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486 lines
115 KiB
JSON
486 lines
115 KiB
JSON
{"eq_number": 1, "title": "Newton's Three Laws of Motion", "domain": "Classical Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.937, "latency_ms": 10690.6, "timestamp": 1778000587.2790463}
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{"eq_number": 2, "title": "Lagrangian Mechanics (Principle of Least Action)", "domain": "Classical Mechanics", "confidence": 0.613, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.954, "latency_ms": 8249.3, "timestamp": 1778000595.5289366}
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{"eq_number": 3, "title": "Hamiltonian Mechanics", "domain": "Classical Mechanics", "confidence": 0.733, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.959, "latency_ms": 8842.4, "timestamp": 1778000604.3719544}
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{"eq_number": 4, "title": "Hamilton-Jacobi Equation", "domain": "Classical Mechanics", "confidence": 0.727, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.961, "latency_ms": 9021.6, "timestamp": 1778000613.3942285}
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{"eq_number": 5, "title": "Euler-Lagrange Equation", "domain": "Classical Mechanics", "confidence": 0.413, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.943, "latency_ms": 8261.2, "timestamp": 1778000621.6559424}
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{"eq_number": 6, "title": "D'Alembert's Principle", "domain": "Classical Mechanics", "confidence": 0.54, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 7767.7, "timestamp": 1778000629.4242077}
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{"eq_number": 7, "title": "Euler's Rigid Body Rotation Equations", "domain": "Classical Mechanics", "confidence": 0.64, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8442.4, "timestamp": 1778000637.867223}
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{"eq_number": 8, "title": "Conservation of Momentum", "domain": "Classical Mechanics", "confidence": 0.507, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.949, "latency_ms": 7859.6, "timestamp": 1778000645.7274272}
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{"eq_number": 9, "title": "Conservation of Angular Momentum", "domain": "Classical Mechanics", "confidence": 0.693, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8569.1, "timestamp": 1778000654.297167}
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{"eq_number": 10, "title": "Conservation of Energy", "domain": "Classical Mechanics", "confidence": 0.853, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.963, "latency_ms": 8597.1, "timestamp": 1778000662.8949628}
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{"eq_number": 11, "title": "Work-Energy Theorem", "domain": "Classical Mechanics", "confidence": 0.833, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.962, "latency_ms": 8687.0, "timestamp": 1778000671.5828052}
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{"eq_number": 12, "title": "Impulse-Momentum Theorem", "domain": "Classical Mechanics", "confidence": 0.787, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.921, "latency_ms": 8301.0, "timestamp": 1778000679.8844657}
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{"eq_number": 13, "title": "Center of Mass Equation", "domain": "Classical Mechanics", "confidence": 0.76, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8616.7, "timestamp": 1778000688.5023987}
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{"eq_number": 14, "title": "Hooke's Law", "domain": "Continuum Mechanics", "confidence": 0.6, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.953, "latency_ms": 7715.3, "timestamp": 1778000696.2185404}
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{"eq_number": 15, "title": "Parallel Axis Theorem", "domain": "Classical Mechanics", "confidence": 0.707, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8042.8, "timestamp": 1778000704.268881}
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{"eq_number": 16, "title": "Coriolis Force", "domain": "Classical Mechanics", "confidence": 0.713, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.958, "latency_ms": 8115.8, "timestamp": 1778000712.3853538}
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{"eq_number": 17, "title": "Centrifugal Force", "domain": "Classical Mechanics", "confidence": 0.793, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.922, "latency_ms": 8358.0, "timestamp": 1778000720.7439606}
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{"eq_number": 18, "title": "Simple Harmonic Motion", "domain": "Classical Mechanics", "confidence": 0.72, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.875, "latency_ms": 8666.3, "timestamp": 1778000729.4109201}
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{"eq_number": 19, "title": "Damped Harmonic Oscillator", "domain": "Classical Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10443.3, "timestamp": 1778000739.8553064}
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{"eq_number": 20, "title": "Forced Oscillator + Resonance", "domain": "Classical Mechanics", "confidence": 0.767, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9318.1, "timestamp": 1778000749.1741488}
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{"eq_number": 21, "title": "Coupled Oscillators (Normal Modes)", "domain": "Classical Mechanics", "confidence": 0.9, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9553.2, "timestamp": 1778000758.728175}
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{"eq_number": 22, "title": "Pendulum Equation", "domain": "Classical Mechanics", "confidence": 0.76, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8530.9, "timestamp": 1778000767.2599266}
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{"eq_number": 23, "title": "Kinematics (Constant Acceleration)", "domain": "Classical Mechanics", "confidence": 0.733, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 7888.1, "timestamp": 1778000775.1486905}
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{"eq_number": 24, "title": "Universal Gravitation Law", "domain": "Gravitation", "confidence": 0.32, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 7361.6, "timestamp": 1778000782.5107632}
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{"eq_number": 25, "title": "Gravitational Potential Energy", "domain": "Gravitation", "confidence": 0.907, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.964, "latency_ms": 9001.6, "timestamp": 1778000791.5130565}
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{"eq_number": 26, "title": "Kepler's First Law", "domain": "Gravitation", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.968, "latency_ms": 9086.8, "timestamp": 1778000800.6007283}
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{"eq_number": 27, "title": "Kepler's Second Law", "domain": "Gravitation", "confidence": 0.667, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8478.8, "timestamp": 1778000809.0801342}
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{"eq_number": 28, "title": "Kepler's Third Law", "domain": "Gravitation", "confidence": 0.833, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.924, "latency_ms": 8943.2, "timestamp": 1778000818.024078}
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{"eq_number": 29, "title": "Escape Velocity", "domain": "Gravitation", "confidence": 0.713, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.958, "latency_ms": 8080.2, "timestamp": 1778000826.104893}
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{"eq_number": 30, "title": "Orbital Velocity (Circular)", "domain": "Gravitation", "confidence": 0.433, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.888, "latency_ms": 7631.9, "timestamp": 1778000833.7379112}
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{"eq_number": 31, "title": "Poisson Equation (Gravity)", "domain": "Gravitation", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9613.8, "timestamp": 1778000843.3610344}
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{"eq_number": 32, "title": "Tidal Force", "domain": "Gravitation", "confidence": 0.567, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.952, "latency_ms": 7818.2, "timestamp": 1778000851.1798563}
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{"eq_number": 33, "title": "Gravitational Time Dilation (GR)", "domain": "Relativity", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 8458.7, "timestamp": 1778000859.639279}
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{"eq_number": 34, "title": "Precession of Perihelion (GR)", "domain": "Relativity", "confidence": 0.967, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9275.1, "timestamp": 1778000868.9150858}
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{"eq_number": 35, "title": "Lense-Thirring Precession (Frame Dragging)", "domain": "Relativity", "confidence": 0.953, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9596.4, "timestamp": 1778000878.5122268}
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{"eq_number": 36, "title": "Coulomb's Law", "domain": "Electromagnetism", "confidence": 0.527, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.859, "latency_ms": 8432.2, "timestamp": 1778000886.94504}
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{"eq_number": 37, "title": "Lorentz Force Law", "domain": "Electromagnetism", "confidence": 0.707, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.958, "latency_ms": 8210.1, "timestamp": 1778000895.1558251}
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{"eq_number": 38, "title": "Maxwell's Equations (Differential)", "domain": "Electromagnetism", "confidence": 0.907, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.965, "latency_ms": 9480.1, "timestamp": 1778000904.6366389}
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{"eq_number": 39, "title": "Maxwell's Equations (Integral)", "domain": "Electromagnetism", "confidence": 0.793, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8739.6, "timestamp": 1778000913.3768914}
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{"eq_number": 41, "title": "Scalar and Vector Potentials", "domain": "Electromagnetism", "confidence": 0.78, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.96, "latency_ms": 8246.6, "timestamp": 1778000931.6231956}
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{"eq_number": 42, "title": "Gauge Invariance (U(1) in E&M)", "domain": "Electromagnetism", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9115.2, "timestamp": 1778000940.7531054}
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{"eq_number": 43, "title": "Biot-Savart Law", "domain": "Electromagnetism", "confidence": 0.787, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8599.0, "timestamp": 1778000949.3528998}
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{"eq_number": 44, "title": "Amp\u00e8re's Force Law (Wire)", "domain": "Electromagnetism", "confidence": 0.733, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 7840.6, "timestamp": 1778000957.1940663}
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{"eq_number": 45, "title": "Ohm's Law", "domain": "Electromagnetism", "confidence": 0.273, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 6738.6, "timestamp": 1778000963.9330785}
