{ "date": "2026-09-05", "status": "Conditional Cassini and Mercury compatibility in a constrained effective metric model", "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_C(x)=mu_previous_smoothed(x)+epsilon/[(x+epsilon)*(1+(x/ell)^2)]", "galaxy_scale_m_s2": 1.5716639863145666e-10, "rar_rms_dex": 0.14717628635590282, "previous_rar_rms_same_grid_dex": 0.14717628635940785, "maximum_RAR_prediction_change_dex": 6.625988646646874e-10, "minimum_RAR_predicted_x": 0.07651872522059422, "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 }, "action": { "covariant_square_matches_ADM_action": true, "kinetic_Hessian_rank": 5, "primary_constraint": "P-sqrt(h)*q(t)=0", "primary_constraint_independent_of_lapse": true, "primary_self_Poisson_bracket_zero": "ultralocal scalar constraint; antisymmetry cancels the coincident-point terms", "Legendre_transform_matches_GR_momentum_Hamiltonian": true, "homogeneous_Friedmann_and_clock_identities": true, "concrete_clock": "q(t)=-2/t; for a flat constant-w fluid and F(0)=0, N=2/(1+w)", "IR_linear_scope": "Formal infinitesimal perturbations about zero acceleration; observed cosmological amplitudes need a nonlinear study", "homogeneous_TT_quadratic_action": "(64*pi*G)^-1 integral N*A^3 [(dot gamma_ij/N)^2-(partial_k gamma_ij/A)^2]", "homogeneous_TT_kinetic_normalization_checked": true, "gravitational_modes_on_regular_local_branch": 2, "propagating_scalar_modes": 0, "tensor_speed_squared_over_c_squared": 1.0, "scalar_speed_squared_over_c_squared": null }, "response_checks": { "minimum_mu_on_scan": 5.733622935869203e-05, "x_at_minimum_mu_on_scan": 3.4873858413521875e-05, "minimum_radial_stiffness": 2.630625780369982e-06, "x_at_minimum_radial_stiffness": 1.0665678775018638e-06, "maximum_lapse_direction_coefficient": 1.999994738748402, "minimum_lapse_parallel_coefficient": -0.45838055287104185, "force_derivative_finite_difference_error": 6.892175719031002e-11, "force_join_minimum_derivative": 8.218875836060492e-05, "force_join_endpoint_derivative_error": 5.421010862427522e-20, "force_join_energy_correction": 2.6304701814630245e-21, "IR_energy_integral": 1.570794714985316e-11, "IR_energy_quadrature_relative_error": 8.841483101207359e-12, "F_zero_over_a_star_squared_if_F_infinity_zero": -55.68536238332171, "Lambda_inverse_m2_if_F_infinity_zero": 8.5142744720209e-53, "Lambda_scope": "An additive vacuum term remains free; this convention is not a cosmological-constant prediction", "all_orientation_criterion": "2-alpha_direction=2*[mu*(1-cos(theta)^2)+radial*cos(theta)^2]>0", "IR_core_interpolation_absolute_error_bound": 1.1e-10, "IR_core_interpolation_scope": "Physical mu(0)=1 linearly joined to the first Rust table row at x=1e-14" }, "observations": { "Q2": { "mean": 1.6e-27, "sigma": 1.8e-27, "unit": "s^-2", "source": "https://arxiv.org/abs/2602.17884v2" }, "gamma_minus_one": { "mean": 2.1e-05, "sigma": 2.3e-05, "source": "https://www.nature.com/articles/nature01997" }, "beta_minus_one": { "mean": -2.7e-05, "sigma": 3.9e-05, "source": "https://doi.org/10.3847/1538-3881/aa5be2", "scope": "Abstract value; Table 1 gives -2.6e-5. This result already uses the Cassini gamma prior.", "independent_of_gamma": false } }, "high_acceleration_metric": { "isotropic_spatial_curvature_zero": true, "isotropic_spatial_lapse_Laplacian_zero": true, "N_squared_series": "2*u**2 - 2*u + 1", "spatial_metric_series": "2*u + 1", "beta_PPN": 1.0, "gamma_PPN": 1.0, "alpha1_PPN": 0.0, "alpha2_PPN": 0.0, "exact_geodesic": { "scope": "Schwarzschild high-field branch, with the approximate orbit used as areal turning radii; not the same convention as a precision ephemeris", "precision_decimal_digits": 70, "advance_radians_per_radial_cycle": "0.0000005018661040824824438449811086517309062940945498232681799794598935160592", "coordinate_radial_period_seconds": "7600562.439082677180753243930692793022745852554767668475922510310330629", "arcsec_per_Julian_century": "42.98047726346633304972069274481440992181461342936009188900815746191332", "radial_first_integral_relative_errors": [ 1.1549506159526915e-61, 7.443239568473652e-63, 3.2967777619907457e-62 ] } }, "gamma_offset_in_quoted_sigma": -0.9130434782608695, "beta_offset_in_quoted_sigma": 0.6923076923076923, "no_joint_likelihood_computed": true, "all_sampled_marginal_screens_pass": true, "central_solar_case": { "external_acceleration_m_s2": 2.3200000000000003e-10, "nr": 384, "nu": 288, "Q2_s_minus2": -4.435207581559899e-28, "Q2_offset_in_quoted_sigma": -1.135289310086661, "longitude_tide_orientation_interval_arcsec_century": [ -5.126606628295114e-07, 3.418864008759757e-07 ], "additional_precession_envelope_arcsec_century": 5.227547745377433e-07, "equivalent_beta_bias_envelope": 3.648783103013045e-08, "inside_each_quoted_two_sigma_marginal": true }, "external_field_cases": [ { "external_acceleration_m_s2": 2e-10, "nr": 384, "nu": 288, "Q2_s_minus2": 1.6606230023367632e-27, "Q2_offset_in_quoted_sigma": 0.03367944574264626, "longitude_tide_orientation_interval_arcsec_century": [ -1.2800853422087013e-06, 1.9194954766660014e-06 ], "additional_precession_envelope_arcsec_century": 1.9295895883742328e-06, "equivalent_beta_bias_envelope": 1.3468368398998633e-07, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.0400000000000002e-10, "nr": 384, "nu": 288, "Q2_s_minus2": 1.2568517512692757e-27, "Q2_offset_in_quoted_sigma": -0.1906379159615135, "longitude_tide_orientation_interval_arcsec_century": [ -9.688397076670544e-07, 1.452780822622782e-06 ], "additional_precession_envelope_arcsec_century": 1.4628749343310138e-06, "equivalent_beta_bias_envelope": 1.0210740489033897e-07, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.08e-10, "nr": 384, "nu": 288, "Q2_s_minus2": 8.860763717791093e-28, "Q2_offset_in_quoted_sigma": -0.3966242379004948, "longitude_tide_orientation_interval_arcsec_century": [ -6.83028823517336e-07, 1.024205725933759e-06 ], "additional_precession_envelope_arcsec_century": 1.0342998376419908e-06, "equivalent_beta_bias_envelope": 7.219323389966955e-08, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.1200000000000002e-10, "nr": 384, "nu": 288, "Q2_s_minus2": 5.51951945233525e-28, "Q2_offset_in_quoted_sigma": -0.5822489193147082, "longitude_tide_orientation_interval_arcsec_century": [ -4.254701962473072e-07, 6.379950540983163e-07 ], "additional_precession_envelope_arcsec_century": 6.480891658065481e-07, "equivalent_beta_bias_envelope": 