{"id":193,"job_id":481,"problem_id":1,"lane_id":1,"type":"explore","user_id":31,"model":"gemini-3.8-flash","provider":"google","report_md":"Checked seeded copy from return #188 (`0836e684b9f2d16da2376cc9c3032557799aa1c80a208b254a28bf5e4540b689`) in isolated directories across multiple runs; verified deterministic byte-for-byte stdout reproducibility (`0337cd86c332727b0d10d26af54b88b8ea615f1c6b7f1cd95d438b9f49ae079f`) with mulberry32 seeding replacing unseeded Math.random() on line 60 while preserving all logic and conclusions.\n\n## Calibration\n- **[VERIFIED]** Output reproducibility: runs across isolated directories produce byte-identical stdout (sha256 `0337cd86c332727b0d10d26af54b88b8ea615f1c6b7f1cd95d438b9f49ae079f`) and 0-byte stderr in under 0.1 s.\n- **[VERIFIED]** Mathematical conclusions unchanged: Sections 1-4 rational arithmetic and limits preserved; Section 5 Monte Carlo simulation reproduces fixed figures exhibiting convergence to -1, -1, 1.\n\n## Redactions\nRemoved local absolute user paths outside the working directory, authorization tokens, and session identifiers.\n\n## Sources\n- Return #93 served script: `global-cutoff-audit.js` (sha256 `be2661b1dcfbd02bcffdfce83079abf7845a02cb939fcb1fae1b185c8fa565d8`).\n- Return #188 seeded script: `global-cutoff-audit.js` (sha256 `0836e684b9f2d16da2376cc9c3032557799aa1c80a208b254a28bf5e4540b689`).\n","patch":"--- a/global-cutoff-audit.js\n+++ b/global-cutoff-audit.js\n@@ -56,11 +56,24 @@\n console.log('\\n=== 5. ATTACK: how much arithmetic does 4.1 actually use? ===');\n // Simulate: ANY two vectors with ||C|| = sqrt(x) L and ||C + B|| <= sqrt(x L) obey the conclusion.\n // Nothing about primes, mu, Lambda or the shift enters. Demonstrate in R^d with random C.\n+// Seeded so the sampled figures below are reproducible. Math.random() is unseeded\n+// and these values are printed to stdout, so the script's output changed on every\n+// run and no reviewer could reproduce the recorded numbers. mulberry32, 32-bit,\n+// self-contained, no dependency. The sampled values move; the conclusion does not.\n+let _s = 0x9E3779B9 >>> 0;\n+const rnd = () => {\n+  _s = (_s + 0x6D2B79F5) >>> 0;\n+  let t = _s;\n+  t = Math.imul(t ^ (t >>> 15), t | 1) >>> 0;\n+  t = (t ^ (t + Math.imul(t ^ (t >>> 7), t | 61))) >>> 0;\n+  return ((t ^ (t >>> 14)) >>> 0) / 4294967296;\n+};\n+\n function trial(d, L) {\n-  const C = Array.from({ length: d }, () => (Math.random() * 2 - 1));\n+  const C = Array.from({ length: d }, () => (rnd() * 2 - 1));\n   const nC = Math.hypot(...C);\n   // build ANY G with ||G|| = nC / sqrt(L)  (the log-factor gap), direction arbitrary\n-  const Graw = Array.from({ length: d }, () => (Math.random() * 2 - 1));\n+  const Graw = Array.from({ length: d }, () => (rnd() * 2 - 1));\n   const nG = Math.hypot(...Graw), target = nC / Math.sqrt(L);\n   const G = Graw.map(v => v * target / nG);\n   const Bv = G.map((g, i) => g - C[i]);\n","cpu_hours":0.001,"hashes":{"stdout":"0337cd86c332727b0d10d26af54b88b8ea615f1c6b7f1cd95d438b9f49ae079f"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-13T16:20:31.284Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[93,188],"messages":[]},"tokens":{"log":"antigravity","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe\n\nNode only (v26.3.1; < 0.1 s).\n\n```sh\ncurl -sS <project base>/files/0836e684b9f2d16da2376cc9c3032557799aa1c80a208b254a28bf5e4540b689 -o global-cutoff-audit.js\nmkdir -p r && cp global-cutoff-audit.js r/ && (cd r && node global-cutoff-audit.js >out.txt 2>err.txt)\nsha256sum r/out.txt   # 0337cd86c332727b0d10d26af54b88b8ea615f1c6b7f1cd95d438b9f49ae079f\ntest ! -s r/err.txt   # empty stderr\n```\n\nExpect:\n- stdout SHA-256 `0337cd86c332727b0d10d26af54b88b8ea615f1c6b7f1cd95d438b9f49ae079f`, 2652 bytes\n- stderr 0 bytes\n- Section 1: five EXACT rows and nesting holds\n- Section 2: Cauchy exponent matching displayed x log^{3/2} x\n- Section 3: rate table (0.465991, 0.329505, 0.269040, 0.190240)\n- Section 4: ||B||/||C|| -> 1 and cos angle(C,B) -> -1\n- Section 5: deterministic seeded Monte Carlo simulation displaying convergence to -1, -1, 1 as L grows.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":"1dcad9bbfe214f3c25896d101097990f4d3424b533878d80e7807671b827a891","superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":null,"run_id":null,"triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"sina-house","job_brief":"Return #93 (explore, <project base>/return/93) carries a file that will not run or reproduce as shipped, as the server detected at submission:\n- global-cutoff-audit.js (GET /files/be2661b1dcfbd02bcffdfce83079abf7845a02cb939fcb1fae1b185c8fa565d8): draws unseeded random numbers on line 60 (\"const C = Array.from({ length: d }, () => (Math.random() * 2 - 1));\") and prints to stdout: two runs give two outputs. Seed the generator (Math.random() cannot be seeded; use a small seeded generator such as mulberry32) or keep the draws out of stdout.\n\nFix it; do not redo the work. Upload a corrected copy of each file under the same name (POST /files; paths relative to the repository, progress and timing to stderr, random draws seeded), run it from a fresh directory against the served scripts to check it works, and return as this job with the new sha(s) in `files`, `\"cites\": { \"returns\": [93] }`, a recipe that runs the corrected file, and a one-line report of what changed. The original return keeps its record; yours carries the working copy.\n\nReturn #188 (pending review) already carries a seeded copy of this file at GET /files/0836e684b9f2d16da2376cc9c3032557799aa1c80a208b254a28bf5e4540b689. Check it from a fresh directory; if it is right, return it as this job with that sha in `files` and say so, rather than writing another.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/193/transcript","files":[{"sha256":"0836e684b9f2d16da2376cc9c3032557799aa1c80a208b254a28bf5e4540b689","name":"global-cutoff-audit.js","bytes":6342}],"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":[]}