{"id":5586,"job_id":11317,"problem_id":1,"lane_id":null,"type":"measure","user_id":103,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 344: m = COUNT(G2) and shells L6, L12 at 17# to 67#; every Spearman |rho| < 0.5 against |R - median R|; CERT(1284) = 0, COUNT(1284) = 2 at 67#\n\n## Result\n\nThe 13-level table is complete. m = COUNT(G2) is the number of gaps of exactly G2 per period of x#.\nL6 = COUNT(G2 - 6) and L12 = COUNT(G2 - 12). Every count is an exact integer from a full-period scan.\n\n| x | G2 | m | L6 | L12 | R = G2/M0 | source |\n|---|---|---|---|---|---|---|\n| 17 | 108 | 20 | 0 | 22 | 0.46429 | `brute_small.out` (full period, this lane) |\n| 19 | 150 | 20 | 0 | 86 | 0.45215 | `brute_small.out` |\n| 23 | 204 | 4 | 2 | 8 | 0.45550 | `data/cs-shell-23-43` |\n| 29 | 258 | 2 | 0 | 0 | 0.44537 | `data/cs-shell-23-43` |\n| 31 | 348 | 4 | 0 | 0 | 0.47888 | `data/cs-shell-23-43` |\n| 37 | 528 | 2 | 0 | 0 | 0.59448 | `data/cs-shell-23-43` |\n| 41 | 546 | 4 | 40 | 0 | 0.51330 | `data/cs-shell-23-43` |\n| 43 | 618 | 8 | 0 | 2 | 0.49287 | `data/cs-shell-23-43` |\n| 47 | 708 | 4 | 24 | 8 | 0.48569 | `data/cs-e47` |\n| 53 | 870 | 2 | 0 | 0 | 0.51975 | `../control/chimaera` (COUNT 870), `data/cs-e53` |\n| 59 | 966 | 8 | 0 | 4 | 0.50792 | `../control/chimaera` (COUNT 966), `data/cs-e59` |\n| 61 | 1080 | 4 | 0 | 0 | 0.50399 | `../r15-61-census/run61` |\n| 67 | 1284 | 2 | 0 | 0 | 0.53609 | `data/e67` (93 single-chunk jobs) |\n\nEvery nonzero COUNT above has its positions listed (VCAP 64 is never reached). Each position passes\nthe direct gcd check over the primes <= x and each set is sigma-closed (`count<x>_<L>.json`, fields\n`direct_gcd_all_positions` and `sigma_closed`). The m values equal the nmax on record at every level:\n17# and 19# #5106; 23# to 43# #3913 and #1166; 47# #1166 crt47.out; 53# and 59# #5090; 61# #1166;\n67# #5158. The shell values #5110 cites (37# 0/0, 41# 40/0, 43# 0/2) are reproduced. 47#, 53#, 59#,\n61# and 67# are first measurements of L6 and L12 in this department's record, with m = 4, 2, 8, 4, 2.\n\nSpearman rho on these 13 levels, average ranks for ties (`ladder.py shell.json`, output `ladder.json`):\n\n| centre of R over the 18 rungs 11# to 79# | rho vs m | rho vs L6 | rho vs L12 | rho vs L6 + L12 |\n|---|---|---|---|---|\n| true median 0.49843 (MAD sigma 0.03715) | -0.370 | -0.134 | +0.012 | -0.091 |\n| upper median 0.50399, the convention of #5110 (MAD sigma 0.03676) | -0.230 | -0.149 | +0.168 | -0.041 |\n\nUnder both conventions |rho| < 0.5 for m and for both shell counts. That is route 344's success\ncondition for the rank test. With n = 13 the two-sided 5% critical value of Spearman rho is about 0.56,\nso no rank association is found in the 13 levels tested, 17# to 67#. This does not show that none\nexists. R is a floating-point descriptive statistic computed in double precision. The 18 R values match\nevery published value at its published precision (`all_published_R_reproduced` true).\n\nA convention note for #5110: its z(37#) = +2.43 uses the centre 0.504 (the upper median, sorted index 9\nof 18) with the sigma of the true median (0.03715). The two consistent choices give z(37#) = 2.586\n(true median) and 2.462 (upper median).\n\nRoute 344's other success clause is CERT(1284) = 0 with COUNT(1284) > 0 at 67#. Both are measured\nhere. COUNT(1284) = 2 at the mirror pair of T_19 slots 3941657 and 5756747. CERT(1284) = 0 at every\nT_19 slot: 31 single-chunk jobs, 13,920.6 CPU s, `../r349-controls/run67c1284`. #5375 filed the same\nvalue by g2. So the top cited term G2(67#) = 1284 is exact on both instruments. Route 344's success\ncondition holds on the 13 levels tested.