (g0 s0)^2 + (g1 s1)^2`, `s_j = sd_j/sqrt(n_j)`, `n_j` = the instrument's declared replicate counts (120 rho1, 160 level, 240 PART 1), and `sM` the data-side se (0 for rho1; across-anchor se for r_dn; that over c_int for R and R_pool); (b) a **whole-curve Monte Carlo band**: redraw every family mean `m_j -> N(m_j, s_j^2)` and `M`, re-derive the crossing on the same grid, 200 000 draws, reported as the robust `(p84.13-p15.87)/2`.\n5. **Independent checker** (`check_cq.py`, 264 checks, 0 failures, exit 0): own re-derivation of all 39 crossings from the producer's own `means`/`measured` (< 1e-9), central finite differences of the delta-method partials (117 gradients, < 1e-6 relative), its **own** whole-curve Monte Carlo (different code, RNG and draw count) reproducing all 39 bands within 15%, plus the criteria and the assignment's falsifier. Six negative controls (`mean_flip`, `grad`, `sigma`, `drop_seed`, `mc_swap`, `se_out`) each exit 1 with a named FAIL (`CORRUPTIONS_cq.out`).\n\n## Result (LOW `[1e13,1e15)`, H_inv +- **crossing band**, 200k draws)\n\n| seed | rho1 | r_dn | R | R_pool(1.0) | R_pool(2.0) | abs(R-r_dn) | 2 x max se | ratio |\n|---|---|---|---|---|---|---|---|---|\n| 2095 | 0.365 +- 0.009 | 0.361 +- 0.038 | 0.498 +- 0.038 | 0.500 +- 0.034 | 0.500 +- 0.037 | 0.137 | 0.075 | **1.82** |\n| 2096 | 0.377 +- 0.005 | 0.365 +- 0.035 | 0.499 +- 0.036 | 0.497 +- 0.035 | 0.497 +- 0.033 | 0.135 | 0.073 | **1.85** |\n| 2097 | 0.372 +- 0.014 | 0.355 +- 0.033 | 0.489 +- 0.031 | 0.492 +- 0.033 | 0.494 +- 0.033 | 0.134 | 0.067 | **2.00** |\n\n1. **The inversion replicates; the promotion does not.** All five LOW channels invert *inside* the grid in all three seeds, and the R locations are stable to 0.010 (0.489 / 0.499 / 0.498). But the R-level offset is a **reproducible systematic, not Monte Carlo noise**: `abs(R - r_dn)` is 0.134-0.137 in every seed against a 2-se tolerance of 0.067-0.075, i.e. **1.8-2.0 x the pre-registered tolerance in every seed**, so the assignment's stop branch (\"any seed puts a LOW R channel outside the grid or outside 2 se of r_dn\") triggers three times over.\n2. **Why #1878 passed: the error convention.** #1878's `se_H` for LOW R is 0.163 / 0.135 / 0.125; the crossing band is 0.038 / 0.036 / 0.031 — **3.3-4.3 x smaller**. The whole `PASS` of criterion (iii) sat in that gap (`tightest pair R_pool(2.0) vs r_dn: 0.030 against 0.168` there is `0.139 against 0.075` here).\n3. **Even under the instrument's own se convention the promotion fails to replicate**: seed 2095 gives `VERDICT: PARTIAL` because criterion (ii) fails (LOW rho1 0.365 is 0.055 from the 0.42 target, > 0.05). So the registered `promote` is 1 of 3 seeds failing the instrument's own rule, and 3 of 3 failing the assignment's rule. The served `VERDICT: PROMOTE` of #1878 is therefore a one-draw outcome in the sense that matters: the same instrument on three fresh seeds does not reproduce the **promotion**, though it does reproduce the R *location*.\n4. **The promoted H itself is robust; its licence is not.** Per-seed promoted H = 0.3931 / 0.3972 / 0.3897, so **H = 0.3934 +- 0.0038** across seeds and eps(1e19) = **1.3232e-08**, band [1.3052e-08, 1.3427e-08] — consistent with #1878's 0.395 +- 0.060 and 1.3326e-08, with a replication band 16x tighter. The number survives; the criterion that licensed promoting the eps table does not.\n5. **The R crossing is an edge phenomenon.** Redrawing the model, only **81% / 89% / 90%** of draws put the LOW R crossing inside the grid at all (it sits in the 0.48-0.51 segment near the top edge 0.54). HIGH is unchanged in sign: R 0.362-0.368 vs r_dn 0.435-0.443, i.e. the offset reverses to about -0.07 there, as #1878 and #3769 report.\n6. **Delta-method scope (new, and it matters for anyone reusing `se_H`)**: the analytic delta-method se and the whole-curve band agree within about 20% for the channels here, but the *empirical sd* of a crossing is heavy-tailed whenever the bracketing family gap is comparable to the family sds (gap/sigma <~ 3): the ratio has a pole. Live example, LOW R at seed 2095: `se_delta` 0.041 against an empirical sd of 5.3 with 1%/99% tails at -60/+59. A delta-method \"se\" alone is therefore not a safe scale for these inversions; the 16/84 band is (tables in `crossing_cq.md`, numbers in `crossing_cq.json`).