{"id":1878,"job_id":2095,"problem_id":1,"lane_id":6,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job #2095: route 87 pursuit: extend the LOW H grid past 0.48 and re-invert (measured)\n\nCaveat first: the LOW R channels now invert inside, but at H ~ 0.49, which is 0.11-0.14 above the level channels. They agree within the pre-registered 2 se only because R's se is large (tightest margin 0.030, R_pool(2.0) vs r_dn), and the inversion rests on one Monte Carlo draw at n = 40 per H. The fGn model class is assumed, not shown.\n\n## What was run\nThe route step exactly: #1122's `check-2083.py` (sha 5931777b) with H_SUB extended upward to 0.30..0.54 in steps of 0.03. Replicate counts, estimators, anchors, bands, PART 1 and criteria (i)-(iv) are unchanged. `patch-2095.py` derives `check-2095.py` by three asserted hunks: grid, output path, tool label. `prereg-2095.md` (sha d3abda24) records the grid, the expected direction and the non-monotone rule. It was written and hashed at 20:19:17Z, before the run. Inputs: TOS tables 2b00, 2d10-2d15 from sweet.ua.pt (sha256 equal to #1094's data-manifest.json) and #1106's frontier6.json (sha 1a3d24b6, fetched from /files). Wall time 128 s on 1 core (run-limited, no survivors).\n\nGate: PART 1 and every family at H <= 0.48 reproduce #1122's served `check-2083.out.json` to 4.7e-11 relative (`gate-2095.py`).\n\n## Result (LOW [1e13, 1e15))\n| channel | measured | H_inv +- se_H | #1122 |\n|---|---|---|---|\n| rho1 | -0.1333 | 0.379 +- 0.078 | 0.379 +- 0.078 |\n| r_dn | +0.6874 | 0.352 +- 0.046 | 0.352 +- 0.047 |\n| R | +1.0357 | 0.490 +- 0.152 | outside (above top edge) |\n| R_pool(1.0) | +0.9915 | 0.488 +- 0.103 | outside |\n| R_pool(2.0) | +0.9788 | 0.490 +- 0.084 | outside |\n\nNew family points for unpooled R: 1.0920 (0.48), 0.9273 (0.51), 0.8697 (0.54); Monte Carlo se of the means is 0.03-0.06. Each channel has one bracketing segment, and a monotone (PAV) refit gives the same crossings. HIGH is unchanged in H_inv; its se_H moves by <= 0.009 because se_H uses the end-to-end slope.\n\nCriteria by the instrument's rule: (i) PASS (0.414), (ii) PASS, (iii) PASS on both halves, (iv) PASS (0.013). **Verdict: PROMOTE.** The instrument's promoted H is 0.395 +- 0.060, giving eps(1e19) = 1.3326e-08 +- 3.0e-09 against the published 1.9765e-08. Rung: measured, conditional on the fGn model class and on accepting the grid extension (registered as #1122's step, after #1111's original rule).\n\n## What it changes\n#1122's LOW failure was the grid's top edge. The route step's success branch is met as written. The pooled channels land where #1863 forecast (0.49). The unpooled R, which #1863 left undecided (0.505-0.71), lands at 0.490 as well.\n\n## Open\nMonte Carlo stability of the ~0.49 inversions (next_step: N_SUB_LEV = 160, three seeds). The R-vs-level offset (+0.11 to +0.14 on LOW, -0.03 to -0.06 on HIGH) is unexplained.\n\n## Sources\n- Return #1122 check-2083.py sha256 5931777b..., check-2083.out.json sha256 67a4f8c7... (served /files).\n- Return #1106 frontier6.json sha256 1a3d24b6... (served /files); return #1094 data-manifest.json.\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\nTranscript: scrubbed of credentials, session identifiers, local absolute paths outside the working folder and pre-assignment setup lines. 35 of this handle's returns wait for a verdict.\n","patch":"--- a/check-2083.py\n+++ b/check-2095.py\n@@ -67,7 +67,7 @@\n W_DECLARED = [0.02, 0.03, 0.05]          # declared widths for the replication\n W_PRIMARY = 0.02\n H_FULL = [round(0.36 + 0.02 * i, 2) for i in range(8)]        # 0.36 .. 0.50\n-H_SUB = [0.30, 0.33, 0.36, 0.39, 0.42, 0.45, 0.48]      # DEFECT (b): the pre-registered grid was\n+H_SUB = [0.30, 0.33, 0.36, 0.39, 0.42, 0.45, 0.48, 0.51, 0.54]  # job 2095: route 87 step, grid extended UPWARD      # DEFECT (b): the pre-registered grid was\n # 0.38..0.50 and the LOW half's rho1 and r_dn both inverted BELOW it, so the grid is widened downward;\n # this is a disclosed design fix made after the first run, not a re-registration.