{
  "date": "2026-09-06",
  "status": "Partial microscopic realization; complete metric dynamics not obtained",
  "all_macro_equations_derived": false,
  "parameters_refitted": false,
  "candidate": {
    "amplitude": -0.45,
    "position": 4.25,
    "IR_epsilon": 1e-09,
    "IR_cutoff": 0.01,
    "mu_at_zero": 1.0,
    "radial_stiffness_at_zero": 1.0,
    "numerical_force_splice_interval": [
      5e-05,
      0.0002
    ],
    "response": "mu_S=mu_previous_smoothed+B*(1/sqrt(x^2+epsilon^2)-1/sqrt(x^2+ell^2))",
    "IR_origin": "Ground energy of two harmonic modes minus a filled four-component fermionic doublet",
    "IR_spectral_coefficient": 1.00000010000001e-09,
    "shape_parameters_refitted": false,
    "metric_sector_derived_from_this_module": false,
    "galaxy_scale_m_s2": 1.5716639863145666e-10,
    "rar_rms_dex": 0.14717628635765218,
    "previous_rar_rms_same_grid_dex": 0.14717628635940785,
    "maximum_RAR_prediction_change_dex": 3.327009778786305e-10,
    "minimum_RAR_predicted_x": 0.07651872527871907,
    "rar_rows": 2693,
    "scale_refitted": false,
    "scope": "Frozen previous galaxy scale; full-sample spherical RAR proxy",
    "IR_parameter_acceleration_m_s2": 1.5716639863145667e-19,
    "IR_cutoff_acceleration_m_s2": 1.5716639863145666e-12
  },
  "microscopic_results": {
    "transition_spectral_checks": 27,
    "largest_transition_absolute_error": 2.954581024283698e-13,
    "transition_quadratic_matching_mu_shift": 0.05536332179930796,
    "IR_spectral_checks": 27,
    "band_basis_checks": 20,
    "fine_band_response_maximum_error": 1.3750920957456003e-07,
    "shape_inertia_rank": 5,
    "shape_inertia_eigenvalues": [
      -7.437768629024741e-18,
      0.07352941176470587,
      0.07352941176470587,
      0.07352941176470587,
      0.0735294117647059,
      0.0735294117647059
    ],
    "minimum_radial_stiffness": 3.530039912784786e-07,
    "minimum_mu_on_scan": 5.7237402431390594e-05,
    "force_energy_is_exact_previous_law": false,
    "spectral_IR_replaces_previous_cutoff": true
  },
  "open_structures": {
    "Berry_clock": "For a passive nondegenerate finite-gap ground state, zero volume inertia forces zero volume-clock Berry curvature. The target clock is not obtained.",
    "finite_frequency_lapse": "The force cells also generate positive acceleration-source inertia. Identifying a_i=partial_i ln(N) introduces time derivatives of the lapse gradient and can change the exact constraints. No controlled elimination of these corrections is established.",
    "spatial_geometry": "The identification Q=h/(det h)^(1/3), proper-time evolution and constant proper density are assumed. Neither R3 nor spatial gauge constraints are derived; five local shape directions are not a proof of two physical gravitons.",
    "matter_and_matching": "Universal metric coupling, physical cell populations, critical quadratic matching and protection of the spectral weights remain assumptions."
