{ "eigenvalue_range": [ 1.3999779272653148, 8.609567621380449e-18 ], "isolated_equations": [], "new_equations": [ { "chiral_new": "left_handed_mass_bias", "domain": "Classical Mechanics", "eq_id": 19, "name": "Damped Harmonic Oscillator", "spectral_mass": 1.053541 } ], "num_edges": 64, "num_eigenvalues": 79, "num_isolated": 0, "num_new_equations": 1, "num_nodes": 79, "num_shifted": 51, "shifted_equations": [ { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Biophysics", "dominant_mode": "1", "eigenvalue": -1.2785, "eq_id": 593, "layer": 4, "name": "Nernst Equation (Membrane Equilibrium Potential)", "spectral_mass": 2.699023 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Statistical Mechanics", "dominant_mode": "1", "eigenvalue": -1.2785, "eq_id": 300, "layer": 2, "name": "Gibbs Entropy Formula", "spectral_mass": 2.680224 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "right_handed_vector_bias", "domain": "Thermodynamics", "dominant_mode": "1", "eigenvalue": -1.2785, "eq_id": 68, "layer": 1, "name": "Second Law of Thermodynamics", "spectral_mass": 2.632046 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Statistical Mechanics", "dominant_mode": "1", "eigenvalue": -1.2785, "eq_id": 296, "layer": 2, "name": "Boltzmann Distribution", "spectral_mass": 2.609717 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Cosmology", "dominant_mode": "7", "eigenvalue": -1.0101, "eq_id": 164, "layer": 2, "name": "CMB Blackbody Spectrum", "spectral_mass": 2.550659 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Surface Science", "dominant_mode": "24", "eigenvalue": -0.7071, "eq_id": 451, "layer": 2, "name": "Kelvin Equation (Capillary Condensation)", "spectral_mass": 2.436894 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Material Physics", "dominant_mode": "17", "eigenvalue": 0.7265, "eq_id": 502, "layer": 2, "name": "Nernst Equation (Electrode Potential)", "spectral_mass": 2.421445 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Plasma Physics", "dominant_mode": "7", "eigenvalue": -1.0101, "eq_id": 272, "layer": 2, "name": "MHD Induction Equation", "spectral_mass": 2.300064 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Quantum Mechanics", "dominant_mode": "29", "eigenvalue": -0.7071, "eq_id": 102, "layer": 1, "name": "Spin-\u00bd Algebra (Pauli Matrices)", "spectral_mass": 2.277911 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Condensed Matter", "dominant_mode": "29", "eigenvalue": -0.7071, "eq_id": 219, "layer": 2, "name": "Bloch's Theorem", "spectral_mass": 2.192643 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Optics", "dominant_mode": "27", "eigenvalue": -0.7071, "eq_id": 203, "layer": 2, "name": "Rayleigh Criterion (Resolution Limit)", "spectral_mass": 2.183978 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Biophysics", "dominant_mode": "9", "eigenvalue": -0.9036, "eq_id": 597, "layer": 4, "name": "Cable Equation (Neuronal Dendrite/Axon)", "spectral_mass": 2.089467 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Quantum Mechanics", "dominant_mode": "7", "eigenvalue": -1.0101, "eq_id": 86, "layer": 1, "name": "Planck's Blackbody Radiation Law", "spectral_mass": 2.087887 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Polymer Physics", "dominant_mode": "33", "eigenvalue": -0.7071, "eq_id": 438, "layer": 2, "name": "Williams-Landel-Ferry (WLF) Equation", "spectral_mass": 2.079654 }, { "chiral_new": "chiral_scarred", "chiral_old": "left_handed_mass_bias", "domain": "Cosmology", "dominant_mode": "40", "eigenvalue": 0.5, "eq_id": 168, "layer": 2, "name": "Dark Energy Equation of