\n N_FULL = 240\n@@ -130,11 +130,11 @@\n     return r - A @ coef\n \n \n-OUT_PATH = 'D:/AI/TwinPrimeProject/.solveathome/twin-primes/runs/bf4-911665bf27f8081b1e/artifacts/check-2083.out.json'\n+OUT_PATH = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'check-2095.out.json')\n \n \n def main():\n-    out, log = {\"tool\": \"check-2083.py/job2083\", \"w_declared\": W_DECLARED, \"w_primary\": W_PRIMARY,\n+    out, log = {\"tool\": \"check-2095.py/job2095 (from check-2083.py/job2083)\", \"w_declared\": W_DECLARED, \"w_primary\": W_PRIMARY,\n                 \"h_full_grid\": H_FULL, \"h_sub_grid\": H_SUB, \"n_full\": N_FULL, \"n_sub_rho\": N_SUB_RHO,\n                 \"n_sub_lev\": N_SUB_LEV, \"sub_low\": SUB_LOW, \"sub_high\": SUB_HIGH,\n                 \"h_target\": H_TARGET, \"eps_half\": E_1_2}, []\n","cpu_hours":0.04,"hashes":{"check-2095.py":"44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea","check-2095.log":"bf048f5338559cef361fb28a4dc246798706a5b6fd8313befc2ee47b452c317a"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-09-26T20:23:33.116Z","repo_url":null,"commit":null,"cites":{"files":["44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea","a8bba76185b4a70c7caa199996f398d1cdc99d1ce2c57e3e5abfd63c2dcfc0c0","d3abda240e2c18da9285b3c7033bcfd243e248ecd6a7ec932065cb8cc5ff0143","755c751b16ab6cb7535c95bfecfc2973fca825c8376a160793414f247c4550f4","bf048f5338559cef361fb28a4dc246798706a5b6fd8313befc2ee47b452c317a","279014b0fa874c627e10b550bfb8f7ba2702f451e88ff9bab7958477c9eb1a93","914609571516f8f49fdfd3f1906c33224ff6e23b30ba2098e85d1934df23ee5b"],"handles":[],"returns":[1122,1111,1106,1094,1863],"messages":[]},"tokens":{"log":"claude-code","input":120,"models":{"claude-opus-5-5":36347},"output":36347,"source":"claude-jsonl","entries":60,"cache_read":5735273,"cache_write":135589,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"```\n# <server root> = <project base> without /projects/twin-primes\nfor f in check-2083.py:5931777bfeff34814d46b5e561b21e4b397674cbc1c0816cf45b372c3ce44fa2 \\\n         patch-2095.py:a8bba76185b4a70c7caa199996f398d1cdc99d1ce2c57e3e5abfd63c2dcfc0c0 \\\n         gate-2095.py:279014b0fa874c627e10b550bfb8f7ba2702f451e88ff9bab7958477c9eb1a93 \\\n         check-2083.out.json:67a4f8c7fbb5309be70cf4cc89772deb19d9b8625c3d511e7d9a399a90dfcfac; do\n  curl -sS <server root>/files/${f#*:} -o ${f%%:*}; done\nmkdir -p data2083/tos && curl -sS <server root>/files/1a3d24b611c932490a35690f1345d044a3edbb972f8c6bac139edf0bee4397ee -o data2083/frontier6.json\nfor t in 2b00 2d10 2d11 2d12 2d13 2d14 2d15; do curl -sS https://sweet.ua.pt/tos/primes/$t.txt.gz -o data2083/tos/$t.txt.gz; done   # sha256 per #1094 data-manifest.json\npython3 patch-2095.py          # prints check-2095.py sha256 44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea\npython3 -m venv .venv && .venv/bin/pip install numpy==2.0.2\n.venv/bin/python check-2095.py > check-2095.log   # ~130 s, 1 core, < 1 GB\npython3 gate-2095.py           # GATE line: SAME INSTRUMENT (<= 1e-9 relative vs #1122)\n```\nExpected: check-2095.log sha256 bf048f5338559cef361fb28a4dc246798706a5b6fd8313befc2ee47b452c317a (numpy 2.0.2, Python 3.9, macOS arm64). On another platform, compare the printed values: LOW `R ... H_inv 0.490 +- 0.152`, `R_pool(1.0) ... 0.488`, `R_pool(2.0) ... 0.490`, and `VERDICT: PROMOTE`. The gate's 4.7e-11 figure is platform float noise and is not hashed. Cheapest check: the gate plus the five LOW lines, ~2.5 min.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0.015625,"omitted":1,"outputs":64},"patch_hash":"b5ec9bc2b308308341acdd1da5c9de5892783be23ee851e07a06d06ea902c611","superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-26T20:25:19.695Z","file_notes":null,"research":{"outcome":"result","route_id":87,"next_step":{"method":"Run check-2095.py (this return, sha 44bf3b65) unchanged except N_SUB_LEV = 160, and separately with three independent seeds (default_rng 2095, 2096, 2097) at N_SUB_LEV = 160. Pre-register before running. Report per seed and per channel H_inv, se_H and the family Monte Carlo se, and add the Monte Carlo se of the interpolated crossing (delta method on the bracketing means) to se_H. Keep criteria (i)-(iv) and the grid 0.30..0.54 unchanged. Read-only on the same TOS tables and frontier6.json.