{
  "status": "passed",
  "checks": {
    "fresh_full_sector_strict_positive_internal_certificate": true,
    "new_action_uses_actual_generators_not_a_scalar_offset": true,
    "positive_mass_shell_and_rest_limit_exact_at_20_rational_cases": true,
    "one_dimensional_boost_commutator_coefficient_identity": true,
    "zero_threshold_far_field_trials_rule_out_positive_full_gap": true,
    "zero_source_action_and_small_action_limits_are_not_hidden": true
  },
  "conditional_result": {
    "internal_rest_gap_model_units": {
      "lower": "13019412352006053/70368744177664000",
      "upper": "52077649408024711/281474976710656000",
      "approximate": 0.1850169774116653
    },
    "center_of_mass_law": "H_cm = sqrt(c^2 |P|^2 + epsilon^2 H_internal^2)",
    "rest_energy_interval": "epsilon * (lower, upper), with epsilon>0",
    "invariant_mass_interval": "epsilon * (lower, upper) / c^2, with c>0",
    "energy_zero": "Adjoin a separate empty vacuum sector with energy 0; no scalar shift of the occupied Hamiltonian.",
    "spectral_argument": "H_internal >= lower>0. Functional calculus gives H_cm^2-c^2|P|^2=epsilon^2 H_internal^2. On the lowest bound-state branch, P=0 gives positive rest energy epsilon*E0.",
    "boost_scope": "For one translation dimension, B=i*hbar/c^2*(H*d/dp+Hprime/2); [B,P]=i*hbar*H/c^2 and [B,H]=i*hbar*P. This does not establish a neutron spin representation or source-derived Lorentz symmetry."
  },
  "exact_mass_shell_cases": [
    {
      "c": "1",
      "energy_unit": "1",
      "momentum": "-312465896448146769/492581209243648000",
      "energy": "104155298816048923/157625986957967360",
      "rest_energy": "104155298816048923/562949953421312000"
    },
    {
      "c": "1",
      "energy_unit": "1",
      "momentum": "-312465896448146769/2251799813685248000",
      "energy": "104155298816048923/450359962737049600",
      "rest_energy": "104155298816048923/562949953421312000"
    },
    {
      "c": "1",
      "energy_unit": "1",
      "momentum": "0",
      "energy": "104155298816048923/562949953421312000",
      "rest_energy": "104155298816048923/562949953421312000"
    },
    {
      "c": "1",
      "energy_unit": "1",
      "momentum": "312465896448146769/2251799813685248000",
      "energy": "104155298816048923/450359962737049600",
      "rest_energy": "104155298816048923/562949953421312000"
    },
    {
      "c": "1",
      "energy_unit": "1",
      "momentum": "312465896448146769/492581209243648000",
      "energy": "104155298816048923/157625986957967360",
      "rest_energy": "104155298816048923/562949953421312000"
    },
    {
      "c": "1",
      "energy_unit": "7/3",
      "momentum": "-104155298816048923/70368744177664000",
      "energy": "104155298816048923/67553994410557440",
      "rest_energy": "729087091712342461/1688849860263936000"
    },
    {
      "c": "1",
      "energy_unit": "7/3",
      "momentum": "-729087091712342461/2251799813685248000",
      "energy": "729087091712342461/1351079888211148800",
      "rest_energy": "729087091712342461/1688849860263936000"
    },
    {
      "c": "1",
      "energy_unit": "7/3",
      "momentum": "0",
      "energy": "729087091712342461/1688849860263936000",
      "rest_energy": "729087091712342461/1688849860263936000"
    },
    {
      "c": "1",
      "energy_unit": "7/3",
      "momentum": "729087091712342461/2251799813685248000",
      "energy": "729087091712342461/1351079888211148800",
      "rest_energy": "729087091712342461/1688849860263936000"
    },
    {
      "c": "1",
      "energy_unit": "7/3",
      "momentum": "104155298816048923/70368744177664000",
      "energy": "104155298816048923/67553994410557440",
      "rest_energy": "729087091712342461/1688849860263936000"
    },
    {
      "c": "3/2",
      "energy_unit": "1",
      "momentum": "-104155298816048923/246290604621824000",
      "energy": "104155298816048923/157625986957967360",
      "rest_energy": "104155298816048923/562949953421312000"
    },
    {
      "c": "3/2",
      "energy_unit": "1",
      "momentum": "-104155298816048923/1125899906842624000",
      "energy": "104155298816048923/450359962737049600",
      "rest_energy": "104155298816048923/562949953421312000"
    },
    {
      "c": "3/2",
      "energy_unit": "1",
      "momentum": "0",
      "energy": "104155298816048923/562949953421312000",
      "rest_energy": "104155298816048923/562949953421312000"
    },
    {