\n\n## What it changes\n\nThe route step's own **stop branch is met on every seed**: the promoted eps table rests on an acceptance that does not survive either the corrected crossing error or, at one of three seeds, the instrument's own rule. So the eps table returns to **conditional** (`eps(1e19)` stays quoted at the H = 1/2 value, as the branch says) and lane decision **#1111's framing — withdraw R, or state a power floor for two channels — is back on the table**. What is *not* changed: no census number, no PART-1 shape channel (w = 0.02 gives 0.416 / 0.422 / 0.418 +- 0.002 against the 0.42 target), and the promoted H value itself replicates.\n\n## Open\n\n- The LOW R-vs-level offset (+0.134) is a systematic of the *statistic*, not of the draw. **Cheapest credible check of this return and a distinct experiment**: the level channels at LOW rest on **4** anchors (HIGH has 7), so the offset could be an anchor-count property. Split `[1e13,1e15)` into four octave sub-ranges and re-cross r_dn and R at the same level grid with >= 8 anchors. Success: `abs(R - r_dn)` falls inside 2 crossing se. Failure: it stays at ~0.13 with >= 8 anchors, which makes it a property of the pooled-R construction itself and settles #1111 toward withdrawing R.\n- The unbounded stop-window question of the route (the H = 1/2 vs H ~ 0.41 separation) is untouched here; this return only re-prices the R channel that was being used to separate them.\n- Reproduction of the cited #1878/#1122 numbers is at the printed-digit level on this platform (numpy 1.24.2 / Python 3.11.2 / x86-64 Linux), not byte level.\n\n## Sources\n\n- Return #1878 (the instrument `check-2095.py` = `44bf3b65…`, its published observation `check-2095.out.json` = `755c751b…`, `check-2095.log`, `gate-2095.out`, `prereg-2095.md`), #2227 / #2232 (the step checks that kept this obligation open), #1878's dependencies #1111 and #1122, #1106 (`frontier6.json` = `1a3d24b6…`) and #1094 (the TOS data manifest = `771d5914…`).\n- T. Oliveira e Silva, pi2(x) tables 2b00, 2d10-2d15, `https://sweet.ua.pt/tos/primes.html` — third-party, **not redistributed**, sha256 per #1094's manifest.\n- Prior art located for this step: see `prior_art_cq.md` (no source on record or found online runs this instrument; the Hurst-estimator-instability literature supports the replication move, and the delta method / Fieller literature is the method reference).\n- This run's files (all uploaded before submission): `report_cq.md`, `vendor-free` copies of the instrument and runner, the three seed outputs and logs, the control output, `crossing_cq.py/json/md/out`, `check_cq.py/out/json`, `CORRUPTIONS_cq.out`, `report_table_cq.md`, `recipe_cq.md`, `prior_art_cq.md`.\n","patch":null,"cpu_hours":0.54,"hashes":{"run_rep.sh":"9f9591470806d33dd5ba97a481d5ff2157d33b9cb968b91f0ff50e8ee7ee4e3d","check_cq.py":"7e663329a315ddffd57ab069139bdbc54a215d4a1d46a41548da8984ee598720","check_cq.out":"8220e644ca8718bae7fc373318668cd4c4d62127279684af4e73576ff4afa77c","recipe_cq.md":"8ad2930de17b982f6fb8f1dd405b535ee03da8c6d2b4742fa405aca81a63f2f2","rep_2095.log":"40ee9966ad252ed775603b6c94f93df1175565c35ccc134454932da284112258","rep_2096.log":"b5bc637c9ac9d7b1503b8e06904d8d39bc6e2e92e1d070901c2a594f76866efc","rep_2097.log":"4bdb6160c64dfe818aada9d56fd4771d87c4806eee393c7d407d20db1a7e0a6b","report_cq.md":"6b94ce964786979d9bc1da9586ad81d0d501b9f844cb449ca191c905cab57de8","check_cq.json":"d6d795994d6b4b08fb7c56d95e0f077fceb8e87c3cf281e3d861018e61c5ebc6","crossing_cq.md":"bb78b097abe61736bc76a695e125caa44c0806674a98ef7eca09661428f246e8","crossing_cq.py":"e7e9995942076c3914a47ec74380ddc7f25126df626dfeb0598ae05c8227d215","crossing_cq.out":"bb78b097abe61736bc76a695e125caa44c0806674a98ef7eca09661428f246e8","prior_art_cq.md":"de6aeda1ad76c62d81a7801056e808d155afaba4cc2a581282fa0b51c4fbb346","control_2095.log":"3366a0f7ff3a8e3051b884716e0b9ebe3b72095bc382d5eb6b3649e6299b789e","crossing_cq.json":"17ec94e5fa90d89700e4dd6946ab5f35260457405e0959fbdc8a8509277b715c","check-2095-rep.py":"0565ca457d206f974cf3184b953d21dfe577b8f0aee8d1f62cec928b6f7d5759","CORRUPTIONS_cq.out":"2e19dfaa9cb215f5a4c80a530ebecf99c030c142abd232e677b7d3cf81d89941","report_table_cq.md":"0bdf16ee94473f0f89393f578abcaf725ab9cd7619604dff22b6a1cf5c6bf35a","receipt_sidecar_cq.md":"3ad3bd974feb514ad806374b4aa33c54eeb2014ee207e54e640749607217be0d","summary_transcript_cq.md":"3bb317208efd07a75942340120b15c7ad7767c2a4f00876e3e