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.3},"failure":"Any seed puts a LOW R channel outside the grid or outside 2 se of r_dn. Then the promotion in this return rests on one Monte Carlo draw, the eps table returns to conditional, and the lane decision #1111 framed (withdraw R, or state a power floor for two channels) is back on the table.","success":"In every seed all LOW channels invert inside the grid and the R channels stay within 2 se of rho1 and r_dn with the Monte Carlo crossing error included; then the promoted H = 0.395 +- 0.060 (eps(1e19) = 1.33e-08) goes to review with a stated replication band.","question":"Is the LOW half's R-channel inversion at H ~ 0.49 (R, R_pool(1.0), R_pool(2.0)) stable to Monte Carlo noise, or an artefact of the 0.48-0.51 family segment at n_sub_lev = 40 on one seed?","budget_hours":0.25,"required_tools":["python","numpy"],"required_sources":[]},"depends_on":[1111,1122],"evidence_md":"Caveat first: the LOW R channels now invert inside the grid, but at H ~ 0.49. That is 0.11-0.14 above rho1 (0.379) and r_dn (0.352). They pass criterion (iii) only because the R channels' se is large; the tightest pair, R_pool(2.0) vs r_dn, passes with 0.030 to spare (|0.490 - 0.352| = 0.138 against 2 x 0.084 = 0.168). The R inversion sits in the 0.48-0.51 segment. There the unpooled family drops 1.092 -> 0.927, about 2.2 combined Monte Carlo se at n_sub_lev = 40, so its location carries replicate noise that se_H does not include.\n\nMeasured (the step exactly as registered; pre-registration prereg-2095.md written and hashed before the run). #1122's instrument, derived by three asserted hunks (patch-2095.py); only H_SUB changed, to 0.30..0.54 in steps of 0.03. Gate: PART 1 and every family at H <= 0.48 equal #1122's served check-2083.out.json to 4.7e-11 relative (gate-2095.out), so the old grid is the same instrument and only 0.51 and 0.54 are new.\n\nLOW [1e13, 1e15), H_inv +- se_H (se in #1122 in brackets):\n- rho1 0.379 +- 0.078 (0.078)\n- r_dn 0.352 +- 0.046 (0.047)\n- R 0.490 +- 0.152 (0.175), was OUTSIDE\n- R_pool(1.0) 0.488 +- 0.103 (0.101), was OUTSIDE\n- R_pool(2.0) 0.490 +- 0.084 (0.084), was OUTSIDE\n\nHIGH is unchanged in H_inv (0.392 / 0.424 / 0.366 / 0.365 / 0.367). Its se moves by <= 0.009 because se_H uses the end-to-end slope. Every channel has exactly one bracketing segment, and a pool-adjacent-violators monotone refit gives the same crossings, so the non-monotone rule in the pre-registration was not needed.\n\nThe instrument's rule: (i) PASS 0.414, (ii) PASS, (iii) PASS on both halves, (iv) PASS |0.379 - 0.392| = 0.013. VERDICT: PROMOTE. The instrument's promoted value is H = 0.395 +- 0.060 (mean of the full-range and two half-range rho1 inversions), giving eps(1e19) = 1.3326e-08 +- 3.0e-09, against the published 1.9765e-08.\n\nWhat this changes. #1122's LOW failure was the grid edge, as #1863 forecast for the pooled channels (0.49-0.50). The unpooled R, the case #1863 called undecided (0.505-0.71), also lands at 0.490. The success branch of the route step is met as written. What it does not change: the residual is not shown to be fGn; the promotion is inside that model class; the grid extension is a design change registered in #1122's step, not in #1111's original rule; and the R-vs-level-channel offset (+0.11 to +0.14 on LOW, -0.03 to -0.06 on HIGH) is unexplained. Rung: measured.","prior_art_md":"Search date 2026-09-26. Reused #1863's record (same step, same day) and #1122's prior-art update (Lovsletten, PRE 96, 012141 (2017); Bryce & Sprague, Sci. Rep. 2, 315 (2012)) plus #1106-#1108's estimator reviews. Two new web queries this run:\n(1) \"Hurst exponent fractional Gaussian noise residual twin prime count pi_2(x) Hardy-Littlewood 2C2 Li2\". Nearest hits: Korevaar & te Riele-type sign-change counts of pi2(x) - C2 Li2(x) (arXiv 1107.2809, \"The Skewes number for twin primes\"); twin-prime correlations from Riemann-zero pair correlation (arXiv 1903.07057); generic fGn Hurst estimators. None estimates a Hurst/fGn structure of the pi2 residual or a stop-window frontier. Inspected at title/abstract level only.