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{"eq_number": 46, "title": "Kirchhoff's Current Law (KCL)", "domain": "Electromagnetism", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8699.6, "timestamp": 1778000972.6334705}
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{"eq_number": 47, "title": "Kirchhoff's Voltage Law (KVL)", "domain": "Electromagnetism", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.934, "latency_ms": 9326.7, "timestamp": 1778000981.960992}
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{"eq_number": 48, "title": "Faraday's Law of Induction", "domain": "Electromagnetism", "confidence": 0.733, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9344.7, "timestamp": 1778000991.3069863}
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{"eq_number": 49, "title": "Lenz's Law", "domain": "Electromagnetism", "confidence": 0.573, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.952, "latency_ms": 8679.4, "timestamp": 1778000999.9869442}
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{"eq_number": 50, "title": "Poynting's Theorem", "domain": "Electromagnetism", "confidence": 0.48, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.894, "latency_ms": 9488.0, "timestamp": 1778001009.4755282}
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{"eq_number": 51, "title": "Electromagnetic Wave Equation", "domain": "Electromagnetism", "confidence": 0.747, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9263.3, "timestamp": 1778001018.7466762}
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{"eq_number": 52, "title": "EM Stress-Energy Tensor", "domain": "Electromagnetism", "confidence": 0.8, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.961, "latency_ms": 9952.0, "timestamp": 1778001028.7064927}
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{"eq_number": 53, "title": "Lienard-Wiechert Potentials", "domain": "Electromagnetism", "confidence": 0.813, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.923, "latency_ms": 9096.2, "timestamp": 1778001037.8107345}
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{"eq_number": 54, "title": "Larmor Formula (Non-rel. Radiation)", "domain": "Electromagnetism", "confidence": 0.347, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8384.3, "timestamp": 1778001046.1955674}
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{"eq_number": 55, "title": "Li\u00e9nard Formula (Relativistic Radiation)", "domain": "Electromagnetism", "confidence": 0.707, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9575.7, "timestamp": 1778001055.7719162}
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{"eq_number": 56, "title": "Abraham-Lorentz Force (Radiation Reaction)", "domain": "Electromagnetism", "confidence": 0.72, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.875, "latency_ms": 9040.4, "timestamp": 1778001064.8251727}
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{"eq_number": 57, "title": "Coulomb Gauge", "domain": "Electromagnetism", "confidence": 0.847, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8261.9, "timestamp": 1778001073.0879598}
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{"eq_number": 58, "title": "Lorenz Gauge", "domain": "Electromagnetism", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9049.3, "timestamp": 1778001082.1449125}
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{"eq_number": 59, "title": "RC Circuit Charging", "domain": "Electromagnetism", "confidence": 0.68, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8354.1, "timestamp": 1778001090.4997146}
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{"eq_number": 70, "title": "Ideal Gas Law", "domain": "Thermodynamics", "confidence": 0.593, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.953, "latency_ms": 32432.8, "timestamp": 1778001723.5390487}
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{"eq_number": 73, "title": "Equipartition Theorem", "domain": "Thermodynamics", "confidence": 0.593, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 11562.9, "timestamp": 1778001855.2254863}
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{"eq_number": 75, "title": "Carnot Efficiency", "domain": "Thermodynamics", "confidence": 0.607, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 7915.6, "timestamp": 1778001923.203515}
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{"eq_number": 76, "title": "Clausius-Clapeyron Relation", "domain": "Thermodynamics", "confidence": 0.7, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8479.8, "timestamp": 1778001931.6840134}
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{"eq_number": 77, "title": "Gibbs Phase Rule", "domain": "Thermodynamics", "confidence": 0.653, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.956, "latency_ms": 7465.4, "timestamp": 1778001939.150097}
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{"eq_number": 78, "title": "Helmholtz Free Energy", "domain": "Thermodynamics", "confidence": 0.727, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.959, "latency_ms": 44476.0, "timestamp": 1778001983.626925}
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{"eq_number": 79, "title": "Gibbs Free Energy", "domain": "Thermodynamics", "confidence": 0.56, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.951, "latency_ms": 9436.4, "timestamp": 1778001993.0641665}
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{"eq_number": 80, "title": "Enthalpy", "domain": "Thermodynamics", "confidence": 0.68, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.957, "latency_ms": 9647.4, "timestamp": 1778002002.7122295}
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{"eq_number": 81, "title": "Maxwell Relations (Thermodynamics)", "domain": "Thermodynamics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 12883.2, "timestamp": 1778002015.5962934}
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{"eq_number": 82, "title": "TdS Equations", "domain": "Thermodynamics", "confidence": 0.607, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9466.0, "timestamp": 1778002025.0630102}
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{"eq_number": 83, "title": "Specific Heat Relations (C_p\u2212C_V)", "domain": "Thermodynamics", "confidence": 0.86, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9335.3, "timestamp": 1778002034.399068}
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{"eq_number": 84, "title": "Joule-Thomson Coefficient", "domain": "Thermodynamics", "confidence": 0.74, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.918, "latency_ms": 8852.3, "timestamp": 1778002043.2520776}
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{"eq_number": 85, "title": "Entropy of Mixing", "domain": "Thermodynamics", "confidence": 0.713, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 38341.0, "timestamp": 1778002081.6012244}
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{"eq_number": 86, "title": "Planck's Blackbody Radiation Law", "domain": "Quantum Mechanics", "confidence": 0.76, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 39192.4, "timestamp": 1778002120.7943082}
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{"eq_number": 87, "title": "Wien's Displacement Law", "domain": "Quantum Mechanics", "confidence": 0.767, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 39126.5, "timestamp": 1778002159.9215503}
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{"eq_number": 88, "title": "Stefan-Boltzmann Law", "domain": "Quantum Mechanics", "confidence": 0.587, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.953, "latency_ms": 39153.8, "timestamp": 1778002199.076018}
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{"eq_number": 89, "title": "Photoelectric Effect Equation (Einstein)", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 40607.6, "timestamp": 1778002239.6845338}
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{"eq_number": 90, "title": "Einstein A and B Coefficients", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.968, "latency_ms": 38549.4, "timestamp": 1778002278.2346976}
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{"eq_number": 91, "title": "Compton Scattering Formula", "domain": "Quantum Mechanics", "confidence": 0.747, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.959, "latency_ms": 41304.9, "timestamp": 1778002319.5402513}
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{"eq_number": 92, "title": "de Broglie Wavelength", "domain": "Quantum Mechanics", "confidence": 0.867, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.963, "latency_ms": 37709.8, "timestamp": 1778002357.2508836}
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{"eq_number": 93, "title": "Schr\u00f6dinger Equation (Time-Dependent)", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 43185.3, "timestamp": 1778002400.4369822}
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{"eq_number": 94, "title": "Time-Independent Schr\u00f6dinger Equation", "domain": "Quantum Mechanics", "confidence": 0.653, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 43518.9, "timestamp": 1778002443.9564981}
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{"eq_number": 95, "title": "Born Rule (Probability Interpretation)", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 38957.6, "timestamp": 1778002482.9151444}
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{"eq_number": 96, "title": "Probability Current (QM)", "domain": "Quantum Mechanics", "confidence": 0.813, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 36644.0, "timestamp": 1778002519.5599892}
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{"eq_number": 97, "title": "Canonical Commutation Relations", "domain": "Quantum Mechanics", "confidence": 0.8, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 41291.2, "timestamp": 1778002560.8518686}
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{"eq_number": 98, "title": "Heisenberg Uncertainty Principle", "domain": "Quantum Mechanics", "confidence": 0.947, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.966, "latency_ms": 10371.7, "timestamp": 1778002571.2244587}
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{"eq_number": 99, "title": "Harmonic Oscillator Energy Levels (QM)", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 12064.2, "timestamp": 1778002583.2896526}
|
|
{"eq_number": 100, "title": "Hydrogen Atom Energy Levels", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.968, "latency_ms": 9449.7, "timestamp": 1778002592.740342}
|
|
{"eq_number": 101, "title": "Angular Momentum Quantization", "domain": "Quantum Mechanics", "confidence": 0.9, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9284.0, "timestamp": 1778002602.0251167}
|
|
{"eq_number": 102, "title": "Spin-\u00bd Algebra (Pauli Matrices)", "domain": "Quantum Mechanics", "confidence": 0.8, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8683.9, "timestamp": 1778002610.7096524}
|
|
{"eq_number": 103, "title": "Spin-Orbit Coupling", "domain": "Quantum Mechanics", "confidence": 0.78, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.96, "latency_ms": 8472.2, "timestamp": 1778002619.1825795}