State", "spectral_mass": 2.069697 }, { "chiral_new": "chiral_scarred", "chiral_old": "left_handed_mass_bias", "domain": "Extremophile Bounds", "dominant_mode": "40", "eigenvalue": 0.5, "eq_id": 745, "layer": 4, "name": "Perchlorate Brine Limit (Don Juan Pond: -50\u00b0C liquid water maintained by CaCl\u2082 e", "spectral_mass": 2.062542 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Electromagnetism", "dominant_mode": "7", "eigenvalue": -1.0101, "eq_id": 38, "layer": 1, "name": "Maxwell's Equations (Differential)", "spectral_mass": 2.039742 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Nuclear Physics", "dominant_mode": "3", "eigenvalue": -1.1176, "eq_id": 241, "layer": 2, "name": "Radioactive Decay Law", "spectral_mass": 1.993108 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Thermodynamics", "dominant_mode": "28", "eigenvalue": -0.7071, "eq_id": 69, "layer": 1, "name": "Third Law of Thermodynamics", "spectral_mass": 1.928032 }, { "chiral_new": "achiral_stable", "chiral_old": "left_handed_mass_bias", "domain": "Biophysics", "dominant_mode": "0", "eigenvalue": 1.4, "eq_id": 773, "layer": 4, "name": "Optimal DNA Sequence Compression (PIST/CFF Biological Analogue)", "spectral_mass": 1.925629 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Material Physics", "dominant_mode": "26", "eigenvalue": -0.7071, "eq_id": 464, "layer": 2, "name": "Fick's First Law (Steady-State Diffusion)", "spectral_mass": 1.808281 }, { "chiral_new": "right_handed_vector_bias", "chiral_old": "achiral_stable", "domain": "Continuum Mechanics", "dominant_mode": "11", "eigenvalue": -0.866, "eq_id": 316, "layer": 2, "name": "Euler-Bernoulli Beam Equation", "spectral_mass": 1.800321 }, { "chiral_new": "right_handed_vector_bias", "chiral_old": "achiral_stable", "domain": "Fluid Dynamics", "dominant_mode": "11", "eigenvalue": -0.866, "eq_id": 181, "layer": 2, "name": "Poiseuille Flow (Hagen-Poiseuille)", "spectral_mass": 1.800321 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Electromagnetism", "dominant_mode": "24", "eigenvalue": -0.7071, "eq_id": 65, "layer": 1, "name": "Magnetic Susceptibility", "spectral_mass": 1.723144 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Electromagnetism", "dominant_mode": "4", "eigenvalue": 1.083, "eq_id": 46, "layer": 1, "name": "Kirchhoff's Current Law (KCL)", "spectral_mass": 1.71528 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Optics", "dominant_mode": "22", "eigenvalue": 0.7071, "eq_id": 200, "layer": 2, "name": "Fresnel Equations (Amplitude Reflection/Transmission)", "spectral_mass": 1.684137 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Radical Adaptations", "dominant_mode": "1", "eigenvalue": -1.2785, "eq_id": 754, "layer": 4, "name": "Primary Endosymbiosis \u2014 Mitochondrial and Plastid Acquisition, the Singular Evol", "spectral_mass": 1.653077 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Quantum Mechanics", "dominant_mode": "29", "eigenvalue": -0.7071, "eq_id": 104, "layer": 1, "name": "Dirac Equation", "spectral_mass": 1.610726 }, { "chiral_new": "achiral_stable", "chiral_old": "left_handed_mass_bias", "domain": "Extremophile Bounds", "dominant_mode": "0", "eigenvalue": 1.4, "eq_id": 744, "layer": 4, "name": "Long-Term Dormancy Survival Limit (~250 million years in salt; ~100 million year", "spectral_mass": 1.577049 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Quantum Mechanics", "dominant_mode": "29", "eigenvalue": -0.7071, "eq_id": 94, "layer": 1, "name": "Time-Independent Schr\u00f6dinger Equation", "spectral_mass": 1.550433 