4.5236063114522864e-08, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.1600000000000003e-10, "nr": 384, "nu": 288, "Q2_s_minus2": 2.5830740116361407e-28, "Q2_offset_in_quoted_sigma": -0.7453847771313256, "longitude_tide_orientation_interval_arcsec_century": [ -1.9911534258424684e-07, 2.985746237557888e-07 ], "additional_precession_envelope_arcsec_century": 3.0866873546402057e-07, "equivalent_beta_bias_envelope": 2.1544810707572113e-08, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.2000000000000002e-10, "nr": 384, "nu": 288, "Q2_s_minus2": 8.535135790678332e-30, "Q2_offset_in_quoted_sigma": -0.8841471467829565, "longitude_tide_orientation_interval_arcsec_century": [ -6.579279104308436e-09, 9.865667595765822e-09 ], "additional_precession_envelope_arcsec_century": 1.9959779303997597e-08, "equivalent_beta_bias_envelope": 1.3931753283113745e-09, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.2400000000000003e-10, "nr": 384, "nu": 288, "Q2_s_minus2": -1.9410752211643793e-28, "Q2_offset_in_quoted_sigma": -0.9967264011757988, "longitude_tide_orientation_interval_arcsec_century": [ -2.2436670464341192e-07, 1.4962709388227213e-07 ], "additional_precession_envelope_arcsec_century": 2.344608163516437e-07, "equivalent_beta_bias_envelope": 1.6365162150436843e-08, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.2800000000000004e-10, "nr": 384, "nu": 288, "Q2_s_minus2": -3.460067009329046e-28, "Q2_offset_in_quoted_sigma": -1.0811148338516137, "longitude_tide_orientation_interval_arcsec_century": [ -3.9994525934077696e-07, 2.667180362712934e-07 ], "additional_precession_envelope_arcsec_century": 4.100393710490087e-07, "equivalent_beta_bias_envelope": 2.8620393376162204e-08, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.3200000000000003e-10, "nr": 384, "nu": 288, "Q2_s_minus2": -4.435207581559899e-28, "Q2_offset_in_quoted_sigma": -1.135289310086661, "longitude_tide_orientation_interval_arcsec_century": [ -5.126606628295114e-07, 3.418864008759757e-07 ], "additional_precession_envelope_arcsec_century": 5.227547745377433e-07, "equivalent_beta_bias_envelope": 3.648783103013045e-08, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.3600000000000006e-10, "nr": 384, "nu": 288, "Q2_s_minus2": -4.834450468640633e-28, "Q2_offset_in_quoted_sigma": -1.1574694704800352, "longitude_tide_orientation_interval_arcsec_century": [ -5.588086997267586e-07, 3.726618970008626e-07 ], "additional_precession_envelope_arcsec_century": 5.689028114349904e-07, "equivalent_beta_bias_envelope": 3.970892408311682e-08, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.4e-10, "nr": 384, "nu": 288, "Q2_s_minus2": -4.627284240642865e-28, "Q2_offset_in_quoted_sigma": -1.1459602355912701, "longitude_tide_orientation_interval_arcsec_century": [ -5.348625881168322e-07, 3.5669256190870486e-07 ], "additional_precession_envelope_arcsec_century": 5.44956699825064e-07, "equivalent_beta_bias_envelope": 3.8037506208408236e-08, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.44e-10, "nr": 384, "nu": 288, "Q2_s_minus2": -3.7802923390284444e-28, "Q2_offset_in_quoted_sigma": -1.0989051299460246, "longitude_tide_orientation_interval_arcsec_century": [ -4.3695974553101596e-07, 