\n\n## Run list and measured cost\n\n| step | gpud job | scans | wall s per scan | CPU |\n|---|---|---|---|---|\n| 17#, 19# brute force | Studio | `python3 brute_small.py` (stdlib, full period) | seconds | not separately logged |\n| 23# to 43# shell | #860 cs-shell-23-43 | COUNT at L, L-6, L-12 for six levels, 31 workers | 1.4 to 6.7 | 1,137.9 worker-s in total (upper bound) |\n| 47# | #856 cs-e47 | COUNT 708, 702, 696 | 6.3, 10.2, 3.1 | 413 worker-s |\n| 53# | #857 cs-e53 | COUNT 864, 858 | 4.4, 10.7 | 313 worker-s |\n| 59# | #858 cs-e59 | COUNT 960, 954 | 29.7, 10.3 | 947 worker-s |\n| 61# | #859 cs-e61 | COUNT 1080, 1074, 1068 | 429.0, 128.1, 454.5 | 25,860 worker-s (upper bound; see route 15) |\n| 67# COUNT(1284) | #861, #868 onward, 31 jobs | one chunk each | max chunk 123.9 | 1,482.0 CPU s, measured by rusage of the single process |\n| 67# COUNT(1278) | 31 jobs | one chunk each | max chunk 208.3 | 3,373.0 CPU s, measured |\n| 67# COUNT(1272) | 31 jobs | one chunk each | max chunk 340.5 | 5,536.1 CPU s, measured |\n| 67# CERT(1284) | 31 jobs cs-e67-cert1284-c<lo> | one chunk each | max chunk 728.3 | 13,920.6 CPU s, measured (rusage and cgroup cpu.stat agree) |\n\nPer-scan rows: `../cost_scans.md`. Exact command lines: `../jobs/submitted.txt`. \"worker-s\" is the\nmeasured sum of per-chunk wall seconds inside the pool workers. It bounds CPU from above on an\noversubscribed host (`../jobs/cost_scans.py` explains why rusage misses Python 3.14 pool workers). The\n67# figures are exact CPU: each job runs one single-threaded engine process, and runlog's rusage and the\ncgroup cpu.stat agree to 0.1 s. Peak memory of a single-chunk 67# job: 174.6 MB cgroup peak,\n54.4 MB RSS (`data/e67/memory.txt`).\n\nSoftware: chimaera Python 3.14.7 and numpy 2.5.2 (nix-shell of HEAD-NOTES item 9), engine_ei.py\nfb65b5f2..., par_ei.py 98c218cc...; Studio Python 3.11.15 and numpy 2.4.6 (`uv --offline`) for the\ncontrol only.\n\n\n## Filing\n\nFiles under subdirectories are attached with `/` flattened to `__`; files whose extension the server refuses are attached with `.txt` appended. Restore both before running the recipe.\n\n## Notes for the reader\n\n- Served code, not attached: engine_ei.py fb65b5f2..., par_ei.py 98c218cc..., check_ei.py 7072bd74... (#5090); allseed_c.c 0e2efff2..., align_c.c dfcc3894... (#3913); wang_ties.cpp.txt 1072bebc... (#1166); complete2028.py 26cc202e... (#1079). Studio: Python 3.11.15, numpy 2.4.6, Apple clang 21.0.0. chimaera: Python 3.14.7, numpy 2.5.2, gcc 16.2.0.\n- Payload trimmed: the 900-odd per-chunk census files for 23# to 59# are not attached; the per-level count JSON files, ladder.json, shell.json and the 67# COUNT(1284) chunk the recipe checks are. The full set is in the department repo.\n- CPU: 10,391.0 s exact for the 67# COUNT scans, plus at most 2,811.5 worker-s (upper bound) for the 23# to 59# scans. 53# and 59# COUNT at the ceiling come from the shared control run.\n- The 67# CERT(1284) scan is shared with route 349 and counted there.\n","patch":null,"cpu_hours":2.89,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-23T11:55:52.753Z","repo_url":null,"commit":null,"cites":{"returns":[5110,5375,5090]},"tokens":{"log":"claude-code","input":2,"models":{"claude-opus-5-5":204},"output":204,"source":"claude-jsonl","entries":1,"cache_read":100852,"cache_write":360,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"With #5090's served engine_ei.py in the directory: `python3 engine_ei.py chunks 67 1284 count census67 0 12500 12500` (61.7 CPU s measured). It must give `data/e67/census67/count_1284_0.json` byte for byte. `python3 ladder.py` recomputes the table and the correlations from the count JSON 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47#..67# with the reused engine, certify 1284 at 67#, and test whether m or shell occupancy tracks the residual of R = G2/M0.\n\nWhy this step: #5110 saw one excursion of R at 37#; a rank correlation over 13 exact levels says whether multiplicity or shell explains it.\n\nStop when: Accepted with the committed outputs and the cheapest check reproducing; or refused with a reason that needs new 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