{
  "date": "2026-09-05",
  "status": "Conditional Solar-System marginal compatibility; candidate metric extension fails local principal scalar stability diagnostic",
  "original_fitted_model": {
    "amplitude": -0.45,
    "position": 4.25,
    "galaxy_scale_m_s2": 1.5716639863145666e-10,
    "rar_rms_dex": 0.14717628635940785
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  "metric_extension": {
    "action_c_equals_one": "S=(16*pi*Gbare)^-1 integral N*sqrt(h) [Kij*Kij-(1+lambda_K)*K^2+R3+F(a)] + Sm[g,matter]",
    "F_matching": "F(a)=2*a^2-2*(2-alpha_K)*a_star^2*U(a/a_star)+constant; U'(x)=x*mu(x)",
    "a_star_inverse_m": 1.748712022470356e-27,
    "alpha_K": 1e-09,
    "lambda_K": 0.01,
    "b_K": 0.0,
    "Gbare_over_Gmeasured": 0.9999999995,
    "assumptions": [
      "Known metric/foliation action imported, not derived from LQ8 bands",
      "Universal matter coupling to this metric postulated",
      "Kinetic values illustrative; Mercury does not independently determine them",
      "No nonlocal or higher-spatial-derivative operators in this candidate",
      "Additive constant chosen to neglect cosmological curvature in this local test"
    ],
    "high_acceleration_PPN": {
      "beta_PPN": 1.0,
      "gamma_PPN": 1.0,
      "alpha1_PPN": -4e-09,
      "alpha2_PPN": -4.9999994925e-10,
      "tensor_speed_squared_over_c_squared": 1.0,
      "scalar_high_acceleration_speed_squared_over_c_squared": 9852216.743842365
    },
    "PPN_scope": "Known constant-coupling high-acceleration limit; no full transition-region relativistic boundary-value solve"
  },
  "observations": {
    "cassini_Q2": {
      "mean": 1.6e-27,
      "sigma": 1.8e-27,
      "units": "s^-2",
      "source": "https://arxiv.org/abs/2602.17884v2"
    },
    "cassini_gamma_minus_one": {
      "mean": 2.1e-05,
      "sigma": 2.3e-05,
      "source": "https://www.nature.com/articles/nature01997"
    },
    "messenger_beta_minus_one": {
      "mean": -2.7e-05,
      "sigma": 3.9e-05,
      "source": "https://doi.org/10.3847/1538-3881/aa5be2",
      "scope": "Published abstract, already conditional on the Cassini gamma prior; Table 1 prints -2.6e-5 with the same error",
      "independent_of_cassini_gamma": false
    }
  },
  "gamma_marginal_offset_in_quoted_sigma": -0.9130434782608695,
  "beta_marginal_offset_in_quoted_sigma": 0.6923076923076923,
  "no_joint_chi_squared_computed": true,
  "conditional_cases": [
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      "external_m_s2": 2e-10,
      "Q2_s_minus2": 1.677840207209982e-27,
      "Q2_offset_in_quoted_sigma": 0.04324455956110114,
      "mercury_additional_precession_bound_arcsec_century": 1.9393966504378207e-06,
      "equivalent_beta_bias_bound": 1.3536820843798325e-07,
      "illustrative_tidal_roundtrip_delay_bound_seconds": 1.6011276035698157e-16,
      "inside_each_quoted_two_sigma_marginal": true
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      "external_m_s2": 2.16e-10,
      "Q2_s_minus2": 2.757967846266399e-28,
      "Q2_offset_in_quoted_sigma": -0.7356684529852001,
      "mercury_additional_precession_bound_arcsec_century": 3.1879040570251864e-07,
      "equivalent_beta_bias_bound": 2.225129453401176e-08,
      "illustrative_tidal_roundtrip_delay_bound_seconds": 2.631870680795099e-17,
      "inside_each_quoted_two_sigma_marginal": true
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      "external_m_s2": 2.32e-10,
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      "Q2_offset_in_quoted_sigma": -1.1391644660474736,
      "mercury_additional_precession_bound_arcsec_century": 5.207233115184957e-07,
      "equivalent_beta_bias_bound": 3.6346036668795713e-08,
      "illustrative_tidal_roundtrip_delay_bound_seconds": 4.2989889028692705e-17,
      "inside_each_quoted_two_sigma_marginal": true
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      "external_m_s2": 2.48e-10,
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      "Q2_offset_in_quoted_sigma": -1.0029389374803706,
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      "illustrative_tidal_roundtrip_delay_bound_seconds": 1.9590401062417964e-17,
      "inside_each_quoted_two_sigma_marginal": true
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      "external_m_s2": 2.64e-10,
      "Q2_s_minus2": 1.132256893608003e-27,
      "Q2_offset_in_quoted_sigma": -0.2598572813288872,
      "mercury_additional_precession_bound_arcsec_century": 1.308763026111405e-06,
      "equivalent_beta_bias_bound": 9.13505270180699e-08,
      "illustrative_tidal_roundtrip_delay_bound_seconds": 1.0804889279072463e-16,
      "inside_each_quoted_two_sigma_marginal": true
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  "Mercury_GR_benchmark_arcsec_century": 42.980475389677416,
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      "beta_PPN": 1.0,
      "gamma_PPN": 1.0,
      "relative_error": 2.4069635173873394e-13
    },
    {
      "beta_PPN": 0.9,
      "gamma_PPN": 1.1,
      "relative_error": 2.1294077612310502e-13
    },
    {
      "beta_PPN": 1.2,
      "gamma_PPN": 0.8,
      "relative_error": 3.157474282033945e-13
    },
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      "beta_PPN": 0.0,
      "gamma_PPN": 0.0,
      "relative_error": 2.9753977059954195e-14
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    "scope": "Synthetic geometry: Earth 1 au, probe 8 au, impact 2 nominal solar radii",
    "round_trip_delay_seconds": 0.00025259877398107615,
    "analytic_relative_error": 2.220446049250313e-16,
    "quadrature_error_seconds": 4.005070241124862e-17,
    "largest_endpoint_radius_m": 1196782965600.0,
    "upper_path_length_m": 1346380836300.0
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  "stationary_AQUAL_matching_max_error": 1.1102230246251565e-16,
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    "radial_stiffness_finite_difference_error": 3.2878588740459236e-11,
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    "parallel_mode_at_peak": {
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    "negative_transverse_lapse_intervals_x": [],
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    "quoted_solar_abs_alpha1_bound": 0.0001,
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  "scope_limits": [
    "No raw Cassini or MESSENGER tracking data, covariance matrix, ephemeris refit, or independent joint likelihood",
    "The published MESSENGER beta constraint already includes Cassini's gamma information",
    "PPN beta=gamma=1 comes from the added known metric framework, not from quantum emergence",
    "Preferred-frame parameters checked against quoted bounds, not integrated into a full Mercury ephemeris",
    "Higher multipoles, finite-acceleration PN corrections and global metric/foliation response remain uncomputed",
    "The stability failure applies to this explicit minimal metric extension, not every possible nonlocal completion",
    "Passing the marginal observational screens is not presented as a viable simultaneous theory fit"
  ],
  "sources": {
    "metric_and_PPN": "https://arxiv.org/abs/1502.05554v3",
    "original_metric_framework": "https://arxiv.org/abs/1107.5264",
    "related_kinetic_stability_conditions": "https://arxiv.org/abs/2302.14846"
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