{
  "schema": "marici.source-gauss-to-coulomb-binding.v1",
  "passed": true,
  "classification": "finite_source_obstruction_and_externally_supplied_nonrelativistic_Coulomb_ground",
  "source_graph_audit": {
    "source_graph_dimensions": [
      12,
      4
    ],
    "selected_graph_kinetics_identified_with_native_spinor": false,
    "electric_bridge_identified_with_coefficient_arrow": false,
    "tests": [
      {
        "attachment": [
          0,
          0
        ],
        "bridge_conductance": "1/2",
        "neutral_pair_electric_energy": [
          [
            "3/5",
            "3/4",
            "3/4",
            "3/4"
          ],
          [
            "63/80",
            "15/16",
            "15/16",
            "15/16"
          ],
          [
            "63/80",
            "15/16",
            "15/16",
            "15/16"
          ],
          [
            "4/5",
            "19/20",
            "19/20",
            "19/20"
          ],
          [
            "59/80",
            "71/80",
            "71/80",
            "71/80"
          ],
          [
            "59/80",
            "71/80",
            "71/80",
            "71/80"
          ],
          [
            "59/80",
            "71/80",
            "71/80",
            "71/80"
          ],
          [
            "63/80",
            "15/16",
            "15/16",
            "15/16"
          ],
          [
            "31/40",
            "37/40",
            "37/40",
            "37/40"
          ],
          [
            "59/80",
            "71/80",
            "71/80",
            "71/80"
          ],
          [
            "63/80",
            "15/16",
            "15/16",
            "15/16"
          ],
          [
            "31/40",
            "37/40",
            "37/40",
            "37/40"
          ]
        ],
        "all_48_Gauss_sources_verified": true,
        "mixed_energy_differences_zero": true
      },
      {
        "attachment": [
          0,
          0
        ],
        "bridge_conductance": "1",
        "neutral_pair_electric_energy": [
          [
            "3/10",
            "9/20",
            "9/20",
            "9/20"
          ],
          [
            "39/80",
            "51/80",
            "51/80",
            "51/80"
          ],
          [
            "39/80",
            "51/80",
            "51/80",
            "51/80"
          ],
          [
            "1/2",
            "13/20",
            "13/20",
            "13/20"
          ],
          [
            "7/16",
            "47/80",
            "47/80",
            "47/80"
          ],
          [
            "7/16",
            "47/80",
            "47/80",
            "47/80"
          ],
          [
            "7/16",
            "47/80",
            "47/80",
            "47/80"
          ],
          [
            "39/80",
            "51/80",
            "51/80",
            "51/80"
          ],
          [
            "19/40",
            "5/8",
            "5/8",
            "5/8"
          ],
          [
            "7/16",
            "47/80",
            "47/80",
            "47/80"
          ],
          [
            "39/80",
            "51/80",
            "51/80",
            "51/80"
          ],
          [
            "19/40",
            "5/8",
            "5/8",
            "5/8"
          ]
        ],
        "all_48_Gauss_sources_verified": true,
        "mixed_energy_differences_zero": true
      },
      {
        "attachment": [
          0,
          0
        ],
        "bridge_conductance": "2",
        "neutral_pair_electric_energy": [
          [
            "3/20",
            "3/10",
            "3/10",
            "3/10"
          ],
          [
            "27/80",
            "39/80",
            "39/80",
            "39/80"
          ],
          [
            "27/80",
            "39/80",
            "39/80",
            "39/80"
          ],
          [
            "7/20",
            "1/2",
            "1/2",
            "1/2"
          ],
          [
            "23/80",
            "7/16",
            "7/16",
            "7/16"
          ],
          [
            "23/80",
            "7/16",
            "7/16",
            "7/16"
          ],
          [
            "23/80",
            "7/16",
            "7/16",
            "7/16"
          ],
          [
            "27/80",
            "39/80",
            "39/80",
            "39/80"
          ],
          [
            "13/40",
            "19/40",
            "19/40",