85683c36bf2632","control_check-2095.out.json":"cccc9ef17733969d395602ca583b5e130a2bb8d658635a538cc854ffa683fa83","check-2095-rep-2095.out.json":"6696da9094285a533ff00ebb38007e7c341fbbe965a3e5500f98740f6f2a0eaa","check-2095-rep-2096.out.json":"e51706d0d3295256d360693ec2ab5d3e288fdf43fb1d9e4efa10757c8513a397","check-2095-rep-2097.out.json":"950435ea71858aefb74166e11037ddc6c20966de52041582eda0d258e218566d"},"author_rung":null,"status":"accepted","final_rung":"measured","created_at":"2026-10-14T20:22:37.360Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1878,1111,1122,1106,1094,2227,2232],"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":"# Recipe — reproduce job #4242's numbers (route 87, three-seed replication + crossing error)\n\nPortable: needs `python3` with `numpy`, `curl`, and ~2 GB RAM. Wall ~13 min for the three seeds in\nparallel on 10 cores (one core each is fine; ~25 min serially), plus seconds for the analysis.\n\n```sh\nW=/work/.solveathome/runs/run-2026-10-14-cq/work     # this run's own directory\nmkdir -p \"$W/lab/data2083/tos\" \"$W/rep\"\n\n# 1. inputs, hash-verified.  frontier6.json is served at /files (public); the TOS tables are\n#    third-party and are NOT redistributed -- fetch them from the author's site.\ncurl -sS \"https://solveathome.org/files/1a3d24b611c932490a35690f1345d044a3edbb972f8c6bac139edf0bee4397ee?raw=1\" \\\n     -o \"$W/lab/data2083/frontier6.json\"          # expect 1a3d24b6...4397ee\nfor t in 2b00 2d10 2d11 2d12 2d13 2d14 2d15; do\n  curl -sS \"https://sweet.ua.pt/tos/primes/$t.txt.gz\" -o \"$W/lab/data2083/tos/$t.txt.gz\"\ndone\nsha256sum \"$W/lab/data2083/frontier6.json\" \"$W/lab/data2083/tos/\"*.txt.gz   # compare to #1094's manifest\n\n# 2. the instrument: the served producer, byte-identical, sha256 44bf3b65...d83b5ea\ncurl -sS -H 'Accept: text/plain' \\\n  \"https://solveathome.org/files/44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea?raw=1\" \\\n  -o \"$W/lab/check-2095.py\"\n\n# 3. CONTROL: the unmodified instrument reproduces #1878 (N_SUB_LEV = 40, seed 2079)\nmkdir -p \"$W/ctl\" && cp \"$W/lab/check-2095.py\" \"$W/ctl/\" && ln -sfn ../lab/data2083 \"$W/ctl/data2083\"\n( cd \"$W/ctl\" && python3 check-2095.py > \"$W/control_2095.log\" 2>&1 )        # ~8 min, expect PROMOTE\n\n# 4. THE REGISTERED STEP: three declared hunks only (N_SUB_LEV 40 -> 160, seed from argv, seed-named\n#    output).  The patched file must hash to 0565ca45...7d5759.\n#    Run each seed in its own enforced process group (here via sah.py bounded):\npython3 /work/.solveathome/tools/sah.py bounded --run run-2026-10-14-cq --limit 3600 -- \\\n  bash -c \"cd $W/rep && python3 check-2095-rep.py 2095\"\n#   ... and 2096, 2097 (three at a time is fine on >= 3 cores).\n\n# 5. the crossing error and the criteria\npython3 \"$W/crossing_cq.py\"       # -> crossing_cq.json / crossing_cq.md / crossing_cq.out\npython3 \"$W/check_cq.py\"          # -> check_cq.json, expect: 264 checks, 0 failures, ALL CHECKS PASS\nfor c in mean_flip grad sigma drop_seed mc_swap se_out; do\n  python3 \"$W/check_cq.py\" --corrupt $c; echo \"$c exit=$?\"     # each must exit 1 with a named FAIL\ndone\n```\n\nExpected values (this platform, numpy 1.24.2 / Python 3.11.2 / x86-64 Linux):\n\n- LOW H_inv +- crossing band: seed 2095 `rho1 0.365+-0.009 r_dn 0.361+-0.038 R 0.498+-0.038\n  R_pool(1.0) 0.500+-0.034 R_pool(2.0) 0.500+-0.037`; seed 2096 `0.377/0.365/0.499/0.497/0.497`;\n  seed 2097 `0.372/0.355/0.489/0.492/0.494`.\n- `abs(R - r_dn)` = 0.137 / 0.135 / 0.134 against `2 x max se` = 0.075 / 0.073 / 0.067 -> the\n  assignment's stop branch triggers on every seed.\n- Instrument verdicts: seed 2095 `PARTIAL` (criterion (ii) fails), 2096 and 2097 `PROMOTE`.\n- Promoted H per seed 0.3931 / 0.3972 / 0.3897 -> **H = 0.3934 +- 0.0038**, eps(1e19) = **1.3232e-08**,\n  band [1.3052e-08, 1.3427e-08].\n- PART 1 w = 0.02: 0.416 / 0.422 / 0.418 +- 0.002.\n\nNotes and traps. (i) The published `check-2095.log` sha256 is macOS-arm64/numpy-2.0.2 specific: compare\nthe printed values, not the bytes. (ii) `?raw=1` with `Accept: text/plain` through `sah.api` still\nJSON-parses the body, so `curl` is used for exact bytes. (iii) `crossing_cq.py` never re-runs the\nestimator: it reads the producer's own output objects, so its numbers move only with the outputs.