{
  "visual_id": "E35-thermal-pairing",
  "title": "All tested normal states resist infinitesimal anomalous pairing",
  "classification": "scoped_public_input_calculation",
  "run_ids": [
    "20260930T213334223420Z-E35-thermal-pairing"
  ],
  "claim_ids": [
    "C02",
    "C06"
  ],
  "input_files": [
    {
      "path": "runs/20260930T213334223420Z-E35-thermal-pairing/anomalous-curvatures.csv",
      "sha256": "fd573bd6438d7d71fd8f2fcccb8744e25315f0495a50a91ccd8204278627cd52"
    },
    {
      "path": "runs/20260930T213334223420Z-E35-thermal-pairing/results.json",
      "sha256": "b752db79c8ce5d14e86179bccf9adf8cc7a4eb5088c0149500a457b86336d68f"
    }
  ],
  "configurations": {
    "E35-thermal-pairing": {
      "parents": [
        "20260930T010050322377Z-E35-lattice-HF",
        "20260930T020233243143Z-E35-HF-unrestricted",
        "20260930T210235602482Z-E35-thermal-density"
      ],
      "channels": [
        "pp",
        "nn",
        "np"
      ],
      "selected_normal_roots": 32,
      "eigensolver_tolerance": 2e-09,
      "finite_difference_step": 0.001
    }
  },
  "assumptions": {
    "E35-thermal-pairing": [
      "Use the unchanged finite-range A/B Hamiltonian. Read Vbar_abcd from complete frozen charge-field contraction K_ac,db, and independently reconstruct pair operators from pinned source terms.",
      "Audit every complex antisymmetric pp/nn and complex np pair amplitude, including both spins and every lattice orbital. No fitted pairing strength or pairing cutoff is introduced.",
      "At kappa=0 normal and anomalous Hessian sectors decouple by charge symmetry. chi_pair=(1-fi-fj)/(xi_i+xi_j); use its positive degenerate limit. I+sqrt(chi_pair)Vpair sqrt(chi_pair) is a congruence, not a dynamical frequency.",
      "Anomalous first variations preserve mean charges. Curvature of Omega along the positive BdG Fermi path removes its second-order charge drift. Independent two-multiplier constrained paths verify fixed-mean-charge Helmholtz curvature.",
      "The ensemble fixes only mean proton/neutron counts; anomalous quasifree states do not have exact charge numbers. Finite-box local stability is not a canonical pairing transition or thermodynamic phase boundary.",
      "At a normal state kappa=0 the gauge orbit is a point: no spurious Goldstone zero mode should be removed. Any paired continuation requires its own gauge and coupled normal/anomalous stability controls."
    ]
  },
  "plotted_values": {
    "path": "E35-thermal-pairing-data.json",
    "sha256": "6b8e199c7ae9386a8ab9e9c94fe47a1b38a2aa4686992903f3add26cb2330c35"
  },
  "caption": "All 96 complete complex pp, nn and np pair-block audits of 32 selected normal states have positive entropy-weighted curvature. The coincident pp/nn results follow the charge-symmetric strong Hamiltonian; electromagnetic pp repulsion is not added. Solid and dashed curves connect the two separately fixed mean fillings across sampled temperatures; they do not locate a critical temperature. Curvature is dimensionless, not an excitation energy, rate or physical uncertainty. Independent finite Fock-space entropy/Wick controls and fixed-mean-charge BdG paths validate the normalization and constraints. Positive local curvature excludes an infinitesimal anomalous instability at these roots only: disconnected finite-amplitude paired minima, colder pairing, proton\u2013neutron coherent normal densities, number projection, beyond-quasifree correlations and thermodynamic limits remain open. No paired state or phase transition is claimed.",
  "alt_text": "For both interactions and both finite boxes, all pp, nn and np anomalous curvatures stay above zero at temperatures from 4 to 16 MeV. The softest value is about 0.152. Coincident pp and nn curves reflect charge symmetry, while np pairing fluctuations are softer.",
  "generator": "src/metastable/public_report.py",
  "generator_sha256": "9e263878b7237d781a41d94693004412279b5cfa808ccd6e335b7b07269910d4",
  "generator_dependencies_sha256": {
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    "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": "75ae2e560d376db422930b82044df57022f1b0d5c3f3c8571f5f2b7fb7950162",
    "png": "f42a8fe19856e70810873f859fc16dcda2dab62a7e22a6069d369d392ae19ad1"
  }
}