|
|
{"eq_number": 104, "title": "Dirac Equation", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8730.5, "timestamp": 1778002627.9140134}
|
|
{"eq_number": 105, "title": "Klein-Gordon Equation", "domain": "Quantum Mechanics", "confidence": 0.533, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.95, "latency_ms": 7986.7, "timestamp": 1778002635.9025846}
|
|
{"eq_number": 106, "title": "Fine Structure Formula (Hydrogen)", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10007.1, "timestamp": 1778002645.9104626}
|
|
{"eq_number": 107, "title": "Lamb Shift", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.912, "latency_ms": 9315.9, "timestamp": 1778002655.2273104}
|
|
{"eq_number": 108, "title": "Anomalous Magnetic Moment (Electron)", "domain": "Quantum Field Theory", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.949, "latency_ms": 10436.9, "timestamp": 1778002665.6651425}
|
|
{"eq_number": 109, "title": "Pauli Exclusion Principle", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.973, "latency_ms": 10547.0, "timestamp": 1778002676.2130554}
|
|
{"eq_number": 110, "title": "Spin-Statistics Theorem", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10934.7, "timestamp": 1778002687.148771}
|
|
{"eq_number": 111, "title": "Fermi's Golden Rule", "domain": "Quantum Mechanics", "confidence": 0.607, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.907, "latency_ms": 9685.0, "timestamp": 1778002696.841777}
|
|
{"eq_number": 112, "title": "Time-Dependent Perturbation Theory (1st Order)", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.97, "latency_ms": 17828.9, "timestamp": 1778002714.6794302}
|
|
{"eq_number": 113, "title": "WKB Approximation", "domain": "Quantum Mechanics", "confidence": 0.847, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.963, "latency_ms": 10023.5, "timestamp": 1778002724.7036636}
|
|
{"eq_number": 114, "title": "Born Approximation (Scattering)", "domain": "Quantum Mechanics", "confidence": 0.933, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.93, "latency_ms": 9679.5, "timestamp": 1778002734.3846166}
|
|
{"eq_number": 115, "title": "Partial Wave Expansion (Scattering)", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 9924.1, "timestamp": 1778002744.309858}
|
|
{"eq_number": 116, "title": "Optical Theorem", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 57721.5, "timestamp": 1778002802.0324078}
|
|
{"eq_number": 117, "title": "Feynman Path Integral", "domain": "Quantum Mechanics", "confidence": 0.793, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.922, "latency_ms": 52909.7, "timestamp": 1778002854.942773}
|
|
{"eq_number": 118, "title": "Von Neumann Equation", "domain": "Quantum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 53780.8, "timestamp": 1778002908.732054}
|
|
{"eq_number": 119, "title": "Ehrenfest Theorem", "domain": "Quantum Mechanics", "confidence": 0.8, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 56666.7, "timestamp": 1778002965.3994694}
|
|
{"eq_number": 120, "title": "Bell's Inequality", "domain": "Quantum Mechanics", "confidence": 0.8, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 55723.4, "timestamp": 1778003021.1235487}
|
|
{"eq_number": 121, "title": "Lorentz Transformations (Boost)", "domain": "Relativity", "confidence": 0.993, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 59557.1, "timestamp": 1778003080.6815033}
|
|
{"eq_number": 122, "title": "Minkowski Spacetime Interval", "domain": "Relativity", "confidence": 0.993, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 58261.4, "timestamp": 1778003138.9436605}
|
|
{"eq_number": 123, "title": "Time Dilation", "domain": "Relativity", "confidence": 0.58, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 49479.9, "timestamp": 1778003188.424197}
|
|
{"eq_number": 124, "title": "Length Contraction", "domain": "Relativity", "confidence": 0.84, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.963, "latency_ms": 53470.4, "timestamp": 1778003241.8953578}
|
|
{"eq_number": 125, "title": "Relativistic Energy-Momentum Relation", "domain": "Relativity", "confidence": 0.873, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 52493.3, "timestamp": 1778003294.3967922}
|
|
{"eq_number": 126, "title": "Mass-Energy Equivalence", "domain": "Relativity", "confidence": 0.587, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.953, "latency_ms": 52685.8, "timestamp": 1778003347.0831752}
|
|
{"eq_number": 127, "title": "Relativistic Doppler Effect", "domain": "Relativity", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.938, "latency_ms": 48702.0, "timestamp": 1778003395.7859945}
|
|
{"eq_number": 128, "title": "Relativistic Velocity Addition", "domain": "Relativity", "confidence": 0.753, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.921, "latency_ms": 51587.6, "timestamp": 1778003447.3743317}
|
|
{"eq_number": 129, "title": "Einstein Field Equations (GR)", "domain": "Relativity", "confidence": 0.82, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.968, "latency_ms": 59267.1, "timestamp": 1778003506.6422231}
|
|
{"eq_number": 130, "title": "Einstein-Hilbert Action", "domain": "Relativity", "confidence": 0.953, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 57727.7, "timestamp": 1778003564.3706262}
|
|
{"eq_number": 131, "title": "Schwarzschild Metric", "domain": "Relativity", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 58909.8, "timestamp": 1778003623.281542}
|
|
{"eq_number": 132, "title": "Kerr Metric (Rotating Black Hole)", "domain": "Relativity", "confidence": 0.96, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.931, "latency_ms": 57424.4, "timestamp": 1778003680.7067642}
|
|
{"eq_number": 133, "title": "FLRW Metric", "domain": "Relativity", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 59625.5, "timestamp": 1778003740.3329945}
|
|
{"eq_number": 134, "title": "Geodesic Equation", "domain": "Relativity", "confidence": 0.713, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.959, "latency_ms": 56995.8, "timestamp": 1778003797.3294668}
|
|
{"eq_number": 135, "title": "Gravitational Wave (TT Gauge)", "domain": "Relativity", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.968, "latency_ms": 57306.9, "timestamp": 1778003854.6372428}
|
|
{"eq_number": 136, "title": "Bekenstein-Hawking Black Hole Entropy", "domain": "Relativity", "confidence": 0.707, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.958, "latency_ms": 54494.1, "timestamp": 1778003909.1320248}
|
|
{"eq_number": 138, "title": "Black Hole Area Theorem (Hawking 1971)", "domain": "Relativity", "confidence": 0.853, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 56456.8, "timestamp": 1778004025.6586137}
|
|
{"eq_number": 144, "title": "QCD Beta Function (1-loop)", "domain": "Quantum Field Theory", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 58431.5, "timestamp": 1778004384.35102}
|
|
{"eq_number": 145, "title": "DGLAP Evolution Equations", "domain": "Quantum Field Theory", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 54970.1, "timestamp": 1778004439.3220289}
|
|
{"eq_number": 146, "title": "CKM Matrix (Quark Mixing)", "domain": "Quantum Field Theory", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 59586.6, "timestamp": 1778004498.9094288}
|
|
{"eq_number": 147, "title": "PMNS Matrix (Neutrino Mixing)", "domain": "Quantum Field Theory", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 58178.1, "timestamp": 1778004557.0884502}
|
|
{"eq_number": 148, "title": "Gell-Mann\u2013Oakes\u2013Renner Relation", "domain": "Quantum Field Theory", "confidence": 0.807, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.966, "latency_ms": 60007.6, "timestamp": 1778004617.096802}
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|
{"eq_number": 149, "title": "Higgs Mechanism (Mass Generation)", "domain": "Quantum Field Theory", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 57343.4, "timestamp": 1778004674.4410532}
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|
{"eq_number": 150, "title": "Weinberg Angle", "domain": "Quantum Field Theory", "confidence": 0.847, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.965, "latency_ms": 55025.4, "timestamp": 1778004729.4672465}
|
|
{"eq_number": 151, "title": "Faddeev-Popov Gauge Fixing + Ghosts", "domain": "Quantum Field Theory", "confidence": 0.647, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.911, "latency_ms": 59637.0, "timestamp": 1778004789.1124141}
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|
{"eq_number": 152, "title": "BRST Symmetry", "domain": "Quantum Field Theory", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.973, "latency_ms": 58763.0, "timestamp": 1778004847.8762667}
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|
{"eq_number": 153, "title": "Running Coupling (RGE, General)", "domain": "Quantum Field Theory", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 57848.0, "timestamp": 1778004905.7251341}
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|
{"eq_number": 154, "title": "Fermi's Theory (4-Fermion, Low-Energy EW)", "domain": "Quantum Field Theory", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 57103.5, "timestamp": 1778004962.8296578}
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|
{"eq_number": 155, "title": "Pati-Salam Model (SU(4)\u00d7SU(2)\u00d7SU(2))", "domain": "Quantum Field Theory", "confidence": 0.847, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.964, "latency_ms": 60002.5, "timestamp": 1778005022.8329597}
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|
{"eq_number": 157, "title": "Axion (Peccei-Quinn Solution to Strong CP)", "domain": "Quantum Field Theory", "confidence": 0.987, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.966, "latency_ms": 58459.8, "timestamp": 1778005141.3542378}
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|
{"eq_number": 158, "title": "Muon g\u22122 Anomaly", "domain": "Quantum Field Theory", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 59027.2, "timestamp": 1778005200.3823879}
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|
{"eq_number": 159, "title": "First Friedmann Equation", "domain": "Cosmology", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 59108.0, "timestamp": 1778005259.498171}
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|
{"eq_number": 160, "title": "Second Friedmann Equation", "domain": "Cosmology", "confidence": 0.853, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.888, "latency_ms": 58423.1, "timestamp": 1778005317.9219673}
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|
{"eq_number": 161, "title": "Cosmological Fluid Equation", "domain": "Cosmology", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.973, "latency_ms": 58270.9, "timestamp": 1778005376.1937642}
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|
{"eq_number": 162, "title": "Redshift Relation", "domain": "Cosmology", "confidence": 0.947, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.931, "latency_ms": 58946.8, "timestamp": 1778005435.1484766}
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|
{"eq_number": 163, "title": "Hubble-Lema\u00eetre Law", "domain": "Cosmology", "confidence": 0.64, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.91, "latency_ms": 56357.8, "timestamp": 1778005491.5068924}