            "19/40"
          ],
          [
            "23/80",
            "7/16",
            "7/16",
            "7/16"
          ],
          [
            "27/80",
            "39/80",
            "39/80",
            "39/80"
          ],
          [
            "13/40",
            "19/40",
            "19/40",
            "19/40"
          ]
        ],
        "all_48_Gauss_sources_verified": true,
        "mixed_energy_differences_zero": true
      },
      {
        "attachment": [
          11,
          3
        ],
        "bridge_conductance": "1/2",
        "neutral_pair_electric_energy": [
          [
            "37/40",
            "37/40",
            "37/40",
            "31/40"
          ],
          [
            "71/80",
            "71/80",
            "71/80",
            "59/80"
          ],
          [
            "15/16",
            "15/16",
            "15/16",
            "63/80"
          ],
          [
            "37/40",
            "37/40",
            "37/40",
            "31/40"
          ],
          [
            "71/80",
            "71/80",
            "71/80",
            "59/80"
          ],
          [
            "15/16",
            "15/16",
            "15/16",
            "63/80"
          ],
          [
            "15/16",
            "15/16",
            "15/16",
            "63/80"
          ],
          [
            "15/16",
            "15/16",
            "15/16",
            "63/80"
          ],
          [
            "19/20",
            "19/20",
            "19/20",
            "4/5"
          ],
          [
            "71/80",
            "71/80",
            "71/80",
            "59/80"
          ],
          [
            "71/80",
            "71/80",
            "71/80",
            "59/80"
          ],
          [
            "3/4",
            "3/4",
            "3/4",
            "3/5"
          ]
        ],
        "all_48_Gauss_sources_verified": true,
        "mixed_energy_differences_zero": true
      },
      {
        "attachment": [
          11,
          3
        ],
        "bridge_conductance": "1",
        "neutral_pair_electric_energy": [
          [
            "5/8",
            "5/8",
            "5/8",
            "19/40"
          ],
          [
            "47/80",
            "47/80",
            "47/80",
            "7/16"
          ],
          [
            "51/80",
            "51/80",
            "51/80",
            "39/80"
          ],
          [
            "5/8",
            "5/8",
            "5/8",
            "19/40"
          ],
          [
            "47/80",
            "47/80",
            "47/80",
            "7/16"
          ],
          [
            "51/80",
            "51/80",
            "51/80",
            "39/80"
          ],
          [
            "51/80",
            "51/80",
            "51/80",
            "39/80"
          ],
          [
            "51/80",
            "51/80",
            "51/80",
            "39/80"
          ],
          [
            "13/20",
            "13/20",
            "13/20",
            "1/2"
          ],
          [
            "47/80",
            "47/80",
            "47/80",
            "7/16"
          ],
          [
            "47/80",
            "47/80",
            "47/80",
            "7/16"
          ],
          [
            "9/20",
            "9/20",
            "9/20",
            "3/10"
          ]
        ],
        "all_48_Gauss_sources_verified": true,
        "mixed_energy_differences_zero": true
      },
      {
        "attachment": [
          11,
          3
        ],
        "bridge_conductance": "2",
        "neutral_pair_electric_energy": [
          [
            "19/40",
            "19/40",
            "19/40",
            "13/40"
          ],
          [
            "7/16",
            "7/16",
            "7/16",
            "23/80"
          ],
          [
            "39/80",
            "39/80",
            "39/80",
            "27/80"
          ],
          [
            "19/40",
            "19/40",
            "19/40",
            "13/40"
          ],
          [
            "7/16",
            "7/16",
            "7/16",
            "23/80"
          ],
          [
            "39/80",
            "39/80",
            "39/80",
            "27/80"
          ],
          [
            "39/80",
            "39/80",
            "39/80",
            "27/80"
          ],
          [
            "39/80",
            "39/80",
            "39/80",
            "27/80"
          ],
