{
  "visual_id": "E09-virial",
  "title": "A binding threshold does not force a dilute-gas phase jump",
  "classification": "scoped_public_input_calculation",
  "run_ids": [
    "20260929T201314827757Z-E35-virial"
  ],
  "claim_ids": [
    "C02",
    "C06"
  ],
  "input_files": [
    {
      "path": "runs/20260929T201314827757Z-E35-virial/dilute-gas-equation-of-state.csv",
      "sha256": "22e66457709ffb22f63949b99da51d6445cde69a702b9ac2327b90bdbcf1fce1"
    }
  ],
  "configurations": {
    "E35-virial": {}
  },
  "assumptions": {
    "E35-virial": [
      "Horowitz--Schwenk virial thermodynamics, restricted here to low-energy neutral singlet S waves with a shallow ERE branch.",
      "Include both bound states and continuum phase-shift derivative. At unitarity the half-bound-state limit is explicit.",
      "Zero-range result is checked against the analytic error-function answer on both sides of the binding threshold.",
      "Finite-range integrals are restricted below 6 MeV, checked against a 4 MeV cutoff, and restricted to kappa*r<0.5.",
      "EOS values are labelled usable only for z<=0.01 and |2*b2*z|<0.1. This is a second-order truncation criterion, not a rigorous bound on an unknown b3.",
      "This dilute phase can illustrate continuity through a two-body threshold, but cannot locate the alpha-gas/nuclear-liquid transition."
    ]
  },
  "plotted_values": {
    "path": "E09-virial-data.json",
    "sha256": "18aad6628c9fdffe837007700836d3794b603d828b767003aa4fc95181a64c56"
  },
  "caption": "Beth\u2013Uhlenbeck includes the physical shallow bound pole and scattering continuum, with an explicit half-bound threshold limit. The zero-range analytic result and energy-cutoff controls agree. The displayed EOS keeps only rows satisfying the stated small-second-virial correction criterion; that criterion is not a measured third-virial error. Positive compressibility in this dilute domain is not a dense alpha-gas/liquid calculation or a statement about nucleation.",
  "alt_text": "The virial coefficient crosses the binding threshold continuously. Compressibility stays positive within the retained dilute approximation.",
  "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": "0c31eaf9630c7cd0419992416680f0d2b48046f4ec1140ac43242dd21e27f5d1",
    "png": "1d60874f27f42ad0b986be640c490da3a6c4ba37207806c434b8f631218a6f7c"
  }
}