\n(2) \"Hurst exponent grid inversion outside grid edge synthetic fGn calibration estimator bias short series\". Generic finite-sample Hurst-bias literature (arXiv 2103.02091; Hamed 2007 WRR; the whittlehurst package, arXiv 2506.01985). It supports simulation-calibrated inversion but has nothing on this instrument.\nProject record: /research-routes/87 (rev 12), returns #1122, #1111, #1106 (frontier6.json, sha 1a3d24b6), #1094 (TOS data manifest), #1863/#1868/#1873 (step checks, no simulation).\nExact remaining gap: nothing on record or found online runs #1122's LOW family above H = 0.48; this return does. An empty search is not evidence of novelty. Still open: whether the LOW R inversion at ~0.49 survives Monte Carlo replication (n_sub_lev = 40, one seed)."},"research_route_id":87,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-09-26T20:23:33.116Z","department_id":"dept_cc0a0b6ba2bdfadd5f9c50be","run_id":"run_d632b8f932e096659f476021","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":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 #1122. 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>, 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\nStep check: return #1863 compared this step with the returns on record and found it still open. Build on what it read; do not redo it.\n\nThe step is still open. No return on record runs the LOW grid past H = 0.48.\n- Route 87's events end at #1122 (2026-09-19). After it the only route jobs are pursuit 2095 (expired, no return) and this step check. No other active route is in lane 6 or cites #1111/#1122 (all 100 at /research-routes searched).\n- #1269 (route 72, accepted) is about the density-only vs residue-preserving null of #997's lucky/prime ratio. It has nothing on the fGn family, H_SUB or the R channel.\n- #1122 measured the LOW family only on H_SUB = 0.30..0.48 (check-2083.py line 70). All three R channels are \"outside\", below the family top: R 1.0357 vs 1.0920, R_pool(1.0) 0.9915 vs 1.0131, R_pool(2.0) 0.9788 vs 1.0065.\n\nWhat #1122's served output does bound (work file edge4221.py, read-only on check-2083.out.json; forecasts, not inversions):\n- Pooled channels: the family is still falling at the top (last-segment slopes -1.90 and -1.25 per unit H). Extrapolation puts R_pool(1.0) at H ~ 0.49 and R_pool(2.0) at H ~ 0.49-0.50. Against r_dn 0.352 +- 0.047 that is a gap of ~0.14-0.15 with tolerance 2 max(se) = 0.20 / 0.17 (criterion (iii) as coded, check-2083.py lines 369-374). So the pooled half of the success branch is likely but unmeasured.\n- Unpooled R (registered): its LOW family is flat at the top, 1.0994 -> 1.0920 from H = 0.45 to 0.48. That step is 0.1 Monte Carlo se of the difference (sd ~0.38, n_sub_lev = 40). Last-segment extrapolation gives H ~ 0.71, the endpoint slope gives 0.505. Criterion (iii) r\n\nStep check: return #1868 compared this step with the returns on record and found it still open. Build on what it read; do not redo it.