{
  "visual_id": "E57-isotropic-domains",
  "title": "Spatial covariance from isotropic expanding-shell noise",
  "classification": "scoped_public_input_calculation",
  "run_ids": [
    "20261002T051103348444Z-E21-isotropic-domains"
  ],
  "claim_ids": [
    "C05",
    "C08"
  ],
  "input_files": [
    {
      "path": "runs/20261002T051103348444Z-E21-isotropic-domains/free-covariance.npz",
      "sha256": "64c38e67f3b8a10b21ba6937091d84be86259f4ed6349c7b5153914e21438382"
    },
    {
      "path": "runs/20261002T051103348444Z-E21-isotropic-domains/OU-covariance.npz",
      "sha256": "9ec875e2c54d68feb2cfff41d9ba551f374fea05f91c9d2f2ff15bce3cef0519"
    },
    {
      "path": "runs/20261002T051103348444Z-E21-isotropic-domains/nonlinear-spatial-histories.npz",
      "sha256": "a9ff70b1a458e7b456729dfa4ea8739efbcfbb97891a29556d52000a6f988ba2"
    },
    {
      "path": "runs/20261002T051103348444Z-E21-isotropic-domains/results.json",
      "sha256": "8f7f79242fe4951d4cfb66b391b3be4835f1547af6c5a03183db45b7a2bc3de8"
    }
  ],
  "configurations": {
    "E21-isotropic-domains": {
      "completed_component": "Isotropic expanding Fourier-shell Gaussian noise and finite-time spatial spectator Langevin controls on declared nonperiodic sample points",
      "remaining": [
        "Physical formation and reheating history",
        "Gradient-resolved domain wall dynamics, coarsening, collisions and radiation",
        "Matter and gravitational backreaction",
        "Same allowed field-to-matter parameters, environmental survival and observer-conditioned population"
      ],
      "predecessor": "20260927T155438746257Z-E21-stochastic",
      "source_equations": "Starobinsky-Yokoyama astro-ph/9407016 Eqs9-12; E21-stochastic frozen PDF",
      "k0": 0.1,
      "duration": 3.0,
      "sample_halfwidth": 2.0,
      "sample_axis_points": 5,
      "shell_polar_orders": [
        8,
        16,
        24
      ],
      "shell_times": [
        0.0,
        0.5,
        1.0,
        2.0,
        3.0
      ],
      "covariance_probe_indices": [
        0,
        4,
        12,
        20,
        24,
        31,
        50,
        62,
        74,
        93,
        100,
        112,
        124
      ],
      "benchmark_seed": 2026100229,
      "production_seed": 2026100329,
      "noise_trials": 8192,
      "noise_chunk": 512,
      "realizations": 512,
      "fine_time_step": 0.01,
      "time_step_ratios": [
        1,
        2,
        4
      ],
      "OU_relaxation": 0.06,
      "initial_width": 0.08,
      "nonlinear_cases": [
        {
          "initial_center": 0.0,
          "tilt": 0.0
        },
        {
          "initial_center": 3.0,
          "tilt": 0.0
        },
        {
          "initial_center": 0.0,
          "tilt": 0.003
        },
        {
          "initial_center": 3.0,
          "tilt": 0.003
        }
      ],
      "FP_grids": [
        401,
        801
      ],
      "save_times": [
        0.4,
        1.0,
        2.0,
        3.0
      ],
      "gates": {
        "normalization_abs": 2e-13,
        "shell_covariance_abs": 1e-10,
        "statistical_z": 6.0,
        "time_covariance_abs": 1e-05,
        "time_refinement_ratio": 0.75,
        "nonlinear_time_absolute": 0.01,
        "FP_grid_absolute": 0.003,
        "FP_KS": 0.1
      },
      "resources": {
        "whole_job_timeout_seconds": 600,
        "maximum_RSS_bytes": 3221225472,
        "threads": 1,
        "maximum_jobs": 4
      },
      "benchmark_only": false,
      "benchmark_parent": "20261002T051027557748Z-E21-isotropic-noise-benchmark"
    }
  },
  "assumptions": {
    "E21-isotropic-domains": [
      "Primary Eq11 fixes temporal white noise and the expanding comoving shell k0 exp(N). Weighted real Fourier plane waves approximate the angular integral with deterministic covariance controls.",
      "Finite nonperiodic sample points, not a spatial PDE mesh or periodic FFT box. No fictitious spatial-grid/box convergence is asserted.",
      "All physical constants H=1, epsilon=.1, potential, initial coherent Gaussian draw and three-efold duration are declared conditional choices. Initial and finite-time sign fractions are not cosmological formation probabilities.",
      "Gaussian covariance has positive semidefinite factorization B B^T by construction. No eigenvalue clipping, jitter, realization normalization or spatial demeaning is used.",
      "Continuum shell angular error, midpoint temporal covariance error, coupled drift time error and Monte Carlo sampling uncertainty are recorded separately. No backreaction, reheating or wall survival."