          [
            "1/2",
            "1/2",
            "1/2",
            "7/20"
          ],
          [
            "7/16",
            "7/16",
            "7/16",
            "23/80"
          ],
          [
            "7/16",
            "7/16",
            "7/16",
            "23/80"
          ],
          [
            "3/10",
            "3/10",
            "3/10",
            "3/20"
          ]
        ],
        "all_48_Gauss_sources_verified": true,
        "mixed_energy_differences_zero": true
      },
      {
        "attachment": [
          4,
          2
        ],
        "bridge_conductance": "1/2",
        "neutral_pair_electric_energy": [
          [
            "71/80",
            "71/80",
            "59/80",
            "71/80"
          ],
          [
            "71/80",
            "71/80",
            "59/80",
            "71/80"
          ],
          [
            "19/20",
            "19/20",
            "4/5",
            "19/20"
          ],
          [
            "15/16",
            "15/16",
            "63/80",
            "15/16"
          ],
          [
            "3/4",
            "3/4",
            "3/5",
            "3/4"
          ],
          [
            "15/16",
            "15/16",
            "63/80",
            "15/16"
          ],
          [
            "71/80",
            "71/80",
            "59/80",
            "71/80"
          ],
          [
            "37/40",
            "37/40",
            "31/40",
            "37/40"
          ],
          [
            "15/16",
            "15/16",
            "63/80",
            "15/16"
          ],
          [
            "37/40",
            "37/40",
            "31/40",
            "37/40"
          ],
          [
            "15/16",
            "15/16",
            "63/80",
            "15/16"
          ],
          [
            "71/80",
            "71/80",
            "59/80",
            "71/80"
          ]
        ],
        "all_48_Gauss_sources_verified": true,
        "mixed_energy_differences_zero": true
      },
      {
        "attachment": [
          4,
          2
        ],
        "bridge_conductance": "1",
        "neutral_pair_electric_energy": [
          [
            "47/80",
            "47/80",
            "7/16",
            "47/80"
          ],
          [
            "47/80",
            "47/80",
            "7/16",
            "47/80"
          ],
          [
            "13/20",
            "13/20",
            "1/2",
            "13/20"
          ],
          [
            "51/80",
            "51/80",
            "39/80",
            "51/80"
          ],
          [
            "9/20",
            "9/20",
            "3/10",
            "9/20"
          ],
          [
            "51/80",
            "51/80",
            "39/80",
            "51/80"
          ],
          [
            "47/80",
            "47/80",
            "7/16",
            "47/80"
          ],
          [
            "5/8",
            "5/8",
            "19/40",
            "5/8"
          ],
          [
            "51/80",
            "51/80",
            "39/80",
            "51/80"
          ],
          [
            "5/8",
            "5/8",
            "19/40",
            "5/8"
          ],
          [
            "51/80",
            "51/80",
            "39/80",
            "51/80"
          ],
          [
            "47/80",
            "47/80",
            "7/16",
            "47/80"
          ]
        ],
        "all_48_Gauss_sources_verified": true,
        "mixed_energy_differences_zero": true
      },
      {
        "attachment": [
          4,
          2
        ],
        "bridge_conductance": "2",
        "neutral_pair_electric_energy": [
          [
            "7/16",
            "7/16",
            "23/80",
            "7/16"
          ],
          [
            "7/16",
            "7/16",
            "23/80",
            "7/16"
          ],
          [
            "1/2",
            "1/2",
            "7/20",
            "1/2"
          ],
          [
            "39/80",
            "39/80",
            "27/80",
            "39/80"
          ],
          [
            "3/10",
            "3/10",
            "3/20",
            "3/10"
          ],
          [
            "39/80",
            "39/80",
            "27/80",
            "39/80"
          ],
          [
            "7/16",
            "7/16",
            "23/80",
            "7/16"
          ],
          [
            "19/40",
            "19/40",