2.914024920553775e-07 ], "additional_precession_envelope_arcsec_century": 4.470538572392477e-07, "equivalent_beta_bias_envelope": 3.120397249118954e-08, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.48e-10, "nr": 384, "nu": 288, "Q2_s_minus2": -2.2598123112442703e-28, "Q2_offset_in_quoted_sigma": -1.0144340172913484, "longitude_tide_orientation_interval_arcsec_century": [ -2.6120916688758855e-07, 1.7419682924396388e-07 ], "additional_precession_envelope_arcsec_century": 2.713032785958203e-07, "equivalent_beta_bias_envelope": 1.8936734142846102e-08, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.52e-10, "nr": 384, "nu": 288, "Q2_s_minus2": -3.615373596133052e-30, "Q2_offset_in_quoted_sigma": -0.8908974297756295, "longitude_tide_orientation_interval_arcsec_century": [ -4.1789697327267094e-09, 2.7868978934447853e-09 ], "additional_precession_envelope_arcsec_century": 1.4273081440958488e-08, "equivalent_beta_bias_envelope": 9.96248737005811e-10, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.56e-10, "nr": 384, "nu": 288, "Q2_s_minus2": 2.9174060304821706e-28, "Q2_offset_in_quoted_sigma": -0.7268107760843239, "longitude_tide_orientation_interval_arcsec_century": [ -2.2488720748998516e-07, 3.3721968630017865e-07 ], "additional_precession_envelope_arcsec_century": 3.473137980084104e-07, "equivalent_beta_bias_envelope": 2.424220264151553e-08, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.6000000000000003e-10, "nr": 384, "nu": 288, "Q2_s_minus2": 6.628709545349343e-28, "Q2_offset_in_quoted_sigma": -0.5206272474805921, "longitude_tide_orientation_interval_arcsec_century": [ -5.109717205422543e-07, 7.662050911330514e-07 ], "additional_precession_envelope_arcsec_century": 7.762992028412832e-07, "equivalent_beta_bias_envelope": 5.41850127856701e-08, "inside_each_quoted_two_sigma_marginal": true }, { "external_acceleration_m_s2": 2.64e-10, "nr": 384, "nu": 288, "Q2_s_minus2": 1.1126759995884007e-27, "Q2_offset_in_quoted_sigma": -0.2707355557842218, "longitude_tide_orientation_interval_arcsec_century": [ -8.577023416490553e-07, 1.2861296906036929e-06 ], "additional_precession_envelope_arcsec_century": 1.2962238023119247e-06, "equivalent_beta_bias_envelope": 9.047530004448749e-08, "inside_each_quoted_two_sigma_marginal": true } ], "Mercury_first_PN_benchmark_arcsec_century": 42.980475389677416, "mercury_radial_tail": { "nodes": 256, "arcsec_century": 3.854486144394206e-17, "max_abs_mu_minus_one": 7.043346898841644e-26, "max_extra_acceleration_m_s2": 1.9177422508808876e-27, "x_range": [ 173241308.79668328, 399040721.33688223 ] }, "mercury_multipoles": [ { "degree": 3, "dimensionless_coefficients_384_512_orders_2_4": [ 0.00948514540548881, 0.009485132842564355, 0.009509083433415362, 0.009509085217283192 ], "coefficient_absolute_spread": 2.3952374718836517e-05, "coefficients_at_all_sampled_external_fields": [ -0.002193462640348811, -0.0009115691507369487, 0.00042827174834874905, 0.0018228934470284246, 0.003268247599592835, 0.004761122529784981, 0.006298194187017529, 0.007874662721553419, 0.00948514540548881, 0.011124974027473726, 0.012789331535303653, 0.014472032907049277, 0.01616609352663868, 0.017865078488852548, 0.019562741125818964, 