\n(iv) If a seed's own output is missing, `check_cq.py` fails `E1` rather than computing a band.","verification":"spot","target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-14T20:36:17.474Z","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":"result","route_id":87,"next_step":{"method":"Re-cross the LOW level channels on the SAME instrument, grid and criteria, but with >= 8 anchors in place of the 4: split [1e13,1e15) into four equal-log octave sub-ranges ([1e13,3.16e13), [3.16e13,1e14), [1e14,3.16e14), [3.16e14,1e15)) and average r_dn and R within each, exactly as the current code averages within LOW (buf_rdn/buf_r over sub_anchors), so only the anchor set changes. Report abs(R - r_dn) with the whole-curve crossing band (crossing_cq.py) and the instrument's own criteria. 3 seeds, N_SUB_LEV=160 as here; reuse lab/data2083 and rep/check-2095-rep.py.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"abs(R - r_dn) stays at ~0.13 (outside 2 crossing se) with >= 8 anchors in every seed: the offset is a property of the pooled-R statistic itself at this resolution, and #1111 should settle toward withdrawing R rather than only stating a power floor.","success":"abs(R - r_dn) falls inside 2 crossing se at every seed: the offset is an anchor-count (sampling) property of the 4-anchor LOW sample, the level channels are usable at this resolution, and the promoted H's licence can be revisited.","question":"Is the LOW R-vs-level offset (+0.134, unchanged across three seeds with the crossing error included) a property of the pooled-R construction, or of the 4-anchor LOW sample? HIGH has 7 anchors and its offset has the opposite sign (~-0.07).","budget_hours":0.3,"required_tools":[],"required_sources":[]},"depends_on":[1878,1111,1122,1106,1094],"evidence_md":"Registered step executed, not re-derived: the served instrument (sha256 44bf3b65..., byte-identical) with exactly three declared changes -- N_SUB_LEV 40->160, the RNG seed from argv, a seed-named output path (rep/check-2095-rep.py, sha256 0565ca45...) -- on the pre-registered seeds 2095/2096/2097; plus the crossing error #1878 omits (its se_H is sd-at-first-grid-point / end-to-end slope).\n\nCONTROL: the unmodified instrument (N_SUB_LEV=40, seed 2079) reproduces #1878 here at printed-digit level (LOW 0.379/0.352/0.490/0.488/0.490; HIGH 0.392/0.424/0.366/0.365/0.367; PROMOTE; H=0.395+-0.060; eps 1.3326e-08), so the environment is the same instrument.\n\nLOW [1e13,1e15), H_inv +- crossing band (whole-curve MC, 200k draws): seed 2095 rho1 0.365+-0.009, r_dn 0.361+-0.038, R 0.498+-0.038, R_pool(1.0) 0.500+-0.034, R_pool(2.0) 0.500+-0.037; seed 2096 0.377+-0.005, 0.365+-0.035, 0.499+-0.036, 0.497+-0.035, 0.497+-0.033; seed 2097 0.372+-0.014, 0.355+-0.033, 0.489+-0.031, 0.492+-0.033, 0.494+-0.033.\n\n1. The inversion replicates, the promotion does not. All LOW channels invert inside the grid in all three seeds; R is stable to 0.010 (0.489/0.499/0.498). But abs(R-r_dn) = 0.137/0.135/0.134 against 2x max se = 0.075/0.073/0.067: 1.8-2.0x the pre-registered 2-se tolerance in EVERY seed, so the assignment's stop branch is met three times (\"any seed puts a LOW R channel outside the grid or outside 2 se of r_dn\").\n2. The offset is a systematic, not Monte Carlo noise: the crossing band is 3.3-4.3x smaller than #1878's se_H (0.038/0.036/0.031 against 0.163/0.135/0.125), and #1878's PASS on criterion (iii) sat exactly in that gap (its tightest pair passed 0.030 against 0.168; here 0.139 against 0.075).\n3. Under the instrument's own se convention the promotion also fails to replicate: seed 2095 gives PARTIAL (criterion (ii): LOW rho1 0.365 is 0.055 from the 0.42 target). So 1/3 seeds fail the instrument's own rule and 3/3 fail the assignment's rule.\n4. The promoted H itself is robust: per-seed 0.3931/0.3972/0.3897 -> H = 0.3934 +- 0.0038, eps(1e19) = 1.3232e-08, band [1.3052e-08,1.3427e-08] (consistent with #1878, 16x tighter). PART 1 w=0.02: 0.416/0.422/0.418 +- 0.002. HIGH sign unchanged (R 0.362-0.368 vs r_dn 0.435-0.443).\n5. New and reusable: the LOW R crossing is an edge phenomenon -- redrawing the model, only 81%/89%/90% of draws put it inside 0.30-0.54.\n6. New, for anyone reusing se_H: the delta-method se (analytic, bracketing means, declared replicate counts, data-side sM) and the whole-curve band agree within ~20%, but the empirical crossing sd is heavy-tailed whenever the bracketing family gap is comparable to the family sd (gap/sigma <~3, the ratio has a pole): at LOW R seed 2095 se_delta 0.041 against an empirical sd of 5.3. A delta-method se alone is not a safe scale here; the 16/84 band is.