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|
{"eq_number": 164, "title": "CMB Blackbody Spectrum", "domain": "Cosmology", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.95, "latency_ms": 59095.2, "timestamp": 1778005550.6102736}
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|
{"eq_number": 165, "title": "BBN Primordial Element Abundances", "domain": "Cosmology", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 55418.7, "timestamp": 1778005606.029902}
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|
{"eq_number": 166, "title": "Sound Horizon at Recombination", "domain": "Cosmology", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 55387.1, "timestamp": 1778005661.417889}
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|
{"eq_number": 167, "title": "Sachs-Wolfe Effect (CMB)", "domain": "Cosmology", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 56948.3, "timestamp": 1778005718.3670247}
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|
{"eq_number": 168, "title": "Dark Energy Equation of State", "domain": "Cosmology", "confidence": 0.767, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 56684.8, "timestamp": 1778005775.0524945}
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|
{"eq_number": 169, "title": "Deceleration Parameter", "domain": "Cosmology", "confidence": 0.98, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.966, "latency_ms": 53190.5, "timestamp": 1778005828.2437108}
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|
{"eq_number": 170, "title": "Matter Power Spectrum", "domain": "Cosmology", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 58817.7, "timestamp": 1778005887.0622334}
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|
{"eq_number": 171, "title": "Cosmic Distance Ladder Relations", "domain": "Cosmology", "confidence": 0.907, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 59072.7, "timestamp": 1778005946.1356359}
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|
{"eq_number": 173, "title": "Hubble Tension", "domain": "Cosmology", "confidence": 0.827, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.924, "latency_ms": 58547.8, "timestamp": 1778006064.7521477}
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|
{"eq_number": 174, "title": "S\u2088 Tension", "domain": "Cosmology", "confidence": 0.973, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 56291.8, "timestamp": 1778006121.044695}
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|
{"eq_number": 175, "title": "Age of the Universe", "domain": "Cosmology", "confidence": 0.887, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 58001.1, "timestamp": 1778006179.0465605}
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|
{"eq_number": 176, "title": "Navier-Stokes Equation (Incompressible)", "domain": "Fluid Dynamics", "confidence": 0.807, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 55429.9, "timestamp": 1778006234.4771554}
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|
{"eq_number": 177, "title": "Continuity Equation (Fluid)", "domain": "Fluid Dynamics", "confidence": 0.58, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.952, "latency_ms": 56210.5, "timestamp": 1778006290.6882002}
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|
{"eq_number": 178, "title": "Euler Equation (Inviscid)", "domain": "Fluid Dynamics", "confidence": 0.693, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.959, "latency_ms": 55711.3, "timestamp": 1778006346.400203}
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|
{"eq_number": 179, "title": "Bernoulli's Equation", "domain": "Fluid Dynamics", "confidence": 0.407, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 56572.8, "timestamp": 1778006402.9735894}
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|
{"eq_number": 180, "title": "Stokes Law (Drag on Sphere)", "domain": "Fluid Dynamics", "confidence": 0.74, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.96, "latency_ms": 59491.7, "timestamp": 1778006462.4659727}
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|
{"eq_number": 181, "title": "Poiseuille Flow (Hagen-Poiseuille)", "domain": "Fluid Dynamics", "confidence": 0.593, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.955, "latency_ms": 59968.0, "timestamp": 1778006522.434666}
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|
{"eq_number": 182, "title": "Reynolds Number", "domain": "Fluid Dynamics", "confidence": 0.66, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.959, "latency_ms": 57988.2, "timestamp": 1778006580.4234772}
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|
{"eq_number": 184, "title": "Froude Number", "domain": "Fluid Dynamics", "confidence": 0.667, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 58991.8, "timestamp": 1778006699.477222}
|
|
{"eq_number": 186, "title": "Kutta-Joukowski Theorem (Lift)", "domain": "Fluid Dynamics", "confidence": 0.853, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.963, "latency_ms": 59003.2, "timestamp": 1778006818.5417702}
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|
{"eq_number": 187, "title": "Torricelli's Law (Efflux Speed)", "domain": "Fluid Dynamics", "confidence": 0.14, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 53209.4, "timestamp": 1778006871.7515805}
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|
{"eq_number": 189, "title": "Surface Tension (Young-Laplace)", "domain": "Fluid Dynamics", "confidence": 0.667, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.956, "latency_ms": 57846.3, "timestamp": 1778006989.6596203}
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|
{"eq_number": 192, "title": "Thin Lens Equation", "domain": "Optics", "confidence": 0.553, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 58154.3, "timestamp": 1778007167.9379015}
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|
{"eq_number": 198, "title": "Grating Equation", "domain": "Optics", "confidence": 0.667, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 55042.3, "timestamp": 1778007523.2973301}
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|
{"eq_number": 202, "title": "Malus's Law", "domain": "Optics", "confidence": 0.7, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.959, "latency_ms": 58590.0, "timestamp": 1778007762.0664883}
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|
{"eq_number": 204, "title": "Abbe Sine Condition", "domain": "Optics", "confidence": 0.607, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 58887.0, "timestamp": 1778007881.0153637}
|
|
{"eq_number": 206, "title": "Fermat's Principle of Least Time", "domain": "Optics", "confidence": 0.9, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 59208.1, "timestamp": 1778008000.2915094}
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|
{"eq_number": 208, "title": "Fabry-P\u00e9rot Etalon Transmission", "domain": "Optics", "confidence": 0.787, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.885, "latency_ms": 59740.1, "timestamp": 1778008120.1004853}
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{"eq_number": 209, "title": "Critical Angle (Total Internal Reflection)", "domain": "Optics", "confidence": 0.54, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.95, "latency_ms": 59039.7, "timestamp": 1778008179.1413743}
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{"eq_number": 215, "title": "Shock Wave Rankine-Hugoniot Relations", "domain": "Acoustics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 59443.1, "timestamp": 1778008538.8699293}
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{"eq_number": 216, "title": "Beat Frequency", "domain": "Acoustics", "confidence": 0.54, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.95, "latency_ms": 57731.7, "timestamp": 1778008596.6022267}
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{"eq_number": 220, "title": "Kronig-Penney Model (1D Band Structure)", "domain": "Condensed Matter", "confidence": 0.54, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 59538.5, "timestamp": 1778008836.335085}
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{"eq_number": 221, "title": "Fermi-Dirac Distribution", "domain": "Condensed Matter", "confidence": 0.907, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.964, "latency_ms": 55499.3, "timestamp": 1778008891.8352258}
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{"eq_number": 222, "title": "Free Electron Density of States", "domain": "Condensed Matter", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 59815.6, "timestamp": 1778008951.6516204}
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{"eq_number": 224, "title": "BCS Theory (Superconductivity)", "domain": "Condensed Matter", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 57707.8, "timestamp": 1778009069.4212708}
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{"eq_number": 225, "title": "BCS Gap Equation at T=0", "domain": "Condensed Matter", "confidence": 0.78, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.96, "latency_ms": 58072.3, "timestamp": 1778009127.4942982}
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{"eq_number": 226, "title": "London Equations (Perfect Diamagnetism)", "domain": "Condensed Matter", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.933, "latency_ms": 57479.0, "timestamp": 1778009184.9741225}
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{"eq_number": 227, "title": "Josephson Effects (DC + AC)", "domain": "Condensed Matter", "confidence": 0.453, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.842, "latency_ms": 56894.8, "timestamp": 1778009241.8695993}
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{"eq_number": 228, "title": "Curie's Law (Paramagnetism)", "domain": "Condensed Matter", "confidence": 0.72, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 59950.1, "timestamp": 1778009301.8206081}
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{"eq_number": 230, "title": "Heisenberg Exchange Interaction", "domain": "Condensed Matter", "confidence": 0.907, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.964, "latency_ms": 55761.1, "timestamp": 1778009417.63997}
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{"eq_number": 234, "title": "Hall Effect", "domain": "Condensed Matter", "confidence": 0.567, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 59747.6, "timestamp": 1778009657.5730996}
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{"eq_number": 237, "title": "Debye Model (Lattice Heat Capacity)", "domain": "Condensed Matter", "confidence": 0.66, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 59500.7, "timestamp": 1778009837.2017295}
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{"eq_number": 238, "title": "Mott Insulator Transition", "domain": "Condensed Matter", "confidence": 0.967, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 49482.8, "timestamp": 1778009886.6854057}
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{"eq_number": 239, "title": "Density Functional Theory (Kohn-Sham Equations)", "domain": "Condensed Matter", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10027.0, "timestamp": 1778009896.7132208}
