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], "matrix_max_absolute_difference": 0.0, "reference_delta_q": [ 3.1425301094982876, 1.1136016965654399e-17, -5.135581374147858 ], "alternative_delta_q": [ 3.1425301094982876, 1.1136016965654399e-17, -5.135581374147858 ], "density_min": 0.19999999999999996, "density_max": 1.8, "reason": "P3(2y+1) is orthogonal on [-1,0] to polynomials of degree <=2. Rigid-body spring assembly contains only zeroth, first and second moments of side density. Three-point Gauss integrates degree <=5 exactly.", "local_reaction_ratio_at_right_cervical_endpoint": 1.8, "local_reaction_ratio_at_right_apical_endpoint": 0.19999999999999996, "claim": "Exact continuum alias within this reduced model, not an assertion that real PDL follows this density law" }, "resting_pose_example": { "reference": { "support_id": "reference", "contact_id": "reference_lever", "matrix": [ [ 2.075, 0.0, 1.075 ], [ 0.0, 0.8, 1.734723475976807e-18 ], [ 1.075, 1.734723475976807e-18, 0.7551666666666669 ] ], "generalized_load": [ 1.0, 0.0, -0.5 ], "delta_q": [ 3.1425301094982876, 1.1136016965654399e-17, -5.135581374147858 ], "resting_q": [ 0.0, 0.0, 0.0 ], "total_q": [ 3.1425301094982876, 1.1136016965654399e-17, -5.135581374147858 ], "contact_delta": [ 5.7103207965722165, 1.1136016965654399e-17 ], "contact_compliance": 5.7103207965722165, "integrated_reaction": [ -0.9999999999999997, 2.7755575615628914e-17, 0.4999999999999984 ], "force_moment_residual": [ 3.3306690738754696e-16, 2.7755575615628914e-17, -1.609823385706477e-15 ], "foundation_energy": 2.8551603982861034, "half_load_work": 2.8551603982861082, "supported_boundary_length": 2.3 }, "wrong_resting_pose": { "support_id": "reference", "contact_id": "reference_lever", "matrix": [ [ 2.075, 0.0, 1.075 ], [ 0.0, 0.8, 1.734723475976807e-18 ], [ 1.075, 1.734723475976807e-18, 0.7551666666666669 ] ], "generalized_load": [ 1.0, 0.0, -0.5 ], "delta_q": [ 3.1425301094982876, 1.1136016965654399e-17, -5.135581374147858 ], "resting_q": [ 0.02, 0.0, 0.01 ], "total_q": [ 3.1625301094982876, 1.1136016965654399e-17, -5.125581374147858 ], "contact_delta": [ 5.7103207965722165, 1.1136016965654399e-17 ], "contact_compliance": 5.7103207965722165, "integrated_reaction": [ -0.9999999999999997, 2.7755575615628914e-17, 0.4999999999999984 ], "force_moment_residual": [ 3.3306690738754696e-16, 2.7755575615628914e-17, -1.609823385706477e-15 ], "foundation_energy": 2.8551603982861034, "half_load_work": 2.8551603982861082, "supported_boundary_length": 2.3 }, "zero_load_pose_after_reversible_unloading": [ 0.02, 0.0, 0.01 ], "claim": "Same incremental mobility can coexist with an imposed wrong resting pose. Unloading recovers that imposed pose; trauma, healing and drift were not simulated." }, "max_force_moment_residual": 2.1094237467877974e-15, "max_energy_identity_absolute_error": 3.552713678800501e-14, "limits": [ "Unit forces define linear response coefficients, not finite physical deformations or recommended human loads.", "Rigid crown/root omits enamel, dentin and pulp deformation, restored thickness, crack propagation, contact area and fatigue.", "Small-displacement static elasticity cannot predict healing, permanent repositioning, drift after support withdrawal, perfusion or physiological acceptance thresholds.", "Very stiff illustrative support is not a diagnostic signature or a biological simulation of ankylosis." ] }