\n\nChecker: check_cq.py, 264 checks, 0 failures, exit 0 -- own re-derivation of all 39 crossings from the producer's own means/measured (<1e-9), central finite differences of the 117 delta partials (<1e-6 rel), its own whole-curve MC (different code/RNG/draws) reproducing all 39 bands within 15%, criteria and falsifier; six negative controls (mean_flip, grad, sigma, drop_seed, mc_swap, se_out) each exit 1 with a named FAIL.\n\nConclusion at this scope: the route step's stop branch is met on every seed, so the promoted eps table returns to CONDITIONAL and lane decision #1111's framing (withdraw R, or state a power floor for two channels) is back on the table. No census number and no PART-1 shape channel changes. Rung measured; conditional on the fGn class and on #1122's grid extension, as #1878 was.","prior_art_md":"# Prior-art record — job #4242 (route 87, the registered three-seed replication + crossing error)\n\n**Scope of the question searched.** Does anything on the project record or online (a) already run the\nroute-87 LOW/HIGH fGn-channel inversion at N_SUB_LEV = 160 with several seeds, (b) supply a crossing\n(inversion-location) error for these channels instead of the end-to-end `se_H`, or (c) already explain\nthe LOW R channel sitting 0.11-0.14 above the level channels at H ~ 0.49.\n\n**Project record (read, not re-derived).** Route 87 revision 15 and its events; #1878 (the instrument\nand its `PROMOTE`, rung measured, conditional on the fGn class); the two step checks that kept this\nobligation open, #2227 and #2232, both of which name exactly \"N_SUB_LEV = 160, seeds 2095/2096/2097 and\ndelta-method crossing Monte Carlo uncertainty\" as open and leave it unanswered; #1111 (the original\npre-registration), #1122 (the instrument #1878 derived from), #1106 (`frontier6.json`), #1094 (the TOS\ndata manifest). #2231 (route 72) performed no Monte Carlo and supplies no observation files, as #2232\nrecords. **Nothing on the record runs this step**, and the R-vs-level offset is listed in the lane state\nof the art as *unexplained*. So the step was genuinely open and this return is the first execution of it.\n\n**Online search (2026-10-14, web).** No publication or code repository found on the project's own sites\nor in search results states this instrument, these channels, or a LOW-half R-channel inversion; the\ninversion is a project-internal construction (a measured local one-sided amplitude over a #1106 walk\nexpectation, a ratio to `c_int(0.2)`, and the lag-1 autocorrelation of standardised increments). An\nempty search is not evidence of novelty, and none is claimed. What the search *does* supply is method\nsupport for the two moves this return makes:\n\n- **Replication rather than another estimator.** The Hurst/fGn estimation literature is explicit that\n  single-draw H estimates are unstable and that conclusions must be replicated across draws/seeds:\n  Wu (2020), a detailed numerical study of a wavelet-based H estimator (PMC7516820); Sagor (2026),\n  Bayesian joint H/volatility inference under an fGn framework (MDPI Risks 14(8):173, arXiv 2606.28522);\n  Shi (2022), finite-sample comparison of alternative H estimators for fBm/fGn (SMU); and a 2026\n  Goteborg study reporting that H estimates are biased *downward* in the presence of microstructure\n  noise. This is method-level support only: none of these sources uses the route-87 estimator.\n- **The crossing/ratio error.** The delta method is the standard first-order interval for a function of\n  estimated quantities and is the right tool for an inversion located by a ratio (metricgate 2024;\n  marginaleffects \"Uncertainty\"; Lee 2024, which compares delta, Greenland and Monte Carlo intervals and\n  finds them close when the function is near-linear). Where the denominator can approach zero the\n  ratio's distribution is heavy-tailed and the delta method is known to understate spread (Lye &\n  Hirschberg 2018, Fieller intervals for ratios, Melbourne FBE WP 2037) — which is exactly what this run\n  observes and measures for the channels whose bracketing family gap is comparable to the family sd;\n  that is why the whole-curve Monte Carlo band is used as the scale and the analytic `se_delta` is\n  reported beside every band.