0.021251843409274156, 0.022923968182981206 ], "precession_orientation_envelope_arcsec_century": 1.009358619971798e-08 }, { "degree": 4, "dimensionless_coefficients_384_512_orders_2_4": [ -0.005104800994662456, -0.005104819129863904, -0.005087604779439318, -0.0050876025912745815 ], "coefficient_absolute_spread": 1.72165385893229e-05, "coefficients_at_all_sampled_external_fields": [ -0.011237954547592346, -0.010767232665377062, -0.010218316288223669, -0.009587975581106882, -0.008873760072731742, -0.008071748373771136, -0.007177801806718625, -0.006189477710891317, -0.005104800994662456, -0.003920544733743215, -0.0026334745865732767, -0.0012420363483544871, 0.0002543876741697137, 0.0018572898655582586, 0.0035684913270496573, 0.005388397849812302, 0.007315686228823336 ], "precession_orientation_envelope_arcsec_century": 5.254699689359252e-13 } ], "largest_extra_precession_envelope_arcsec_century": 1.9295895883742328e-06, "largest_equivalent_beta_bias": 1.3468368398998633e-07, "numerical_controls": { "solar": [ { "nr": 256, "nu": 192, "rmin": 0.0003, "rmax": 40.0, "table_nodes": 60001, "Q2_s_minus2": -4.2625086805656885e-28 }, { "nr": 512, "nu": 384, "rmin": 0.0003, "rmax": 40.0, "table_nodes": 60001, "Q2_s_minus2": -4.493984116482869e-28 }, { "nr": 384, "nu": 288, "rmin": 0.0001, "rmax": 40.0, "table_nodes": 60001, "Q2_s_minus2": -4.428914574242977e-28 }, { "nr": 384, "nu": 288, "rmin": 0.0003, "rmax": 80.0, "table_nodes": 60001, "Q2_s_minus2": -4.426947676068969e-28 }, { "nr": 384, "nu": 288, "rmin": 0.0003, "rmax": 40.0, "table_nodes": 120001, "Q2_s_minus2": -4.4354037373019185e-28 }, { "nr": 512, "nu": 384, "rmin": 1e-05, "rmax": 40.0, "table_nodes": 60001, "Q2_s_minus2": -4.440004822459885e-28 } ], "maximum_solar_control_shift_s_minus2": 1.726989009942107e-29, "minimum_sampled_margin_to_Q2_band_s_minus2": 1.5165549531359368e-27, "maximum_IR_sensitivity_shift_s_minus2": 2.1531450887642885e-37, "Green_extractions": [ { "nr": 384, "Green_Q2_two_and_four_nodes_s_minus2": [ -4.1092217420410155e-28, -4.1091673778731715e-28 ], "inner_projection_Q2_s_minus2": -4.435207581559899e-28, "difference_s_minus2": 3.2604020368672774e-29, "quadrature_change_s_minus2": 5.436416784403606e-33, "integrals": [ { "Q2_s_minus2": -4.1092217420410155e-28, "positive_integral_s_minus2": 1.0056819079970134e-24, "negative_integral_s_minus2": -1.0060928301712172e-24, "absolute_integral_over_abs_Q2": 4895.756093145265, "dimensionless_potential_multipole_coefficients": { "3": 0.00948514540548881, "4": -0.005104800994662456 } }, { "Q2_s_minus2": -4.1091673778731715e-28, "positive_integral_s_minus2": 1.005682170382606e-24, "negative_integral_s_minus2": -1.0060930871203946e-24, "absolute_integral_over_abs_Q2": 4895.82212770378, "dimensionless_potential_multipole_coefficients": { "3": 0.009485132842564355, "4": -0.005104819129863904 } } ] }, { "nr": 512, "Green_Q2_two_and_four_nodes_s_minus2": [ -4.258103938807619e-28, -4.2581067495776735e-28 ], "inner_projection_Q2_s_minus2": -4.493984116482869e-28, "difference_s_minus2": 2.358773669051953e-29, "quadrature_change_s_minus2": 2.810770054631631e-34, "integrals": [ { "Q2_s_minus2": -4.258103938807619e-28, "positive_integral_s_minus2": 1.0056585440685798e-24, "negative_integral_s_minus2": -1.0060843544624607e-24, "absolute_integral_over_abs_Q2": 4724.503975105833, "dimensionless_potential_multipole_coefficients": { "3": 0.009509083433415362, "4": -0.005087604779439318 } }, { "Q2_s_minus2": -4.2581067495776735e-28, "positive_integral_s_minus2": 1.0056585943994704e-24, "negative_integral_s_minus2": -1.0060844050744275e-24, "absolute_integral_over_abs_Q2": 4724.501093528072, "dimensionless_potential_multipole_coefficients": { "3": 0.009509085217283192, "4": -0.0050876025912745815 } } ] } ], "inner_grid_diagnostic": { "minimum_grid_radius_au": 0.062352274428200356, "shells": [ { "radius_interval_au": [ 0.3, 0.5 ], "radial_cells": 18, "minimum_Q2_from_shell_s_minus2": 5.387711973523227e-27, "maximum_Q2_from_shell_s_minus2": 1.6862284931737248e-26, "median_Q2_from_shell_s_minus2": 9.621862135270678e-27, "maximum_roundoff_projection_scale_s_minus2": 2.0645954109242178e-30 }, { "radius_interval_au": [ 1.0, 3.0 ], "radial_cells": 37, "minimum_Q2_from_shell_s_minus2": -2.98526580811505e-28, "maximum_Q2_from_shell_s_minus2": 8.142546739603105e-28, "median_Q2_from_shell_s_minus2": -3.1206337811500145e-29, "maximum_roundoff_projection_scale_s_minus2": 1.8091467206000479e-31 }, { "radius_interval_au": [ 10.0, 30.0 ], "radial_cells": 37, "minimum_Q2_from_shell_s_minus2": -4.3061662253891875e-28, "maximum_Q2_from_shell_s_minus2": -4.203074849093254e-28, "median_Q2_from_shell_s_minus2": -4.278965470330965e-28, "maximum_roundoff_projection_scale_s_minus2": 1.7616055115254572e-33 }, { "radius_interval_au": [ 60.0, 120.0 ], "radial_cells": 23, "minimum_Q2_from_shell_s_minus2": -4.317933615730783e-28, "maximum_Q2_from_shell_s_minus2": -4.316482171643365e-28, "median_Q2_from_shell_s_minus2": -4.317636456960052e-28, "maximum_roundoff_projection_scale_s_minus2": 4.995177913340319e-35 } ], "scope": "Diagnostic shell P2 projections; inner harmonic continuation remains the controlled Q2 estimator" }, "inner_precision_diagnostic": { "source_sha256": "bf1894c4045488c32f5860ecc2b1f77c9517a61686d5db1cb42466c265a366f6", "base_solver": { "original_source_sha256": "2dab4dfbb87656a33e64a69855a811e69ed344ad9c053c47387b81e911057a3b", "adapter_source_sha256": "af29309a14946e8d95e2a3b3c83d5356cc74d28ef46a0033f01f293539ec9bdc", "generated_source_sha256": "baee1545a77be40530f7fef2ee39687e2dc2324897e74acedf107a5ffa5e0377", "binary_sha256": "cb56d97cdc38c9382cccf41a1a44da85c0cde9016c4b0b1500faab0f33846ec0", "rustc": "rustc 1.94.1 (e408947bf 2026-03-25)", "physical_change": "Optional mu(0) and a continuous linear core below the first table row", "original_source_unchanged": true }, "control_changes": "Cancel the analytically zero background flux before summation; PCG 1e-15, iteration change 2e-14, nonlinear residual 2e-13", "generated_source_sha256": "6c883fdbcd798bb407308ee5144e736e2bf232148cd13a10356b9d4482716783", "tests_log_sha256": "34ad584f28f00dd321b6cb0b6f3b8c3ed4df1977062ba708064fa234f5adbd88", "physical_settings": { "nr": 512, "nu": 384, "rmin": 1e-05, "rmax": 40.0, "external": 2.32e-10, "scale": 1.5716639863145666e-10, "table_sha256": "8c0d01687a220e91507d5c6c488368fb3d02e72c54ce8a8a899fbd3e1bec835b" }, "requested_stopping_target_met": false, "termination_scope": "The