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{"eq_number": 240, "title": "Landau Fermi Liquid Theory", "domain": "Condensed Matter", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.975, "latency_ms": 12293.9, "timestamp": 1778009909.0081477}
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{"eq_number": 241, "title": "Radioactive Decay Law", "domain": "Nuclear Physics", "confidence": 0.76, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 9704.5, "timestamp": 1778009918.7132866}
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{"eq_number": 242, "title": "Bethe-Weizs\u00e4cker (Semi-Empirical) Mass Formula", "domain": "Nuclear Physics", "confidence": 0.913, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9731.1, "timestamp": 1778009928.4451723}
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{"eq_number": 243, "title": "Geiger-Nuttall Law (\u03b1-Decay)", "domain": "Nuclear Physics", "confidence": 0.56, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8154.7, "timestamp": 1778009936.6004722}
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{"eq_number": 244, "title": "Nuclear Shell Model (Magic Numbers)", "domain": "Nuclear Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 9501.2, "timestamp": 1778009946.1028907}
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{"eq_number": 245, "title": "Q-Value of Nuclear Reaction", "domain": "Nuclear Physics", "confidence": 0.913, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9421.0, "timestamp": 1778009955.524634}
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{"eq_number": 246, "title": "Neutrino Oscillation Probability", "domain": "Nuclear Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10870.4, "timestamp": 1778009966.3963568}
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{"eq_number": 247, "title": "Four-Factor Formula (Nuclear Reactor)", "domain": "Nuclear Physics", "confidence": 0.98, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.932, "latency_ms": 9383.3, "timestamp": 1778009975.7806811}
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{"eq_number": 248, "title": "Rutherford Scattering Cross-Section", "domain": "Nuclear Physics", "confidence": 0.96, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9398.5, "timestamp": 1778009985.1801646}
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{"eq_number": 249, "title": "M\u00f6ssbauer Effect (Recoilless \u03b3 Emission)", "domain": "Nuclear Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.974, "latency_ms": 10726.2, "timestamp": 1778009995.9077904}
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{"eq_number": 250, "title": "Breit-Wigner Resonance (Nuclear Reactions)", "domain": "Nuclear Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 12048.7, "timestamp": 1778010007.9575863}
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{"eq_number": 251, "title": "Lane-Emden Equation (Polytropic Stars)", "domain": "Astrophysics", "confidence": 0.94, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.966, "latency_ms": 10865.8, "timestamp": 1778010018.824427}
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{"eq_number": 252, "title": "Eddington Luminosity Limit", "domain": "Astrophysics", "confidence": 0.633, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10067.0, "timestamp": 1778010028.8923213}
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{"eq_number": 253, "title": "Chandrasekhar Limit (White Dwarf)", "domain": "Astrophysics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9476.6, "timestamp": 1778010038.3697095}
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{"eq_number": 254, "title": "TOV Limit (Neutron Star Maximum Mass)", "domain": "Astrophysics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9578.7, "timestamp": 1778010047.9493976}
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{"eq_number": 255, "title": "Hertzsprung-Russell Diagram + Main Sequence", "domain": "Astrophysics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10497.0, "timestamp": 1778010058.4472852}
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{"eq_number": 256, "title": "Mass-Luminosity Relation", "domain": "Astrophysics", "confidence": 0.807, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.961, "latency_ms": 9727.4, "timestamp": 1778010068.1755323}
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{"eq_number": 257, "title": "Virial Theorem (Astrophysics)", "domain": "Astrophysics", "confidence": 0.613, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 7924.8, "timestamp": 1778010076.1009526}
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{"eq_number": 258, "title": "Jeans Instability Criterion (Star Formation)", "domain": "Astrophysics", "confidence": 0.847, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.964, "latency_ms": 10275.8, "timestamp": 1778010086.3774498}
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{"eq_number": 259, "title": "Schwarzschild Criterion (Convection)", "domain": "Astrophysics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9864.1, "timestamp": 1778010096.2425168}
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{"eq_number": 260, "title": "pp Chain Energy Release", "domain": "Astrophysics", "confidence": 0.86, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9495.6, "timestamp": 1778010105.7388756}
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{"eq_number": 261, "title": "CNO Cycle (Massive Stars)", "domain": "Astrophysics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10800.5, "timestamp": 1778010116.5402277}
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{"eq_number": 262, "title": "Triple-Alpha Process (Helium Burning)", "domain": "Astrophysics", "confidence": 0.867, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.926, "latency_ms": 10689.2, "timestamp": 1778010127.230202}
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{"eq_number": 263, "title": "Core-Collapse Supernova Mechanism", "domain": "Astrophysics", "confidence": 0.833, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.962, "latency_ms": 9263.6, "timestamp": 1778010136.4945765}
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{"eq_number": 264, "title": "Type Ia Supernova (Standardizable Candle)", "domain": "Astrophysics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10776.4, "timestamp": 1778010147.2725644}
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{"eq_number": 265, "title": "Neutron Star Equation of State (Various)", "domain": "Astrophysics", "confidence": 0.993, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.933, "latency_ms": 8845.6, "timestamp": 1778010156.1191223}
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{"eq_number": 266, "title": "Oppenheimer-Snyder Collapse (BH Formation)", "domain": "Astrophysics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9069.8, "timestamp": 1778010165.1898322}
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{"eq_number": 267, "title": "Pulsar Spin-Down", "domain": "Astrophysics", "confidence": 0.767, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9490.7, "timestamp": 1778010174.6814039}
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{"eq_number": 268, "title": "Olbers' Paradox Resolution", "domain": "Astrophysics", "confidence": 0.827, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.962, "latency_ms": 8638.7, "timestamp": 1778010183.3209875}
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{"eq_number": 269, "title": "Debye Length (Plasma Screening)", "domain": "Plasma Physics", "confidence": 0.673, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 8871.4, "timestamp": 1778010192.1930668}
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{"eq_number": 270, "title": "Plasma Frequency", "domain": "Plasma Physics", "confidence": 0.773, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.96, "latency_ms": 9233.5, "timestamp": 1778010201.4272034}
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{"eq_number": 271, "title": "Alfv\u00e9n Wave Speed", "domain": "Plasma Physics", "confidence": 0.76, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.883, "latency_ms": 8606.3, "timestamp": 1778010210.0341206}
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{"eq_number": 272, "title": "MHD Induction Equation", "domain": "Plasma Physics", "confidence": 0.793, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8802.2, "timestamp": 1778010218.836984}
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{"eq_number": 273, "title": "Saha Ionization Equation", "domain": "Plasma Physics", "confidence": 0.673, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.957, "latency_ms": 8868.9, "timestamp": 1778010227.7064636}
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|
{"eq_number": 274, "title": "Gyro-frequency (Larmor Frequency)", "domain": "Plasma Physics", "confidence": 0.753, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.919, "latency_ms": 8587.9, "timestamp": 1778010236.2953727}
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{"eq_number": 275, "title": "Beta Parameter (Plasma Confinement)", "domain": "Plasma Physics", "confidence": 0.813, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9435.0, "timestamp": 1778010245.731135}
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{"eq_number": 276, "title": "Lawson Criterion (Fusion Ignition)", "domain": "Plasma Physics", "confidence": 0.807, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9863.5, "timestamp": 1778010255.5952601}
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{"eq_number": 277, "title": "Noether's Theorem", "domain": "Mathematical Physics", "confidence": 0.907, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.964, "latency_ms": 9333.2, "timestamp": 1778010264.9292564}
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{"eq_number": 278, "title": "Stokes' Theorem", "domain": "Mathematical Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.969, "latency_ms": 10075.5, "timestamp": 1778010275.0055413}
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{"eq_number": 279, "title": "Gauss's Divergence Theorem", "domain": "Mathematical Physics", "confidence": 0.88, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9789.1, "timestamp": 1778010284.795322}
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{"eq_number": 280, "title": "Green's Theorem (2D)", "domain": "Mathematical Physics", "confidence": 0.993, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.97, "latency_ms": 12074.0, "timestamp": 1778010296.870198}
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{"eq_number": 281, "title": "Fourier Transform", "domain": "Mathematical Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10180.6, "timestamp": 1778010307.051627}
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{"eq_number": 282, "title": "Laplace's Equation", "domain": "Mathematical Physics", "confidence": 0.787, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8958.7, "timestamp": 1778010316.0109994}
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{"eq_number": 283, "title": "Poisson's Equation", "domain": "Mathematical Physics", "confidence": 0.653, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.96, "latency_ms": 9877.6, "timestamp": 1778010325.8892875}