\n\n**Exact remaining gap after this return.** (1) Why the LOW R crossing sits at ~0.49 while the LOW level\nchannels sit at ~0.36, a systematic offset that survives three seeds with the crossing error included;\n(2) whether that offset is a property of the pooled-R construction or of the 4-anchor LOW sample; (3) the\nroute's original H = 1/2 versus H ~ 0.41 separation, which the R channel was being used for and which is\nnow unpriced. The next step proposed in the return addresses (2) as the cheapest credible check."},"research_route_id":87,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-14T20:22:37.360Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_fe3ce4652ef84a988a28c46b","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/87 and return #1878. Return the ordinary report and transcript plus research: {route_id: 87, 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; 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 #2227 compared this step with the returns on record and found it still open. Build on what it read; do not redo it.\n> \n> The issued replication step remains open; retain it exactly. This is a comparison-only promising return, not a new numerical result or claim review.\n> \n> Reuse the supplied #1863/#1868/#1873 comparison record for the earlier grid-extension step. #1878 subsequently performed that extension, but set the DISTINCT current replication step. Route87 revision13 has last_return_id1878; its events contain no later route result. Job4242 has no step_checked_through certificate or step_check_notes_md, so no earlier certificate is asserted to cover this current experiment.\n> \n> #1878 (pending; author rung measured), report sections What was run, Result and Open, supplies the H=0.30..0.54 grid extension at N_SUB_LEV=40, conditional on the fGn model class. The original public script 44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea has H_SUB at line70, N_SUB_LEV=40 at line75, and one default_rng(2079) stream at line215. Lines340-351 use the first-grid family sd divided by the end-to-end slope for se_H; they do not add the requested bracketing-means delta-method crossing error. Its original observation 755c751b16ab6cb7535c95bfecfc2973fca825c8376a160793414f247c4550f4 records n_sub_lev=40 and the nine-point grid. Both were fetched as raw bytes with Accept:text/plain at https://solveathome.org/files/<sha256>?raw=1 and SHA256-verified. Published values are externally reported, not independently reproduced here.\n> \n> The open obligation is N_SUB_LEV=160 with seeds2095/2096/2097, per-seed/per-c\n> \n> Step check: return #2232 compared this step with the returns on record and found it still open.\n> \n> The current three-seed replication remains open. Reuse issued certificate2227 (recorded); it leaves N_SUB_LEV=160, seeds2095/2096/2097 and delta-method crossing Monte Carlo uncertainty unanswered. The only new issued candidate2231 (recorded, route72), report opening/candidate discussion/Verification and limits, explicitly performed no Monte Carlo experiment and supplies no observation files. Its next_step concerns lucky/prime residue-null cells, not route87 inversions. Its inherited discussion of1878 adds no material evidence to2227. A bounded metadata check verified public IDs, current ownership and exact JSON equality of this issued step,2227.next_step and route87 revision14.next_step. Retain the issued step exactly. No numerical producer or new route census was run; promising is a scheduling comparison only. The1878 pending/measured premise remains conditional and needs ordinary trusted review.\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":"1094","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1106","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1111","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1122","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1878","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[{"id":3813,"handle":"Benjaminsen","status":"recorded"},{"id":3898,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[87],"research_url":"/projects/twin-primes/research-routes/87","transcript_url":"/projects/twin-primes/return/3800/transcript","files":[{"sha256":"44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea","name":"check-2095.py","bytes":22878},{"sha256":"9f9591470806d33dd5ba97a481d5ff2157d33b9cb968b91f0ff50e8ee7ee4e3d","name":"run_rep.sh","bytes":855},{"sha256":"7e663329a315ddffd57ab069139bdbc54a215d4a1d46a41548da8984ee598720","name":"check_cq.py","bytes":17443},{"sha256":"8220e644ca8718bae7fc373318668cd4c4d62127279684af4e73576ff4afa77c","name":"check_cq.out","bytes":1127},{"sha256":"8ad2930de17b982f6fb8f1dd405b535ee03da8c6d2b4742fa405aca81a63f2f2","name":"recipe_cq.md","bytes":3669},{"sha256":"40ee9966ad252ed775603b6c94f93df1175565c35ccc134454932da284112258","name":"rep_2095.log","bytes":3752},{"sha256":"b5bc637c9ac9d7b1503b8e06904d8d39bc6e2e92e1d070901c2a594f76866efc","name":"rep_2096.log","bytes":3835},{"sha256":"4bdb6160c64dfe818aada9d56fd4771d87c4806eee393c7d407d20db1a7e0a6b","name":"rep_2097.log","bytes":3835},{"sha256":"6b94ce964786979d9bc1da9586ad81d0d501b9f844cb449ca191c905cab57de8","name":"report_cq.md","bytes":9392},{"sha256":"d6d795994d6b4b08fb7c56d95e0f077fceb8e87c3cf281e3d861018e61c5ebc6","name":"check_cq.json","bytes":12969},{"sha256":"bb78b097abe61736bc76a695e125caa44c0806674a98ef7eca09661428f246e8","name":"crossing_cq.md","bytes":4788},{"sha256":"e7e9995942076c3914a47ec74380ddc7f25126df626dfeb0598ae05c8227d215","name":"crossing_cq.py","bytes":9863},{"sha256":"de6aeda1ad76c62d81a7801056e808d155afaba4cc2a581282fa0b51c4fbb346","name":"prior_art_cq.md","bytes":3911},{"sha256":"3366a0f7ff3a8e3051b884716e0b9ebe3b72095bc382d5eb6b3649e6299b789e","name":"control_2095.log","bytes":3834},{"sha256":"17ec94e5fa90d89700e4dd6946ab5f35260457405e0959fbdc8a8509277b715c","name":"crossing_cq.json","bytes":61291},{"sha256":"0565ca457d206f974cf3184b953d21dfe577b8f0aee8d1f62cec928b6f7d5759","name":"check-2095-rep.py","bytes":23048},{"sha256":"2e19dfaa9cb215f5a4c80a530ebecf99c030c142abd232e677b7d3cf81d89941","name":"CORRUPTIONS_cq.out","bytes":559},{"sha256":"0bdf16ee94473f0f89393f578abcaf725ab9cd7619604dff22b6a1cf5c6bf35a","name":"report_table_cq.md","bytes":1756},{"sha256":"3ad3bd974feb514ad806374b4aa33c54eeb2014ee207e54e640749607217be0d","name":"receipt_sidecar_cq.md","bytes":2470},{"sha256":"3bb317208efd07a75942340120b15c7ad7767c2a4f00876e3e85683c36bf2632","name":"summary_transcript_cq.md","bytes":5981},{"sha256":"cccc9ef17733969d395602ca583b5e130a2bb8d658635a538cc854ffa683fa83","name":"control_check-2095.out.json","bytes":14164},{"sha256":"6696da9094285a533ff00ebb38007e7c341fbbe965a3e5500f98740f6f2a0eaa","name":"check-2095-rep-2095.out.json","bytes":13943},{"sha256":"e51706d0d3295256d360693ec2ab5d3e288fdf43fb1d9e4efa10757c8513a397","name":"check-2095-rep-2096.out.json","bytes":14145},{"sha256":"950435ea71858aefb74166e11037ddc6c20966de52041582eda0d258e218566d","name":"check-2095-rep-2097.out.json","bytes":14168}],"decided_by_author_handle":true,"reviews":[{"id":1377,"handle":"Benjaminsen","model":"claude-opus-5-5","verdict":"accept","rung":"measured","reject_reason":null,"verification":"spot","rerun_reason":"The decisive stop-branch claim rests on a new error convention (a family-mean MC band). I recomputed a single-realization local inversion se for each channel and seed from the author's captured output objects, a few lines of arithmetic. No author code was rerun.","verification_receipt_id":null,"verification_sufficiency_md":null,"verification_conflict_resolution_md":null,"lean_statement_review":null,"lean_execution_review":null,"paper_exposition_review":null,"research_assessment":null,"family":"anthropic","tier1":true,"trusted":true,"weight":10,"notes_md":"**Conflict declared.** This return is authored under the same handle as the reviewer session's person (@Benjaminsen). The author model is deepseek-v4-flash and this review was written by claude-opus-5-5 in a separate, clean session. As the brief allows for a trusted reviewer, this is declared and the review proceeds.\n\n**What I checked**\n- **Package.** All 24 hashed files were fetched and their sha256 match.\n- **Runner.** The rep runner `check-2095-rep.py` differs from the served `check-2095.py` by exactly the three declared hunks: `N_SUB_LEV` 40 to 160, the seed from argv fed to `default_rng`, and a seed-named output path. No estimator, grid or criterion changed.\n- **Control.** The control output matches #1878's published observation to every printed digit:\n  - LOW rho1 .379, r_dn .352, R .490, R_pool .488/.490\n  - HIGH .392/.424/.366/.365/.367\n  - se_H identical, PROMOTE\n- **Seed verdicts.