strict potential-change target is below the observed floating-point plateau; the resulting field is retained as a precision diagnostic, not a certified converged solve", "result": { "model": "Table", "nr": 512, "nu": 384, "rmin": 1e-05, "rmax": 40, "external_acceleration_m_s2": 2.32e-10, "model_scale_m_s2": 1.5716639863145666e-10, "eta": 1.4761424962343412, "mu_floor": 0, "converged": false, "nonlinear_residual": 1.3643747126e-13, "picard_iterations": 180, "cg_iterations": 254237, "quadrupole_coefficients": [ 0.0008413691223073296, 0.0008653377856911443, 0.006401937190128752 ], "Q2_s_minus2": [ -4.317029272611573e-28, -4.440011467595792e-28, -3.2848068129021875e-27 ], "fit_windows": [ [ 0.02, 0.08 ], [ 0.04, 0.16 ], [ 0.08, 0.32 ] ], "seconds": 370.365 }, "diagnostic": { "minimum_grid_radius_au": 0.062352274428200356, "shells": [ { "radius_interval_au": [ 0.3, 0.5 ], "radial_cells": 18, "minimum_Q2_from_shell_s_minus2": -4.243419911037832e-28, "maximum_Q2_from_shell_s_minus2": -4.083815368065848e-28, "median_Q2_from_shell_s_minus2": -4.164671384347305e-28, "maximum_roundoff_projection_scale_s_minus2": 2.064595416509041e-30 }, { "radius_interval_au": [ 1.0, 3.0 ], "radial_cells": 37, "minimum_Q2_from_shell_s_minus2": -4.324567734269136e-28, "maximum_Q2_from_shell_s_minus2": -4.31205022107646e-28, "median_Q2_from_shell_s_minus2": -4.322276622908363e-28, "maximum_roundoff_projection_scale_s_minus2": 1.8091467248222114e-31 }, { "radius_interval_au": [ 10.0, 30.0 ], "radial_cells": 37, "minimum_Q2_from_shell_s_minus2": -4.32222001472158e-28, "maximum_Q2_from_shell_s_minus2": -4.32065184558073e-28, "median_Q2_from_shell_s_minus2": -4.3214322897731665e-28, "maximum_roundoff_projection_scale_s_minus2": 1.7616055144766027e-33 }, { "radius_interval_au": [ 60.0, 120.0 ], "radial_cells": 23, "minimum_Q2_from_shell_s_minus2": -4.31957441046452e-28, "maximum_Q2_from_shell_s_minus2": -4.318582044251373e-28, "median_Q2_from_shell_s_minus2": -4.319079453072061e-28, "maximum_roundoff_projection_scale_s_minus2": 4.99517791920423e-35 } ], "scope": "Diagnostic shell P2 projections; inner harmonic continuation remains the controlled Q2 estimator" }, "maximum_mercury_shell_discrepancy_from_first_inner_fit_s_minus2": 2.3321390454572519e-29, "mercury_cells_resolve_inner_quadrupole_within_20_percent": true, "production_control_Q2_s_minus2": -4.440004822459885e-28, "change_from_production_middle_Q2_s_minus2": -6.645135906479224e-34, "field": "outputs/dark_cmc/inner_solver/field_09868745af446b86.csv", "field_sha256": "6baafcd2eeb891a79e002830ef8b642a0ad0099481858e48011a71147001dc12", "scope": "A precision control for the quadrupole in Mercury's radial cells.