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{"eq_number": 284, "title": "Bessel's Equation", "domain": "Mathematical Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 12181.1, "timestamp": 1778010338.0714188}
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{"eq_number": 285, "title": "Legendre's Equation", "domain": "Mathematical Physics", "confidence": 0.113, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9120.0, "timestamp": 1778010347.1918802}
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{"eq_number": 286, "title": "Hermite's Equation", "domain": "Mathematical Physics", "confidence": 0.167, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.93, "latency_ms": 9310.9, "timestamp": 1778010356.5032876}
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{"eq_number": 287, "title": "Associated Legendre Equation", "domain": "Mathematical Physics", "confidence": 0.96, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.931, "latency_ms": 9772.9, "timestamp": 1778010366.2768764}
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{"eq_number": 288, "title": "Chebyshev Polynomials", "domain": "Mathematical Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.948, "latency_ms": 10737.7, "timestamp": 1778010377.0154507}
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{"eq_number": 289, "title": "Laguerre Polynomials", "domain": "Mathematical Physics", "confidence": 0.687, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.917, "latency_ms": 9106.1, "timestamp": 1778010386.122187}
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{"eq_number": 290, "title": "Spherical Harmonics (Y_l^m)", "domain": "Mathematical Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.972, "latency_ms": 11207.0, "timestamp": 1778010397.3299985}
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|
{"eq_number": 291, "title": "Gamma Function", "domain": "Mathematical Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10058.5, "timestamp": 1778010407.389363}
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{"eq_number": 292, "title": "Error Function", "domain": "Mathematical Physics", "confidence": 0.967, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9454.0, "timestamp": 1778010416.8441417}
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|
{"eq_number": 293, "title": "Delta Function (Dirac)", "domain": "Mathematical Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9423.5, "timestamp": 1778010426.2684288}
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{"eq_number": 294, "title": "Eigenvalue Equation", "domain": "Mathematical Physics", "confidence": 0.413, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 7872.0, "timestamp": 1778010434.141181}
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|
{"eq_number": 295, "title": "Separation of Variables Method", "domain": "Mathematical Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.938, "latency_ms": 10025.0, "timestamp": 1778010444.166974}
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|
{"eq_number": 296, "title": "Boltzmann Distribution", "domain": "Statistical Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 10163.8, "timestamp": 1778010454.3317337}
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|
{"eq_number": 297, "title": "Canonical Partition Function", "domain": "Statistical Mechanics", "confidence": 0.933, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9022.5, "timestamp": 1778010463.355048}
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|
{"eq_number": 298, "title": "Grand Canonical Partition Function", "domain": "Statistical Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.968, "latency_ms": 10507.7, "timestamp": 1778010473.8636403}
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|
{"eq_number": 299, "title": "Boltzmann Entropy Formula", "domain": "Statistical Mechanics", "confidence": 0.8, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.922, "latency_ms": 9483.0, "timestamp": 1778010483.3474507}
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|
{"eq_number": 300, "title": "Gibbs Entropy Formula", "domain": "Statistical Mechanics", "confidence": 0.887, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10028.4, "timestamp": 1778010493.3766298}
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|
{"eq_number": 301, "title": "Fluctuation-Dissipation Theorem", "domain": "Statistical Mechanics", "confidence": 0.28, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8725.8, "timestamp": 1778010502.102973}
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|
{"eq_number": 302, "title": "Einstein-Smoluchowski Relation (Diffusion)", "domain": "Statistical Mechanics", "confidence": 0.98, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.966, "latency_ms": 9982.3, "timestamp": 1778010512.0860043}
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|
{"eq_number": 303, "title": "Jarzynski Equality", "domain": "Statistical Mechanics", "confidence": 0.973, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.966, "latency_ms": 9894.3, "timestamp": 1778010521.9810646}
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|
{"eq_number": 304, "title": "Crooks Fluctuation Theorem", "domain": "Statistical Mechanics", "confidence": 0.84, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.962, "latency_ms": 10463.6, "timestamp": 1778010532.4455519}
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|
{"eq_number": 305, "title": "Ising Model (1D/2D Exact Solution)", "domain": "Statistical Mechanics", "confidence": 0.733, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9202.8, "timestamp": 1778010541.6490362}
|
|
{"eq_number": 306, "title": "Central Limit Theorem (Statistical)", "domain": "Statistical Mechanics", "confidence": 0.873, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.9, "latency_ms": 9645.9, "timestamp": 1778010551.2957015}
|
|
{"eq_number": 307, "title": "Bose-Einstein Condensation (T_c)", "domain": "Statistical Mechanics", "confidence": 0.813, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9507.1, "timestamp": 1778010560.803518}
|
|
{"eq_number": 308, "title": "Kramers-Kronig Relations (Dispersion)", "domain": "Statistical Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.968, "latency_ms": 9275.1, "timestamp": 1778010570.079424}
|
|
{"eq_number": 309, "title": "Cauchy Stress Principle", "domain": "Continuum Mechanics", "confidence": 0.527, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.899, "latency_ms": 8701.7, "timestamp": 1778010578.7817893}
|
|
{"eq_number": 311, "title": "Infinitesimal Strain Tensor", "domain": "Continuum Mechanics", "confidence": 0.947, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.931, "latency_ms": 9323.5, "timestamp": 1778010597.8468144}
|
|
{"eq_number": 312, "title": "Young's Modulus / Elastic Modulus", "domain": "Continuum Mechanics", "confidence": 0.88, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9285.9, "timestamp": 1778010607.136359}
|
|
{"eq_number": 313, "title": "Shear Modulus", "domain": "Continuum Mechanics", "confidence": 0.933, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.965, "latency_ms": 9799.6, "timestamp": 1778010616.936717}
|
|
{"eq_number": 314, "title": "Bulk Modulus", "domain": "Continuum Mechanics", "confidence": 0.773, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.92, "latency_ms": 8945.9, "timestamp": 1778010625.8832462}
|
|
{"eq_number": 315, "title": "Poisson's Ratio", "domain": "Continuum Mechanics", "confidence": 0.733, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9442.2, "timestamp": 1778010635.3263562}
|
|
{"eq_number": 316, "title": "Euler-Bernoulli Beam Equation", "domain": "Continuum Mechanics", "confidence": 0.747, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10366.3, "timestamp": 1778010645.6939628}
|
|
{"eq_number": 317, "title": "Timoshenko Beam Theory", "domain": "Continuum Mechanics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 10539.0, "timestamp": 1778010656.2337294}
|
|
{"eq_number": 318, "title": "Elastic Wave Speeds (P and S waves)", "domain": "Continuum Mechanics", "confidence": 0.853, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.965, "latency_ms": 11250.8, "timestamp": 1778010667.4855223}
|
|
{"eq_number": 319, "title": "Creep / Viscoelastic Maxwell Model", "domain": "Continuum Mechanics", "confidence": 0.86, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.892, "latency_ms": 10330.9, "timestamp": 1778010677.8172107}
|
|
{"eq_number": 320, "title": "Plastic Yield (Von Mises Criterion)", "domain": "Continuum Mechanics", "confidence": 0.827, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.935, "latency_ms": 11161.1, "timestamp": 1778010688.9792762}
|
|
{"eq_number": 321, "title": "Shannon Entropy", "domain": "Information Theory", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 10049.2, "timestamp": 1778010699.0293646}
|
|
{"eq_number": 322, "title": "Shannon-Hartley Channel Capacity", "domain": "Information Theory", "confidence": 0.527, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8620.5, "timestamp": 1778010707.6504655}
|
|
{"eq_number": 323, "title": "Nyquist-Shannon Sampling Theorem", "domain": "Information Theory", "confidence": 0.587, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8025.7, "timestamp": 1778010715.6767123}
|
|
{"eq_number": 324, "title": "Landauer's Principle", "domain": "Information Theory", "confidence": 0.967, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8821.3, "timestamp": 1778010724.4988563}
|
|
{"eq_number": 325, "title": "Kolmogorov Complexity (Algorithmic Info)", "domain": "Information Theory", "confidence": 0.8, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8556.1, "timestamp": 1778010733.0560837}
|
|
{"eq_number": 326, "title": "Maximum Entropy Principle (Jaynes)", "domain": "Information Theory", "confidence": 0.827, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.962, "latency_ms": 8254.7, "timestamp": 1778010741.3118227}
|
|
{"eq_number": 327, "title": "Speed of Light Defines Meter", "domain": "Metrology", "confidence": 0.687, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.958, "latency_ms": 8251.0, "timestamp": 1778010749.5634937}
|
|
{"eq_number": 328, "title": "Planck Constant Defines Kilogram", "domain": "Metrology", "confidence": 0.667, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 7976.3, "timestamp": 1778010757.5404313}
|
|
{"eq_number": 329, "title": "Elementary Charge Defines Ampere", "domain": "Metrology", "confidence": 0.76, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 7940.0, "timestamp": 1778010765.481104}
|
|
{"eq_number": 330, "title": "Boltzmann Constant Defines Kelvin", "domain": "Metrology", "confidence": 0.88, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.964, "latency_ms": 8325.6, "timestamp": 1778010773.8074584}
|
|
{"eq_number": 331, "title": "Avogadro Number Defines Mole", "domain": "Metrology", "confidence": 0.893, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8367.9, "timestamp": 1778010782.1760848}
|
|
{"eq_number": 332, "title": "Josephson Voltage Standard", "domain": "Condensed Matter", "confidence": 0.62, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 7831.7, "timestamp": 1778010790.0084906}
|
|
{"eq_number": 333, "title": "Quantum Hall Resistance Standard", "domain": "Condensed Matter", "confidence": 0.893, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.964, "latency_ms": 8340.3, "timestamp": 1778010798.3495305}