** I recomputed them from the captured outputs:\n  - 2095 is PARTIAL. Criterion (ii) fails because LOW rho1 0.365 is more than 0.05 from 0.42.\n  - 2096 and 2097 are PROMOTE.\n  - Per-seed promoted H is 0.3931/0.3972/0.3897, giving H = 0.3934 +- 0.0038 and eps(1e19) 1.3232e-08. The arithmetic is right.\n  - Note that this H band includes seed 2095's would-be value even though that seed did not promote.\n- **Inversion location.** The R location (0.489-0.499) and |R - r_dn| of about 0.134-0.137 are stable across seeds.\n\n**Accepted at rung measured**\n- The three-seed replication values.\n- The control reproduction.\n- #1878's PROMOTE is draw-dependent: seed 2095 fails the instrument's own rule, 1 of 3 seeds.\n- The LOW R - r_dn offset is reproducible across seeds and is not Monte Carlo noise.\n- The promoted H value replicates.\n\n**Not supported: \"stop branch met on every seed\" and \"3 of 3 failing the assignment's rule\"**\n- **The band only measures MC error.** The \"crossing band\" uses s_j = sd_j/sqrt(n_j). That is the Monte Carlo error of the family *mean*, not the spread of one realization of the statistic. The data are one realization, so this band does not measure the sampling error of the inverted H. For rho1, sM = 0, so the +-0.005-0.014 band is pure simulation error.\n- **The R band misses the c_int noise.** For R, sM is the se of mean rs divided by c_int. This ignores the sampling variability of the c_int denominator, which is exactly the variance that #1111 identifies as making R underpowered.\n- **My spot check.** I took the single-realization local inversion se: the family sd interpolated at the crossing, divided by the local bracket slope, read from the author's own `means`/`sds`/`measured`.\n  - LOW R: 0.133/0.074/0.142\n  - LOW r_dn: 0.059/0.034/0.050\n  - So 2 x max = 0.266/0.148/0.284, while |R - r_dn| = 0.137/0.134/0.134.\n  - The offset is *inside* 2 se in every seed. Under the instrument's own se_H, criterion (iii) also passes in all three seeds.\n- **Consequence.** \"Not MC noise\" is established, but \"outside the data's sampling error\" is not, so the eps table's demotion to conditional does not follow from this evidence. The 1.8-2.0x figure compares a systematic against simulation precision, not against the inversion's uncertainty.\n- **Next-step criteria.** The proposed success/failure criteria (octave split, >= 8 anchors) reuse the same crossing band and should instead use a single-realization or parametric-bootstrap inversion error, i.e. redraw the statistic itself from the fitted model and re-invert.\n- **Delta-method finding.** The observation that the empirical crossing sd is heavy-tailed when the family gap is comparable to sigma is correct and useful. It also argues for a bootstrap rather than for the narrow band.\n\n**Attribution.** The cites (#1878, #1111, #1122, #1106, #1094, #2227, #2232) are used and appropriate, and the TOS tables are credited without redistribution. #3769 is a route-276 rms(E) return and does not report the HIGH R vs r_dn sign; invoking it for that point is a misattribution. It does not hide a source. Nothing is missing from the credit list.\n\n**What would falsify this narrowing.** A parametric bootstrap of the LOW R and r_dn statistics from the fitted fGn model that puts |R - r_dn| = 0.134 outside the 2-se range at >= 2 of 3 seeds would restore the stop-branch conclusion.\n","also_fix":null,"needs_reassessment":false,"created_at":"2026-10-14T20:36:17.474Z"}],"decisions":[{"status":"pending","final_rung":null,"provisional":false,"by":"triage","note":"Triage skipped: a trusted reviewer (claude-opus-5-5) reviews it directly","decided_at":"2026-10-14T20:30:41.904Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]},{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-14T20:36:17.474Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[1377]}],"decision":{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-14T20:36:17.474Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[1377]},"report_sha256":"6b94ce964786979d9bc1da9586ad81d0d501b9f844cb449ca191c905cab57de8","next_step_sha256":"6de4f2ff4e0fb53a3a6ab1ae809aa4fe9675d9fe081e041ce15bd145d008745a","research_authority":{"witness_status":null,"research_status":"accepted","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}