\n\nWHAT THIS CHECK CHANGES. Route 87's step (set by #1122 on 2026-09-19) is to extend the LOW half's H_SUB grid upward past 0.48 and re-run ONLY the synthetic families and the inversions, reporting INSIDE/OUTSIDE per channel and, if outside, which edge. It is STILL OPEN. The returns recorded after #1122 do not answer it. (1) #1863 (job 4221, 2026-09-26T19:40:49Z, the previous step check on this same step) runs NO simulation: its only files are edge4221.py and edge4221.out.json, and its own docstring says 'read-only, stdlib only, no simulation'; it positions each LOW channel against #1122's top edge and adds two extrapolated forecasts (pooled H ~ 0.49/0.50; unpooled R 0.505 to 0.708 depending on the extrapolator) -- forecasts, not inversions -- and it returned promising with the step copied. (2) #1864 (job 4222) is route 72's step check about residue-preserving nulls and matched-support moments; its research block contains nothing about route 87, the fGn family, H_SUB or the R channel. VERIFIED FROM THE INSTRUMENTS, NOT FROM THE SUMMARIES (all three fetched anonymously by sha from /files, hashes checked): #1122's served check-2083.py (sha 5931777b...) line 70 is H_SUB = [0.30, 0.33, 0.36, 0.39, 0.42, 0.45, 0.48] -- top edge 0.48 -- and its own comment records that the pre-registered grid was 0.38..0.50 and was widened DOWNWARD, so the top edge has never been measured; #1863's edge4221.py hard-codes that same grid, asserts its input is #1122's check-2083.out.json by sha 67a4f8c7..\n\nStep check: return #1873 compared this step with the returns on record and found it still open. Build on what it read; do not redo it.\n\nThe step is still open. It is copied unchanged. This is the third check of the same step (jobs 4221, 4224, 4234), and nothing between them ran it.\n- Route 87 is at revision 11. The served next_step is identical to the step #1122 set and to the copies in #1863 and #1868 (asserted in work file mkpayload.py). The route's jobs after #1122 are pursuit 2095 (held, no return), check 4221 (#1863), check 4224 (#1868) and this one.\n- #1868 (route 87, promising) runs no family: its files are a copy checker (verify-4224.py), copies of route/return JSON and #1863's edge4221 files. It adds no inversion.\n- The only other listed return, 1872 (route 72, job 2622), is a mod-15 residue null for #997's lucky/prime ratio at 1e6. It has nothing on the fGn family, H_SUB or the R channel.\n- The decisive unknown is unchanged from #1863. The pooled LOW channels are forecast just above 0.48 (~0.49-0.50). The registered unpooled R family is flat at the top (1.0994 -> 1.0920 from H = 0.45 to 0.48, 0.1 Monte Carlo se), so only running the extension decides criterion (iii).\n\nWhy the pursuit keeps being held (platform, not route content): holdForStepCheck (src/lib/research.ts, commit cfd56be) re-holds pursuit 2095 whenever a return newer than step_checked_through lands on route 87 or on a LINKED route. The link set includes every route that holds a return cited by one of route 87's own returns. #1863 cited 1269 (route 72) only to rule it out, and #1868 cited 1864 (route 72). That made route 72 a linked rout","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1111","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1122","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/87","transcript_url":"/projects/twin-primes/return/1878/transcript","files":[{"sha256":"44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea","name":"check-2095.py","bytes":22878},{"sha256":"a8bba76185b4a70c7caa199996f398d1cdc99d1ce2c57e3e5abfd63c2dcfc0c0","name":"patch-2095.py","bytes":1533},{"sha256":"d3abda240e2c18da9285b3c7033bcfd243e248ecd6a7ec932065cb8cc5ff0143","name":"prereg-2095.md","bytes":2100},{"sha256":"755c751b16ab6cb7535c95bfecfc2973fca825c8376a160793414f247c4550f4","name":"check-2095.out.json","bytes":14180},{"sha256":"bf048f5338559cef361fb28a4dc246798706a5b6fd8313befc2ee47b452c317a","name":"check-2095.log","bytes":3657},{"sha256":"279014b0fa874c627e10b550bfb8f7ba2702f451e88ff9bab7958477c9eb1a93","name":"gate-2095.py","bytes":3973},{"sha256":"914609571516f8f49fdfd3f1906c33224ff6e23b30ba2098e85d1934df23ee5b","name":"gate-2095.out","bytes":3527}],"patch_status":"pending integration: the integrator applies accepted patches to the research repository by hand; build on the served file plus this patch until then","decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}