            "13/40",
            "19/40"
          ],
          [
            "39/80",
            "39/80",
            "27/80",
            "39/80"
          ],
          [
            "19/40",
            "19/40",
            "13/40",
            "19/40"
          ],
          [
            "39/80",
            "39/80",
            "27/80",
            "39/80"
          ],
          [
            "7/16",
            "7/16",
            "23/80",
            "7/16"
          ]
        ],
        "all_48_Gauss_sources_verified": true,
        "mixed_energy_differences_zero": true
      }
    ],
    "neutral_charge_sources_checked": 432,
    "bridge_resistance_identity": "R_pair(i,j)=R_p(i,a)+1/w+R_e(b,j)",
    "pair_internal_electric_potential_is_separable": true,
    "relative_R3_or_Coulomb_kernel_source_selected": false
  },
  "external_physics": [
    "Homogeneous isotropic Euclidean relative space R3 and Maxwell electrostatics with positive permittivity epsilon",
    "Point charges q_p=+e,q_e=-e and subtraction of position-independent self energies, setting separated particles to interaction energy0",
    "Nonrelativistic two-body kinetic energy with positive supplied masses m_p,m_e, reduced mass mu=m_p m_e/(m_p+m_e), and supplied hbar",
    "Leading spin-independent electric interaction; proton internal line held fixed, hyperfine, magnetic, relativistic and radiative effects excluded"
  ],
  "Coulomb": {
    "Green_kernel": "1/(4pi epsilon r)",
    "interaction": "q_p q_e/(4pi epsilon r)=-kappa/r",
    "self_energies_subtracted": true,
    "coefficient_assembly_derived_Maxwell_kernel": false,
    "ground_orbital": "(pi a^3)^(-1/2) exp(-r/a)",
    "a": "hbar^2/(mu kappa)",
    "ground_energy": "-mu kappa^2/(2 hbar^2)",
    "reduced_mass": "mp me/(mp+me)",
    "ground_lower_bound": "<psi,(H-E0)psi>=A integral |grad psi+b rhat psi|^2 >=0",
    "ground_spin_degeneracy": 2,
    "binding_for_every_kappa_positive": true,
    "calibrated_constants_used": false,
    "controls": [
      {
        "external_controls": {
          "mp": "2",
          "me": "1",
          "hbar": "1",
          "kappa": "1"
        },
        "mu": "2/3",
        "A": "3/4",
        "b": "2/3",
        "radius": "3/2",
        "ground_energy": "-1/3",
        "kinetic_expectation": "1/3",
        "potential_expectation": "-2/3",
        "mean_radius": "9/4",
        "ground_residual_zero": true,
        "normalization_and_virial_exact": true
      },
      {
        "external_controls": {
          "mp": "7",
          "me": "3",
          "hbar": "2",
          "kappa": "5"
        },
        "mu": "21/10",
        "A": "20/21",
        "b": "21/8",
        "radius": "8/21",
        "ground_energy": "-105/16",
        "kinetic_expectation": "105/16",
        "potential_expectation": "-105/8",
        "mean_radius": "4/7",
        "ground_residual_zero": true,
        "normalization_and_virial_exact": true
      },
      {
        "external_controls": {
          "mp": "5",
          "me": "2",
          "hbar": "3",
          "kappa": "1/2"
        },
        "mu": "10/7",
        "A": "63/20",
        "b": "5/63",
        "radius": "63/5",
        "ground_energy": "-5/252",
        "kinetic_expectation": "5/252",
        "potential_expectation": "-5/126",
        "mean_radius": "189/10",
        "ground_residual_zero": true,
        "normalization_and_virial_exact": true
      }
    ]
  },
  "native_retention": {
    "electron_stage_intertwiners": true,
    "proton_port_still_a_readout": true,
    "all_24_folds_have_ground_doublet_witnesses": true,
    "original_single_arrow_dark_phase_resolved_by_Coulomb": false
  },
  "physical_law_and_scales_derived_from_native_sources": false,
  "numerical_hydrogen_prediction_from_arrows": false,
  "source_stores_modified": false,
  "scope": "Source insufficiency certificate plus a standard-physics conditional Coulomb ground-state realization. Coulomb kernel, dimensional charges, masses, hbar, permittivity and relative space are external inputs, not arrow-count derivations. No numerical hydrogen benchmark is used.",
  "source_hashes": {
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    "research/strominger/contracts/common-endpoint-charging.json": "ded295df4d97d4d7a4cb6d2ca22db0dcd0848b163869052d9cb30267a057f2b3",
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    "research/nima/results/twelve-triangle-1836-arrows.json": "b9d6416fe3af3e7e85fcd1a9b8c48aa3e0ea142501368d726fc0601ea73b52ff",
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  }
}