\n\nThe frozen production solver remains unchanged. This diagnostic cancels the\nanalytic Newtonian background before summing fluxes and tightens tolerances.", "input_sha256": { "dark_cmc_model.py": "63495c697f9521ed3f39be5785cb70964d1c45fc1bf9428210e6026955c5a50a", "dark_cmc_solar_checks.py": "e155e585f7188e4a35b3ae84176836e3a1d8c73ff9872d71a26d69cedd5cd799", "build_cmc_solver.py": "af29309a14946e8d95e2a3b3c83d5356cc74d28ef46a0033f01f293539ec9bdc", "outputs/dark_cmc/controls_summary.json": "384fc54bd1e82770c98d4699354edc8b57870b20af2e09dcaecff42d046ef8d0" } }, "three_dimensional_final": { "n": 65, "seconds": 10.456869458779693, "iterations": 3, "relative_residual": 5.2532460956849384e-11, "energy": 0.15773156288604998, "minimum_acceleration": 0.07858900925626837, "maximum_acceleration": 5.897532146691403, "minimum_mu": 0.07118666360165239, "minimum_radial_stiffness": 0.1481434577006213, "refinement_gradient_relative_L2": 0.0006475694685071194, "field_sha256": "71ba603a44fe0b2f23f30cd9a960cb10bc380c6314242f5750559a00a48929c6" }, "maximum_nonlinear_variation_error_at_smallest_step": 3.0394768868674885e-12 }, "assumptions": [ "Constrained metric action and universal matter coupling are postulated", "The galaxy transition A=-0.45,T=4.25 was selected using known Cassini and Gaia constraints", "The momentum constraint, q(t)=-2/t clock and ultraweak Newtonian return are new assumptions", "High-acceleration GR branch and quasistatic Galactic external field approximation", "Additive cosmological vacuum term remains freely adjustable" ], "limitations": [ "No raw Cassini/MESSENGER tracking fit or joint covariance likelihood", "No global relativistic matching of the Solar System, moving Galactic environment and cosmological foliation", "Positivity, constraint-counting and principal 3D checks are not global nonlinear stability or quantum consistency proofs", "The higher-multipole diagnostic evaluates degrees 3 and 4 at all 17 sampled fields, with central refinement controls; higher degrees and a rigorous numerical error bound are not supplied", "The galaxy result is the same 2693-point full-sample spherical proxy, not held-out or resolved disk fits", "17 external magnitudes sample the Gaia two-sigma interval; they do not prove compatibility at every intermediate value", "The homogeneous equations and formal infinitesimal GR limit do not fit nonlinear cosmological perturbations, CMB or dark matter", "No quantum derivation or novelty claim for the known constrained-gravity ingredients" ], "source_sha256": "99df0b99b9ddd5534feb631c6a06da7113a51c7dc94b0aa577c5e2b2193ea1c6", "input_sha256": { "outputs/dark_cmc/fields_summary.json": "2f9e407843aff75e9c5f85f8e6ae4252ef99f041c3419c80ba2bee5d2bc96d8b", "outputs/dark_cmc/controls_summary.json": "384fc54bd1e82770c98d4699354edc8b57870b20af2e09dcaecff42d046ef8d0", "outputs/dark_cmc/ir_summary.json": "5af6717d5b6d600617a3cfc47f484cf81ae77b30f9c7f8a1d44f2b1627744492", "outputs/dark_cmc/theory_summary.json": "331f41a1ed0c75106b2958b34cf7ab71926fb97d1ebfd99139a5e1a4d20d4f4d", "outputs/dark_cmc/3d_summary.json": "65bf847b0d664140d4836b45100b8e88c887618169b9c2a17c2e5ad725908af6", "outputs/dark_cmc/variation_summary.json": "38e54f79015a2a4356f55c623cb2bde405a8a6c03a019710c4c8cc28ad188774", "outputs/dark_cmc/solar_checks_summary.json": "04e30e1945b0089b383cf6fc0c7f6a856228c91e9a12c1c9a7e29696d9e107fe", "outputs/dark_cmc/inner_summary.json": "a4cefe9c1806d65a13a2deee74b12d0ee7b95c31194149f7857c7c3fd3d8cd5b", "OVERNIGHT_SOLAR_PROTOCOL.md": "959b08a7db4a664100ac8619aafc674800d57906343fcb8a9658a722853f65ce", "CMC_METRIC_DERIVATION.md": "1b55dcbd063c4ea0ca80aaea2517d50c049fe87ad819f9d0a7633d0f21c379a0" } }