  },
  "physical_matching": {
    "reference_energy_density_J_m3": 2.945125565794609e-11,
    "common_density_gap_product_s_minus2": 2.7483879829907663e-55,
    "maximum_possible_smaller_gap_common_density_rad_s": 5.24250701763075e-28,
    "gap_product_formula": "omega_s*omega_IR,0 = B*epsilon*(g_dark/c)^2 * (n_s/n_IR)",
    "examples_with_common_density": [
      {
        "cell_length_m": 1.61625502392855e-35,
        "mode_density_m_minus3": 2.3684833522454663e+104,
        "shear_gap_rad_s": 2.3308840986373006e+44,
        "IR_boson_gap_at_zero_rad_s": 1.1791182515670987e-99
      },
      {
        "cell_length_m": 1e-12,
        "mode_density_m_minus3": 1e+36,
        "shear_gap_rad_s": 9.841251771634708e-25,
        "IR_boson_gap_at_zero_rad_s": 2.7927219491654547e-31
      },
      {
        "cell_length_m": 1e-06,
        "mode_density_m_minus3": 1.0000000000000001e+18,
        "shear_gap_rad_s": 9.841251771634708e-43,
        "IR_boson_gap_at_zero_rad_s": 2.792721949165455e-13
      },
      {
        "cell_length_m": 0.0001,
        "mode_density_m_minus3": 999999999999.9999,
        "shear_gap_rad_s": 9.841251771634705e-49,
        "IR_boson_gap_at_zero_rad_s": 2.7927219491654556e-07
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      {
        "cell_length_m": 0.001,
        "mode_density_m_minus3": 999999999.9999999,
        "shear_gap_rad_s": 9.841251771634707e-52,
        "IR_boson_gap_at_zero_rad_s": 0.0002792721949165456
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    ],
    "cosmic_frequency_benchmark_rad_s": 1e-18,
    "minimum_density_ratio_for_both_gaps_above_cosmic_benchmark": 3.63849647935009e+18,
    "Mercury_mean_motion_rad_s": 8.266737939701787e-07,
    "minimum_density_ratio_for_both_gaps_above_Mercury_frequency": 2.486510514041006e+42,
    "scope": "Conditional matching of these specific Gaussian and spectral cells. Equal mode densities fail a common adiabatic interpretation; separate sectors can evade this bound and require their own microscopic account."
  },
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        "external_acceleration_m_s2": 2e-10,
        "Q2_s_minus2": 1.660622194425119e-27,
        "extra_Mercury_advance_envelope_arcsec_century": 1.929588655037626e-06
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      {
        "external_acceleration_m_s2": 2.0400000000000002e-10,
        "Q2_s_minus2": 1.2568503701398952e-27,
        "extra_Mercury_advance_envelope_arcsec_century": 1.4628733384184631e-06
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      {
        "external_acceleration_m_s2": 2.08e-10,
        "Q2_s_minus2": 8.86074959913277e-28,
        "extra_Mercury_advance_envelope_arcsec_century": 1.0342982062015206e-06
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      {
        "external_acceleration_m_s2": 2.1200000000000002e-10,
        "Q2_s_minus2": 5.519507210252455e-28,
        "extra_Mercury_advance_envelope_arcsec_century": 6.480877512773359e-07
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      {
        "external_acceleration_m_s2": 2.1600000000000003e-10,
        "Q2_s_minus2": 2.5830609553584855e-28,
        "extra_Mercury_advance_envelope_arcsec_century": 3.0866722682293874e-07
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      {
        "external_acceleration_m_s2": 2.2000000000000002e-10,
        "Q2_s_minus2": 8.533850111952114e-30,
        "extra_Mercury_advance_envelope_arcsec_century": 1.995829372178622e-08
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        "external_acceleration_m_s2": 2.2400000000000003e-10,
        "Q2_s_minus2": -1.9410893445453362e-28,
        "extra_Mercury_advance_envelope_arcsec_century": 2.344624493767732e-07
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      {
        "external_acceleration_m_s2": 2.2800000000000004e-10,
        "Q2_s_minus2": -3.460080984465146e-28,
        "extra_Mercury_advance_envelope_arcsec_century": 4.100409869386818e-07
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      {
        "external_acceleration_m_s2": 2.3200000000000003e-10,
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        "extra_Mercury_advance_envelope_arcsec_century": 5.227555390809696e-07
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      {
        "external_acceleration_m_s2": 2.3600000000000006e-10,
        "Q2_s_minus2": -4.834465391764465e-28,
        "extra_Mercury_advance_envelope_arcsec_century": 5.689045369015007e-07