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Optics", "dominant_mode": "27", "eigenvalue": -0.7071, "eq_id": 191, "layer": 2, "name": "Snell's Law of Refraction", "spectral_mass": 1.544305 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "right_handed_vector_bias", "domain": "Information Theory", "dominant_mode": "2", "eigenvalue": 1.2785, "eq_id": 324, "layer": 4, "name": "Landauer's Principle", "spectral_mass": 1.476851 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Nuclear Physics", "dominant_mode": "1", "eigenvalue": -1.2785, "eq_id": 247, "layer": 2, "name": "Four-Factor Formula (Nuclear Reactor)", "spectral_mass": 1.476851 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Polymer Physics", "dominant_mode": "33", "eigenvalue": -0.7071, "eq_id": 443, "layer": 2, "name": "Flory-Fox Equation (T_g vs Molecular Weight)", "spectral_mass": 1.470538 }, { "chiral_new": "right_handed_vector_bias", "chiral_old": "left_handed_mass_bias", "domain": "Radical Adaptations", "dominant_mode": "11", "eigenvalue": -0.866, "eq_id": 766, "layer": 4, "name": "Pterosaur Giant Flight \u2014 Quetzalcoatlus 11m Wingspan, Estimated 200-250 kg, Larg", "spectral_mass": 1.434296 }, { "chiral_new": "right_handed_vector_bias", "chiral_old": "left_handed_mass_bias", "domain": "Radical Adaptations", "dominant_mode": "12", "eigenvalue": 0.866, "eq_id": 764, "layer": 4, "name": "Sauropod Hemodynamics \u2014 Pumping Blood 8-10m Vertically Against Gravity, the Larg", "spectral_mass": 1.434296 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Thermodynamics", "dominant_mode": "28", "eigenvalue": -0.7071, "eq_id": 70, "layer": 1, "name": "Ideal Gas Law", "spectral_mass": 1.363325 }, { "chiral_new": "right_handed_vector_bias", "chiral_old": "left_handed_mass_bias", "domain": "Radical Adaptations", "dominant_mode": "45", "eigenvalue": 0.5, "eq_id": 752, "layer": 4, "name": "Biological Cavitation / Sonoluminescence \u2014 Pistol Shrimp, Mantis Shrimp", "spectral_mass": 1.329916 }, { "chiral_new": "right_handed_vector_bias", "chiral_old": "achiral_stable", "domain": "Fluid Dynamics", "dominant_mode": "45", "eigenvalue": 0.5, "eq_id": 176, "layer": 2, "name": "Navier-Stokes Equation (Incompressible)", "spectral_mass": 1.329916 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Material Physics", "dominant_mode": "26", "eigenvalue": -0.7071, "eq_id": 465, "layer": 2, "name": "Fick's Second Law (Time-Dependent Diffusion)", "spectral_mass": 1.278648 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Optics", "dominant_mode": "22", "eigenvalue": 0.7071, "eq_id": 197, "layer": 2, "name": "Single-Slit Diffraction", "spectral_mass": 1.190865 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "right_handed_vector_bias", "domain": "Classical Mechanics", "dominant_mode": "4", "eigenvalue": 1.083, "eq_id": 4, "layer": 1, "name": "Hamilton-Jacobi Equation", "spectral_mass": 1.175209 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "achiral_stable", "domain": "Extremophile Bounds", "dominant_mode": "4", "eigenvalue": 1.083, "eq_id": 738, "layer": 4, "name": "Upper Temperature Limit of Carbon-Based Life (~122\u00b0C at depth, ~113\u00b0C at surface", "spectral_mass": 1.175209 }, { "chiral_new": "achiral_stable", "chiral_old": "left_handed_mass_bias", "domain": "Quantum Information", "dominant_mode": "46", "eigenvalue": 0.5, "eq_id": 668, "layer": 4, "name": "Concatenated Quantum Error Correction Threshold Theorem", "spectral_mass": 1.148621 }, { "chiral_new": "achiral_stable", "chiral_old": "left_handed_mass_bias", "domain": "Radical Adaptations", "dominant_mode": "14", "eigenvalue": -0.809, "eq_id": 