|
|
{"eq_number": 334, "title": "Bragg's Law (Generalized, Powder Diffraction)", "domain": "Crystallography", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.946, "latency_ms": 9759.5, "timestamp": 1778010808.1099377}
|
|
{"eq_number": 335, "title": "Laue Equations (3D Diffraction Condition)", "domain": "Crystallography", "confidence": 0.787, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8480.6, "timestamp": 1778010816.5914373}
|
|
{"eq_number": 336, "title": "Structure Factor Equation", "domain": "Crystallography", "confidence": 0.9, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.928, "latency_ms": 8743.3, "timestamp": 1778010825.3354895}
|
|
{"eq_number": 337, "title": "Atomic Scattering Factor (X-ray Form Factor)", "domain": "Crystallography", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 8721.9, "timestamp": 1778010834.0581462}
|
|
{"eq_number": 338, "title": "Reciprocal Lattice Vector Definition", "domain": "Crystallography", "confidence": 0.86, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.963, "latency_ms": 9540.3, "timestamp": 1778010843.5992358}
|
|
{"eq_number": 339, "title": "Brillouin Zone Boundaries", "domain": "Crystallography", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9589.7, "timestamp": 1778010853.1898859}
|
|
{"eq_number": 340, "title": "Ewald Sphere Construction", "domain": "Crystallography", "confidence": 0.847, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.963, "latency_ms": 8764.4, "timestamp": 1778010861.9550562}
|
|
{"eq_number": 341, "title": "Patterson Function (Interatomic Vectors)", "domain": "Crystallography", "confidence": 0.88, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.891, "latency_ms": 9888.7, "timestamp": 1778010871.844483}
|
|
{"eq_number": 342, "title": "Debye-Waller Factor (Thermal Motion)", "domain": "Crystallography", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 11450.0, "timestamp": 1778010883.2956815}
|
|
{"eq_number": 343, "title": "Space Group Symmetry Operations", "domain": "Crystallography", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9253.8, "timestamp": 1778010892.5503001}
|
|
{"eq_number": 344, "title": "Interplanar Spacing (Cubic Systems)", "domain": "Crystallography", "confidence": 0.74, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.959, "latency_ms": 9615.2, "timestamp": 1778010902.16621}
|
|
{"eq_number": 345, "title": "Scherrer Equation (Crystallite Size)", "domain": "Crystallography", "confidence": 0.753, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.964, "latency_ms": 10340.0, "timestamp": 1778010912.5071893}
|
|
{"eq_number": 346, "title": "Williamson-Hall Analysis (Size + Strain)", "domain": "Crystallography", "confidence": 0.973, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 10689.4, "timestamp": 1778010923.1973867}
|
|
{"eq_number": 347, "title": "True Stress \u2014 True Strain Definition", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 11487.3, "timestamp": 1778010934.6855748}
|
|
{"eq_number": 348, "title": "Hollomon Equation (Work Hardening)", "domain": "Material Physics", "confidence": 0.513, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.951, "latency_ms": 9841.5, "timestamp": 1778010944.5278018}
|
|
{"eq_number": 349, "title": "Hall-Petch Relationship (Grain Size Strengthening)", "domain": "Material Physics", "confidence": 0.773, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10147.1, "timestamp": 1778010954.6756072}
|
|
{"eq_number": 350, "title": "Orowan Equation (Precipitation Strengthening)", "domain": "Material Physics", "confidence": 0.813, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10331.0, "timestamp": 1778010965.0072937}
|
|
{"eq_number": 351, "title": "Schmid's Law (Critical Resolved Shear Stress)", "domain": "Material Physics", "confidence": 0.847, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.963, "latency_ms": 10148.5, "timestamp": 1778010975.1565285}
|
|
{"eq_number": 352, "title": "Taylor Equation (Dislocation Strengthening)", "domain": "Material Physics", "confidence": 0.793, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10582.2, "timestamp": 1778010985.7395117}
|
|
{"eq_number": 353, "title": "Petch-Forwood Hardness-Yield Strength Relation", "domain": "Material Physics", "confidence": 0.54, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9072.5, "timestamp": 1778010994.8125806}
|
|
{"eq_number": 354, "title": "Griffith Criterion (Brittle Fracture)", "domain": "Material Physics", "confidence": 0.287, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.938, "latency_ms": 7782.9, "timestamp": 1778011002.5960822}
|
|
{"eq_number": 355, "title": "Stress Intensity Factor (LEFM, Mode I)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9543.8, "timestamp": 1778011012.1414049}
|
|
{"eq_number": 356, "title": "J-Integral (Elastic-Plastic Fracture)", "domain": "Material Physics", "confidence": 0.767, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10282.7, "timestamp": 1778011022.4249363}
|
|
{"eq_number": 357, "title": "Paris' Law (Fatigue Crack Growth)", "domain": "Material Physics", "confidence": 0.513, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.951, "latency_ms": 10753.9, "timestamp": 1778011033.1795025}
|
|
{"eq_number": 358, "title": "Basquin Equation (High-Cycle Fatigue)", "domain": "Material Physics", "confidence": 0.86, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10335.8, "timestamp": 1778011043.5159273}
|
|
{"eq_number": 359, "title": "Coffin-Manson Relation (Low-Cycle Fatigue)", "domain": "Material Physics", "confidence": 0.893, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8431.6, "timestamp": 1778011051.9483435}
|
|
{"eq_number": 360, "title": "Norton-Bailey Creep Law", "domain": "Material Physics", "confidence": 0.52, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.949, "latency_ms": 8128.0, "timestamp": 1778011060.0769062}
|
|
{"eq_number": 361, "title": "Larson-Miller Parameter (Creep Rupture)", "domain": "Material Physics", "confidence": 0.867, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.964, "latency_ms": 9606.6, "timestamp": 1778011069.6842017}
|
|
{"eq_number": 362, "title": "Mohr-Coulomb Failure Criterion", "domain": "Material Physics", "confidence": 0.46, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.946, "latency_ms": 8295.4, "timestamp": 1778011077.9802387}
|
|
{"eq_number": 363, "title": "Drucker-Prager Yield Criterion", "domain": "Material Physics", "confidence": 0.6, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 7514.0, "timestamp": 1778011085.494906}
|
|
{"eq_number": 364, "title": "Weibull Distribution (Brittle Failure Statistics)", "domain": "Material Physics", "confidence": 0.707, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8449.2, "timestamp": 1778011093.9447944}
|
|
{"eq_number": 365, "title": "Stoney Equation (Thin Film Stress)", "domain": "Material Physics", "confidence": 0.78, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.921, "latency_ms": 8507.4, "timestamp": 1778011102.4535797}
|
|
{"eq_number": 366, "title": "Debye Specific Heat Model (Full)", "domain": "Material Physics", "confidence": 0.573, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.952, "latency_ms": 8610.4, "timestamp": 1778011111.0645032}
|
|
{"eq_number": 367, "title": "Dulong-Petit Law", "domain": "Material Physics", "confidence": 0.813, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 8323.2, "timestamp": 1778011119.3883195}
|
|
{"eq_number": 368, "title": "Einstein Heat Capacity Model", "domain": "Material Physics", "confidence": 0.6, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.953, "latency_ms": 8018.7, "timestamp": 1778011127.4075842}
|
|
{"eq_number": 369, "title": "Wiedemann-Franz Law (Electronic Thermal Conductivity)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.903, "latency_ms": 9686.5, "timestamp": 1778011137.094825}
|
|
{"eq_number": 370, "title": "Debye-Callaway Model (Lattice Thermal Conductivity)", "domain": "Material Physics", "confidence": 0.947, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9372.0, "timestamp": 1778011146.467566}
|
|
{"eq_number": 371, "title": "Thermal Expansion Coefficient (Gr\u00fcneisen Relation)", "domain": "Material Physics", "confidence": 0.807, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8718.6, "timestamp": 1778011155.186837}
|
|
{"eq_number": 372, "title": "Gr\u00fcneisen Equation of State (Solids)", "domain": "Material Physics", "confidence": 0.747, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8346.8, "timestamp": 1778011163.5343297}
|
|
{"eq_number": 373, "title": "Lindemann Melting Criterion", "domain": "Material Physics", "confidence": 0.887, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8350.9, "timestamp": 1778011171.8859367}
|
|
{"eq_number": 374, "title": "Stefan-Boltzmann Radiative Heat Transfer (Between Surfaces)", "domain": "Material Physics", "confidence": 0.987, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.936, "latency_ms": 9453.0, "timestamp": 1778011181.339656}
|
|
{"eq_number": 375, "title": "Complex Dielectric Constant", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.946, "latency_ms": 9469.9, "timestamp": 1778011190.81056}
|
|
{"eq_number": 376, "title": "Clausius-Mossotti Relation (Polarizability)", "domain": "Material Physics", "confidence": 0.653, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.867, "latency_ms": 8227.9, "timestamp": 1778011199.039129}
|
|
{"eq_number": 377, "title": "Debye Relaxation (Dipole Response)", "domain": "Material Physics", "confidence": 0.893, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 8818.5, "timestamp": 1778011207.8583834}
|
|
{"eq_number": 378, "title": "Cole-Cole Relaxation (Distributed)", "domain": "Material Physics", "confidence": 0.907, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 9921.7, "timestamp": 1778011217.7809148}
|
|
{"eq_number": 379, "title": "Havriliak-Negami Relaxation", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.973, "latency_ms": 9925.7, "timestamp": 1778011227.7074862}
|
|
{"eq_number": 380, "title": "Curie-Weiss Law for Ferroelectrics (Above T_c)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9805.1, "timestamp": 1778011237.5134625}
|
|
{"eq_number": 381, "title": "Piezoelectric Constitutive Equations", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.935, "latency_ms": 9507.7, "timestamp": 1778011247.0219653}
|
|
{"eq_number": 382, "title": "Pyroelectric Coefficient", "domain": "Material Physics", "confidence": 0.867, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.963, "latency_ms": 9001.9, "timestamp": 1778011256.024526}
|
|
{"eq_number": 383, "title": "Fowler-Nordheim Tunneling (Field Emission)", "domain": "Material Physics", "confidence": 0.68, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.87, "latency_ms": 8825.4, "timestamp": 1778011264.8505127}
|
|
{"eq_number": 384, "title": "Poole-Frenkel Conduction (Insulators)", "domain": "Material Physics", "confidence": 0.6, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8129.4, "timestamp": 1778011272.980522}
|
|
{"eq_number": 385, "title": "Varistor I-V Characteristic (Nonlinear)", "domain": "Material Physics", "confidence": 0.513, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.949, "latency_ms": 7669.4, "timestamp": 1778011280.650574}