      "c": "3/2",
      "energy_unit": "1",
      "momentum": "104155298816048923/1125899906842624000",
      "energy": "104155298816048923/450359962737049600",
      "rest_energy": "104155298816048923/562949953421312000"
    },
    {
      "c": "3/2",
      "energy_unit": "1",
      "momentum": "104155298816048923/246290604621824000",
      "energy": "104155298816048923/157625986957967360",
      "rest_energy": "104155298816048923/562949953421312000"
    },
    {
      "c": "3/2",
      "energy_unit": "7/3",
      "momentum": "-104155298816048923/105553116266496000",
      "energy": "104155298816048923/67553994410557440",
      "rest_energy": "729087091712342461/1688849860263936000"
    },
    {
      "c": "3/2",
      "energy_unit": "7/3",
      "momentum": "-729087091712342461/3377699720527872000",
      "energy": "729087091712342461/1351079888211148800",
      "rest_energy": "729087091712342461/1688849860263936000"
    },
    {
      "c": "3/2",
      "energy_unit": "7/3",
      "momentum": "0",
      "energy": "729087091712342461/1688849860263936000",
      "rest_energy": "729087091712342461/1688849860263936000"
    },
    {
      "c": "3/2",
      "energy_unit": "7/3",
      "momentum": "729087091712342461/3377699720527872000",
      "energy": "729087091712342461/1351079888211148800",
      "rest_energy": "729087091712342461/1688849860263936000"
    },
    {
      "c": "3/2",
      "energy_unit": "7/3",
      "momentum": "104155298816048923/105553116266496000",
      "energy": "104155298816048923/67553994410557440",
      "rest_energy": "729087091712342461/1688849860263936000"
    }
  ],
  "zero_threshold_trial_packets": [
    {
      "length": 10,
      "zero_threshold_energy_upper_bound": "121/1225"
    },
    {
      "length": 100,
      "zero_threshold_energy_upper_bound": "121/122500"
    },
    {
      "length": 1000,
      "zero_threshold_energy_upper_bound": "121/12250000"
    },
    {
      "length": 10000,
      "zero_threshold_energy_upper_bound": "121/1225000000"
    },
    {
      "length": 100000,
      "zero_threshold_energy_upper_bound": "121/122500000000"
    },
    {
      "length": 1000000,
      "zero_threshold_energy_upper_bound": "121/12250000000000"
    }
  ],
  "small_beta_trial": {
    "beta": "1/100000000",
    "energy_upper_bound": "7383/1464100000000"
  },
  "assumption_ledger": [
    {
      "input": "Stationary source action beta*(sum P)/3",
      "status": "new law; not implied by time-ordered source pulses"
    },
    {
      "input": "beta=1",
      "status": "fixture value, not source-selected"
    },
    {
      "input": "lead threshold Delta=1/2",
      "status": "supplied; essential for full-sector positivity"
    },
    {
      "input": "eta=2, ell=1, kappa=1",
      "status": "supplied autonomous contact fixture"
    },
    {
      "input": "relativistic center-of-mass functional calculus",
      "status": "additional kinematic completion, not derived from source records"
    },
    {
      "input": "physical energy unit epsilon",
      "status": "unselected; no MeV value inferred"
    },
    {
      "input": "identify lowest branch as physical neutron",
      "status": "not established by these algebraic records"
    }
  ],
  "conclusion": "Positive invariant rest energy is established for the explicitly completed model. Physical neutron rest energy is not derived from the available source data alone.",
  "identifiability": "Removing either the stationary source action or the positive lead threshold defeats the full-sector strict gap. Both zero-gap and positive-gap laws fit the existing carrier and pulse matrices; those matrices alone do not select the rest law.",
  "source_hashes": {
    "research/strominger/results/neutron-source-action-rest-gap.json": "de65118f465d000e3ceb16bc8a62d4a91ffd969765029f404bfb32877f4c4bc5",
    "research/strominger/results/neutron-positive-gap-certificate.json": "44862c5cd6d05ced5143674f97f0d16ca52df09c60a476bcdf6d5cdcb0bf6a4b",
    "research/strominger/results/neutron-seam-control-transport.json": "d650bfba4b535084deacff9be15878d898bd4008ae565524785326879797462a",
    "research/strominger/checkers/check_neutron_rest_energy_completion.py": "4881b6d1c313ad4c66bbdc6022c5deb8e50def63f2361d0d3270f8f707be516f",
    "research/strominger/checkers/check_neutron_positive_gap_certificate.py": "3d0bb77fc7079965e154f5021d9557aa46bab4b8cd286be13029a9c73ab0dca0"
  }
}