748, "layer": 4, "name": "Biological Immortality via Cellular Transdifferentiation \u2014 Turritopsis dohrnii (", "spectral_mass": 1.08631 }, { "chiral_new": "achiral_stable", "chiral_old": "left_handed_mass_bias", "domain": "Astrophysics", "dominant_mode": "15", "eigenvalue": -0.809, "eq_id": 254, "layer": 2, "name": "TOV Limit (Neutron Star Maximum Mass)", "spectral_mass": 1.08631 }, { "chiral_new": "achiral_stable", "chiral_old": "left_handed_mass_bias", "domain": "Radical Adaptations", "dominant_mode": "48", "eigenvalue": 0.5, "eq_id": 757, "layer": 4, "name": "Biological Sonar \u2014 Echolocation Convergent Evolution in Bats and Toothed Whales ", "spectral_mass": 1.077442 }, { "chiral_new": "left_handed_mass_bias", "chiral_old": "unknown", "domain": "Classical Mechanics", "dominant_mode": "0", "eigenvalue": 1.4, "eq_id": 19, "layer": 1, "name": "Damped Harmonic Oscillator", "spectral_mass": 1.053541 }, { "chiral_new": "achiral_stable", "chiral_old": "left_handed_mass_bias", "domain": "Radical Adaptations", "dominant_mode": "36", "eigenvalue": 0.6296, "eq_id": 767, "layer": 4, "name": "Megalodon Bite Force \u2014 108,000-182,000 N (~11-19 tonnes-force), Largest Bite For", "spectral_mass": 0.92388 }, { "chiral_new": "achiral_stable", "chiral_old": "left_handed_mass_bias", "domain": "Extremophile Bounds", "dominant_mode": "5", "eigenvalue": 1.0505, "eq_id": 739, "layer": 4, "name": "Maximum Hydrostatic Pressure for Cell Division (~100-200 MPa confirmed; ~1 GPa s", "spectral_mass": 0.92388 }, { "chiral_new": "achiral_stable", "chiral_old": "left_handed_mass_bias", "domain": "Radical Adaptations", "dominant_mode": "5", "eigenvalue": 1.0505, "eq_id": 755, "layer": 4, "name": "Spider Silk \u2014 Tensile Strength Exceeding Steel, Toughness Exceeding Kevlar, Mole", "spectral_mass": 0.92388 } ], "spectral_gap_max_idx": 2, "spectral_gap_max_value": -0.16095547241916908, "top_eigenmodes": [ { "eigenvalue": 1.4, "mode": 0, "num_nodes_below_threshold": 10, "top_nodes": [ { "coordinate": 0.839756, "eq_id": 773, "name": "Optimal DNA Sequence Compression (PIST/CFF Biological Analog" }, { "coordinate": 0.37185, "eq_id": 744, "name": "Long-Term Dormancy Survival Limit (~250 million years in sal" }, { "coordinate": 0.299918, "eq_id": 19, "name": "Damped Harmonic Oscillator" }, { "coordinate": 0.201408, "eq_id": 241, "name": "Radioactive Decay Law" }, { "coordinate": 0.120151, "eq_id": 605, "name": "Arrhenius Equation (Chemical Reaction Rate)" }, { "coordinate": 0.071933, "eq_id": 741, "name": "Maximum Ionizing Radiation Dose Survived (Deinococcus radiod" }, { "coordinate": 0.049186, "eq_id": 46, "name": "Kirchhoff's Current Law (KCL)" }, { "coordinate": 0.042912, "eq_id": 4, "name": "Hamilton-Jacobi Equation" }, { "coordinate": 0.042912, "eq_id": 738, "name": "Upper Temperature Limit of Carbon-Based Life (~122\u00b0C at dept" }, { "coordinate": 0.017567, "eq_id": 758, "name": "Explosive Biochemistry \u2014 Bombardier Beetle, Skunk Spray, Ven" } ] }, { "eigenvalue": -1.2785, "mode": 1, "num_nodes_below_threshold": 19, "top_nodes": [ { "coordinate": -0.571024, "eq_id": 68, "name": "Second Law of Thermodynamics" }, { "coordinate": 0.468627, "eq_id": 593, "name": "Nernst Equation (Membrane Equilibrium Potential)" }, { "coordinate": 0.281256, "eq_id": 296, "name": "Boltzmann Distribution" }, { "coordinate": 0.263633, "eq_id": 300, "name": "Gibbs Entropy Formula" }, { "coordinate": -0.227656, "eq_id": 597, "name": "Cable Equation (Neuronal Dendrite/Axon)" }, { "coordinate": 0.223313, "eq_id": 247, "name": "Four-Factor Formula (Nuclear