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      {
        "external_acceleration_m_s2": 2.4e-10,
        "Q2_s_minus2": -4.627302910281404e-28,
        "extra_Mercury_advance_envelope_arcsec_century": 5.449588583470011e-07
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      {
        "external_acceleration_m_s2": 2.44e-10,
        "Q2_s_minus2": -3.7803149802389575e-28,
        "extra_Mercury_advance_envelope_arcsec_century": 4.470564748307287e-07
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      {
        "external_acceleration_m_s2": 2.48e-10,
        "Q2_s_minus2": -2.2598214990189256e-28,
        "extra_Mercury_advance_envelope_arcsec_century": 2.7130434111976106e-07
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      {
        "external_acceleration_m_s2": 2.52e-10,
        "Q2_s_minus2": -3.61688968690119e-30,
        "extra_Mercury_advance_envelope_arcsec_century": 1.4274834392636806e-08
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      {
        "external_acceleration_m_s2": 2.56e-10,
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        "extra_Mercury_advance_envelope_arcsec_century": 3.473117291259655e-07
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      {
        "external_acceleration_m_s2": 2.6000000000000003e-10,
        "Q2_s_minus2": 6.6287018388093615e-28,
        "extra_Mercury_advance_envelope_arcsec_century": 7.762983125703704e-07
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      {
        "external_acceleration_m_s2": 2.64e-10,
        "Q2_s_minus2": 1.112674907165592e-27,
        "extra_Mercury_advance_envelope_arcsec_century": 1.2962225401120578e-06
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    ],
    "all_17_sampled_Cassini_Q2_screens_pass": true,
    "maximum_Q2_change_from_previous_candidate_s_minus2": 2.2641210513147716e-33,
    "maximum_extra_Mercury_advance_arcsec_century": 1.929588655037626e-06,
    "scope": "Static response under the assumed CMC metric action. Gamma=beta=1 are inherited high-acceleration branch assumptions. Mercury uses approximate orbital averages and diagnostic multipoles through degree 4; no new tracking fit or certified microscopic spacetime solution."
  },
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            "IR_origin": "Ground energy of two harmonic modes minus a filled four-component fermionic doublet",
            "IR_spectral_coefficient": 1.00000010000001e-09,
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            "metric_sector_derived_from_this_module": false
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            "IR_origin": "Ground energy of two harmonic modes minus a filled four-component fermionic doublet",
            "IR_spectral_coefficient": 1.00000010000001e-09,
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            "IR_origin": "Ground energy of two harmonic modes minus a filled four-component fermionic doublet",
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            "IR_origin": "Ground energy of two harmonic modes minus a filled four-component fermionic doublet",
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            "IR_origin": "Ground energy of two harmonic modes minus a filled four-component fermionic doublet",
            "IR_spectral_coefficient": 1.00000010000001e-09,
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    "maximum_control_Q2_shift_s_minus2": 1.7269285263204706e-29,
    "Green_extraction_count": 21,
    "three_dimensional_final": {
      "n": 65,
      "seconds": 8.714982916135341,
      "iterations": 3,
      "relative_residual": 5.253387295387883e-11,
      "energy": 0.15773156288037532,
      "minimum_acceleration": 0.07858900926758412,
      "maximum_acceleration": 5.897532146691387,
      "minimum_mu": 0.07118666351177025,
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      "field_sha256": "1d3d600cef7568c145172fd6eff2e50f74cafac2794af56f8df4bf2004d988e9"
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    "interpolation": "Positive power-law response-table intervals, 10 Rust tests; grid, boundary, table-density and Green controls. Static synthetic Cartesian grids through 65 cubed.",
    "precision_limit": "The previously published strict Mercury inner-grid diagnostic did not meet its stopping target. This stage does not replace that diagnostic with a newly certified inner solution."
  },
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}