    ]
  },
  "plotted_values": {
    "path": "E57-isotropic-domains-data.json",
    "sha256": "d0e6a0f3b8074a9da46feb8865c9466067af264388fe6137833144b0fc39197d"
  },
  "caption": "The source separate-patch Langevin equation has temporally independent noise with sinc(k r) spatial covariance and expanding comoving shell. Angular quadrature and timestep errors are controlled separately from sampling uncertainty.125 nonperiodic positions are correlated observations of512 independent realizations. The shaded pointwise two-standard-error bands use Gaussian covariance sampling variance (Cii Cjj+Cij\u00b2)/512; they are not simultaneous confidence regions or independent spatial errors. Free and linear-drift covariance have independent integral solutions; nonlinear one-point distributions also pass separate probability-equation controls. No wall dynamics, reheating, matter matching or physical domain abundance is supplied.",
  "alt_text": "Measured free and linear-drift covariance follow the analytic decrease with separation, with finite-ensemble scatter.",
  "generator": "src/metastable/public_report.py",
  "generator_sha256": "9e263878b7237d781a41d94693004412279b5cfa808ccd6e335b7b07269910d4",
  "generator_dependencies_sha256": {
    "src/metastable/render.py": "ff4837be5102588b6614aeb2b7880b10c0a0c20a155e2eb7b409014a47a3de01",
    "src/metastable/spin_report.py": "dd5c64c5c658938948672a7dc767aa02c34dde012c3fc4aedfc3642f88796847",
    "src/metastable/continuation_report.py": "f9bbce6d0e201a9f55c826d6e9c47ab901e51a71b4a1f962b52eb08a63ba5fe9",
    "src/metastable/refinement_report.py": "4539c0ec814603105ab3a2b5cc82ce291c0151113b5bd3916cdc235aadb9bfb0",
    "src/metastable/atomic_mass_report.py": "46dd1cdb56a5a02cafe001a1f6a7fb201e149461850df41e012f77a580c3694b",
    "src/metastable/closure_report.py": "b34a03a9e0058eed65722df542dbb92691dd138787e2078b43ee9f18e221f75c",
    "src/metastable/october_report.py": "f93e7f89e43165d8d25e2184b9b32e6e21c3e1ffe66020d35944f263aaecb726",
    "src/metastable/october_followup_report.py": "925d905ff3bddf97a7ace2f68a4a28e7dfea2238c4f81d891dda2a9e70c6d4f6",
    "src/metastable/october_dynamics_report.py": "6b8d84c0ce0d78f52d064c68697f0d9c885cdc736e215b54eba46821dbe59a33",
    "src/metastable/october_calibration_report.py": "f714ef7ccfaa26e847c6135054f53528b3ff1d7096e7d113cffeea333e77e3d2",
    "src/metastable/october_interface_report.py": "2fc8826a33c952d7898154f84830748c26842c9a165d14aa7b7fb9721fac00bd",
    "src/metastable/october_checkpoint8_report.py": "f3b54f23510b9bfeffc5ff04e6df54e967228f43ba25a15e12e34f898cdfe0af",
    "src/metastable/october_checkpoint9_report.py": "4bd987aac59964ccb4768a95e0cb6f7d1fdccbeffe9483860da7b431f2224ae4",
    "src/metastable/october_checkpoint10_report.py": "9da673d773b63298e041914447ffd97065c1cf2b8966c90fc4ebcbee25a0ed63",
    "src/metastable/october_checkpoint11_report.py": "5f01064f02f4c76d0059d348a763b285c92c3677e6cb0ba0bbf7faa1a4b98248",
    "src/metastable/october_checkpoint12_report.py": "46022030652e3a1e274dfd27b36dfab25d90a97fde439b1da44d6f1fdc5140b5",
    "src/metastable/october_checkpoint13_report.py": "997c59be3af1b6b7be95fd4314e0f3b98c562629901a639572284045a65980c2",
    "src/metastable/october_checkpoint14_report.py": "d84de7d8516d8a4d8e21b5f9f279476f3035f719c1c8ab03b7ac1e44bf822240",
    "src/metastable/october_checkpoint15_report.py": "1f6e17b9549dc31fbb58ba578c4d8ed8e219b4ad30810df0a9d7d2d00e63efdc",
    "src/metastable/october_checkpoint16_report.py": "74cb8aac45d1d5ce0e6eb6678e9b6cdf98cd46fd6e264a513b612ab763fcd034",
    "src/metastable/october_checkpoint17_report.py": "9daceb74e91f6f8db0f7d89929226d46c464c284d06d0694f525fecf0c736bf6",
    "src/metastable/october_checkpoint18_report.py": "f33f88e316cae93af87cef75d8df41ce82970c8f8bc466dd7a094a92c5f00f8b",
    "src/metastable/october_checkpoint19_report.py": "ce2250507145354b6478cafaaff98c2b8ae2795c3c309f0d903a920365a77090",
    "src/metastable/october_checkpoint20_report.py": "e2ea0a8a374036254008cf6de8f10352dfb2585c4ccb18c1e850c017e6128294",
    "src/metastable/october_checkpoint21_report.py": "596b873676167227b2c92d358fcdbc0614908a5a9daad1da6227b81fce203eec",
    "src/metastable/publication_files.py": "e68bd0ee4e849a72fa828f0cfcf34cb6b1b9f2a8bbdbb3d51085054915039607"
  },
  "command": "python run.py full public-report",
  "output_sha256": {
    "svg": "a5a4fa1e2a711f638ac397b84afccc9a8eba59ba8beab6f1beb64c6f8a70eeb9",
    "png": "29df6d87183adb344dbab9bfe20e32d5595153b6328c8388bde4cb7123c16b49"
  }
}