Reactor)" }, { "coordinate": 0.223313, "eq_id": 324, "name": "Landauer's Principle" }, { "coordinate": -0.216358, "eq_id": 502, "name": "Nernst Equation (Electrode Potential)" }, { "coordinate": -0.183268, "eq_id": 754, "name": "Primary Endosymbiosis \u2014 Mitochondrial and Plastid Acquisitio" }, { "coordinate": -0.148165, "eq_id": 742, "name": "Absolute Minimum Metabolic Rate for Sustained Life (~10\u207b\u00b3 to" } ] }, { "eigenvalue": 1.2785, "mode": 2, "num_nodes_below_threshold": 19, "top_nodes": [ { "coordinate": -0.571024, "eq_id": 68, "name": "Second Law of Thermodynamics" }, { "coordinate": -0.468627, "eq_id": 593, "name": "Nernst Equation (Membrane Equilibrium Potential)" }, { "coordinate": -0.281256, "eq_id": 296, "name": "Boltzmann Distribution" }, { "coordinate": -0.263633, "eq_id": 300, "name": "Gibbs Entropy Formula" }, { "coordinate": -0.227656, "eq_id": 597, "name": "Cable Equation (Neuronal Dendrite/Axon)" }, { "coordinate": -0.223313, "eq_id": 324, "name": "Landauer's Principle" }, { "coordinate": -0.223313, "eq_id": 247, "name": "Four-Factor Formula (Nuclear Reactor)" }, { "coordinate": -0.216358, "eq_id": 502, "name": "Nernst Equation (Electrode Potential)" }, { "coordinate": -0.183268, "eq_id": 754, "name": "Primary Endosymbiosis \u2014 Mitochondrial and Plastid Acquisitio" }, { "coordinate": -0.148165, "eq_id": 742, "name": "Absolute Minimum Metabolic Rate for Sustained Life (~10\u207b\u00b3 to" } ] }, { "eigenvalue": -1.1176, "mode": 3, "num_nodes_below_threshold": 10, "top_nodes": [ { "coordinate": -0.611076, "eq_id": 605, "name": "Arrhenius Equation (Chemical Reaction Rate)" }, { "coordinate": 0.477243, "eq_id": 241, "name": "Radioactive Decay Law" }, { "coordinate": 0.341813, "eq_id": 46, "name": "Kirchhoff's Current Law (KCL)" }, { "coordinate": 0.273394, "eq_id": 4, "name": "Hamilton-Jacobi Equation" }, { "coordinate": 0.273394, "eq_id": 738, "name": "Upper Temperature Limit of Carbon-Based Life (~122\u00b0C at dept" }, { "coordinate": -0.242116, "eq_id": 744, "name": "Long-Term Dormancy Survival Limit (~250 million years in sal" }, { "coordinate": -0.213518, "eq_id": 741, "name": "Maximum Ionizing Radiation Dose Survived (Deinococcus radiod" }, { "coordinate": -0.152926, "eq_id": 758, "name": "Explosive Biochemistry \u2014 Bombardier Beetle, Skunk Spray, Ven" }, { "coordinate": 0.063921, "eq_id": 773, "name": "Optimal DNA Sequence Compression (PIST/CFF Biological Analog" }, { "coordinate": -0.028598, "eq_id": 19, "name": "Damped Harmonic Oscillator" } ] }, { "eigenvalue": 1.083, "mode": 4, "num_nodes_below_threshold": 10, "top_nodes": [ { "coordinate": -0.623289, "eq_id": 605, "name": "Arrhenius Equation (Chemical Reaction Rate)" }, { "coordinate": -0.40892, "eq_id": 241, "name": "Radioactive Decay Law" }, { "coordinate": -0.365687, "eq_id": 46, "name": "Kirchhoff's Current Law (KCL)" }, { "coordinate": -0.287748, "eq_id": 738, "name": "Upper Temperature Limit of Carbon-Based Life (~122\u00b0C at dept" }, { "coordinate": -0.287748, "eq_id": 4, "name": "Hamilton-Jacobi Equation" }, { "coordinate": 0.249307, "eq_id": 773, "name": "Optimal DNA Sequence Compression (PIST/CFF Biological Analog" }, { "coordinate": -0.188782, "eq_id": 741, "name": "Maximum Ionizing Radiation Dose Survived (Deinococcus radiod" }, { "coordinate": -0.168823, "eq_id": 758, "name": "Explosive Biochemistry \u2014 Bombardier Beetle, Skunk Spray, Ven" }, { "coordinate": 0.115095, "eq_id": 19, "name": "Damped Harmonic Oscillator" }, { "coordinate": -0.073687, "eq_id": 744, "name": "Long-Term Dormancy Survival Limit (~250 million years in sal" } ] } ] }