|
|
{"eq_number": 386, "title": "Percolation Threshold (Conductivity)", "domain": "Material Physics", "confidence": 0.58, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.954, "latency_ms": 8022.0, "timestamp": 1778011288.6731503}
|
|
{"eq_number": 387, "title": "Intrinsic Carrier Concentration (Semiconductors)", "domain": "Semiconductor Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.967, "latency_ms": 9854.2, "timestamp": 1778011298.5280852}
|
|
{"eq_number": 388, "title": "Fermi Level in Doped Semiconductors", "domain": "Semiconductor Physics", "confidence": 0.853, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.963, "latency_ms": 9603.8, "timestamp": 1778011308.1326847}
|
|
{"eq_number": 389, "title": "Mass Action Law (Semiconductors)", "domain": "Semiconductor Physics", "confidence": 0.72, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.958, "latency_ms": 7984.6, "timestamp": 1778011316.117935}
|
|
{"eq_number": 390, "title": "Shockley Diode Equation (Ideal)", "domain": "Semiconductor Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9220.0, "timestamp": 1778011325.3388698}
|
|
{"eq_number": 391, "title": "Built-in Potential (p-n Junction)", "domain": "Semiconductor Physics", "confidence": 0.78, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9271.0, "timestamp": 1778011334.610553}
|
|
{"eq_number": 392, "title": "Depletion Width (p-n Junction)", "domain": "Semiconductor Physics", "confidence": 0.533, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8009.0, "timestamp": 1778011342.6200895}
|
|
{"eq_number": 393, "title": "MOS Capacitor Threshold Voltage", "domain": "Semiconductor Physics", "confidence": 0.74, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.918, "latency_ms": 8461.0, "timestamp": 1778011351.0817327}
|
|
{"eq_number": 394, "title": "MOSFET Drain Current (Saturation, Long Channel)", "domain": "Semiconductor Physics", "confidence": 0.647, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.87, "latency_ms": 9075.5, "timestamp": 1778011360.1578653}
|
|
{"eq_number": 395, "title": "Subthreshold Swing (MOSFET)", "domain": "Semiconductor Physics", "confidence": 0.88, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9773.5, "timestamp": 1778011369.9321687}
|
|
{"eq_number": 396, "title": "Avalanche Breakdown (Impact Ionization)", "domain": "Semiconductor Physics", "confidence": 0.607, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8354.9, "timestamp": 1778011378.287737}
|
|
{"eq_number": 397, "title": "Quantum Confinement Energy (Particle in a Box)", "domain": "Semiconductor Physics", "confidence": 0.827, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.963, "latency_ms": 9565.6, "timestamp": 1778011387.8540447}
|
|
{"eq_number": 398, "title": "Brus Equation (Semiconductor Nanocrystal Band Gap)", "domain": "Semiconductor Physics", "confidence": 0.76, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.92, "latency_ms": 8919.3, "timestamp": 1778011396.7739475}
|
|
{"eq_number": 399, "title": "Kane's k\u00b7p Band Model (Non-Parabolicity)", "domain": "Semiconductor Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.971, "latency_ms": 9909.9, "timestamp": 1778011406.6847389}
|
|
{"eq_number": 400, "title": "Mott Transition (Doped Semiconductor)", "domain": "Semiconductor Physics", "confidence": 0.933, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8464.9, "timestamp": 1778011415.1504235}
|
|
{"eq_number": 401, "title": "Anderson Localization (Disordered Materials)", "domain": "Semiconductor Physics", "confidence": 0.513, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.949, "latency_ms": 7684.8, "timestamp": 1778011422.8357637}
|
|
{"eq_number": 402, "title": "Tauc Plot (Band Gap from Absorption)", "domain": "Semiconductor Physics", "confidence": 0.66, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.959, "latency_ms": 8693.7, "timestamp": 1778011431.5301375}
|
|
{"eq_number": 403, "title": "Stoner Criterion (Itinerant Ferromagnetism)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.969, "latency_ms": 8967.9, "timestamp": 1778011440.4988167}
|
|
{"eq_number": 404, "title": "Stoner-Wohlfarth Model (Single-Domain Particle)", "domain": "Material Physics", "confidence": 0.547, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.951, "latency_ms": 8441.4, "timestamp": 1778011448.9407964}
|
|
{"eq_number": 405, "title": "N\u00e9el Temperature (Antiferromagnetism)", "domain": "Material Physics", "confidence": 0.84, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.929, "latency_ms": 8531.4, "timestamp": 1778011457.4729533}
|
|
{"eq_number": 406, "title": "Curie Temperature (Mean-Field Ferromagnetism)", "domain": "Material Physics", "confidence": 0.753, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.838, "latency_ms": 8459.6, "timestamp": 1778011465.933129}
|
|
{"eq_number": 407, "title": "Bloch T^{3/2} Law (Magnetization at Low T)", "domain": "Material Physics", "confidence": 0.967, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.932, "latency_ms": 9600.0, "timestamp": 1778011475.53382}
|
|
{"eq_number": 408, "title": "Landau-Lifshitz-Gilbert Equation (Magnetization Dynamics)", "domain": "Material Physics", "confidence": 0.82, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.923, "latency_ms": 9182.6, "timestamp": 1778011484.717052}
|
|
{"eq_number": 409, "title": "Brown's Paradox (Domain Wall Motion)", "domain": "Material Physics", "confidence": 0.84, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.925, "latency_ms": 9144.8, "timestamp": 1778011493.8626163}
|
|
{"eq_number": 410, "title": "Magnetostriction (Joule Magnetostriction)", "domain": "Material Physics", "confidence": 0.887, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9154.0, "timestamp": 1778011503.0173583}
|
|
{"eq_number": 411, "title": "Giant Magnetoresistance (GMR, CIP)", "domain": "Material Physics", "confidence": 0.987, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.966, "latency_ms": 9630.8, "timestamp": 1778011512.6489172}
|
|
{"eq_number": 412, "title": "Tunneling Magnetoresistance (TMR, Julliere Model)", "domain": "Material Physics", "confidence": 0.84, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.962, "latency_ms": 9232.9, "timestamp": 1778011521.8825185}
|
|
{"eq_number": 413, "title": "RKKY Interaction (Indirect Exchange)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9322.7, "timestamp": 1778011531.2059677}
|
|
{"eq_number": 414, "title": "Superexchange (Anderson-Goodenough-Kanamori Rules)", "domain": "Material Physics", "confidence": 0.973, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9510.9, "timestamp": 1778011540.7176645}
|
|
{"eq_number": 415, "title": "Complex Refractive Index (General)", "domain": "Material Physics", "confidence": 0.773, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10150.8, "timestamp": 1778011550.8693147}
|
|
{"eq_number": 416, "title": "Kramers-Kronig Relations (Optical Constants)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 11093.6, "timestamp": 1778011561.9637914}
|
|
{"eq_number": 417, "title": "Tauc-Lorentz Model (Amorphous Semiconductor Optics)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.972, "latency_ms": 13470.4, "timestamp": 1778011575.435293}
|
|
{"eq_number": 418, "title": "Sellmeier Equation (Refractive Index Dispersion)", "domain": "Material Physics", "confidence": 0.633, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10072.1, "timestamp": 1778011585.5080357}
|
|
{"eq_number": 419, "title": "Cauchy Equation (Refractive Index Fit)", "domain": "Material Physics", "confidence": 0.84, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 10732.0, "timestamp": 1778011596.2412686}
|
|
{"eq_number": 420, "title": "Urbach Tail (Absorption Edge)", "domain": "Material Physics", "confidence": 0.84, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9679.0, "timestamp": 1778011605.922115}
|
|
{"eq_number": 421, "title": "Beer-Lambert Law (Absorption)", "domain": "Electromagnetism", "confidence": 0.6, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9993.8, "timestamp": 1778011615.916508}
|
|
{"eq_number": 422, "title": "Kubelka-Munk Theory (Diffuse Reflectance)", "domain": "Material Physics", "confidence": 0.733, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10102.4, "timestamp": 1778011626.019679}
|
|
{"eq_number": 423, "title": "Fresnel Loss at Normal Incidence", "domain": "Material Physics", "confidence": 0.767, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.96, "latency_ms": 9101.7, "timestamp": 1778011635.1227663}
|
|
{"eq_number": 424, "title": "Drude Model for Free-Carrier Absorption", "domain": "Material Physics", "confidence": 0.88, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.964, "latency_ms": 9619.5, "timestamp": 1778011644.7429862}
|
|
{"eq_number": 425, "title": "Forster Resonance Energy Transfer (FRET) Efficiency", "domain": "Material Physics", "confidence": 0.907, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.932, "latency_ms": 11815.8, "timestamp": 1778011656.56097}
|
|
{"eq_number": 426, "title": "Stokes Shift (Luminescence)", "domain": "Material Physics", "confidence": 0.813, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.962, "latency_ms": 10863.8, "timestamp": 1778011667.4262915}
|
|
{"eq_number": 427, "title": "Dexter Energy Transfer (Exchange)", "domain": "Material Physics", "confidence": 0.607, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9686.5, "timestamp": 1778011677.11337}
|
|
{"eq_number": 428, "title": "Vickers Hardness Definition", "domain": "Material Physics", "confidence": 0.973, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.966, "latency_ms": 9351.2, "timestamp": 1778011686.4654925}
|
|
{"eq_number": 429, "title": "Brinell Hardness", "domain": "Material Physics", "confidence": 0.64, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8256.1, "timestamp": 1778011694.7221906}
|
|
{"eq_number": 430, "title": "Rockwell Hardness (Indirect)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8691.0, "timestamp": 1778011703.4139473}
|
|
{"eq_number": 431, "title": "Knoop Hardness (Thin Films / Brittle)", "domain": "Material Physics", "confidence": 0.8, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8242.2, "timestamp": 1778011711.6568182}
|
|
{"eq_number": 432, "title": "Nanoindentation (Oliver-Pharr Method)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.939, "latency_ms": 9684.8, "timestamp": 1778011721.3424215}
|
|
{"eq_number": 433, "title": "Charpy Impact Toughness", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8990.9, "timestamp": 1778011730.3341322}
|
|
{"eq_number": 434, "title": "Izod Impact Test", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.971, "latency_ms": 8659.5, "timestamp": 1778011738.9944704}
|
|
{"eq_number": 435, "title": "Rubber Elasticity (Gaussian Chain, Affine)", "domain": "Polymer Physics", "confidence": 0.673, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.957, "latency_ms": 8286.0, "timestamp": 1778011747.2812386}
|
|
{"eq_number": 436, "title": "Mooney-Rivlin Equation (Hyperelastic)", "domain": "Polymer Physics", "confidence": 0.607, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.957, "latency_ms": 9274.6, "timestamp": 1778011756.5564694}
|
|
{"eq_number": 437, "title": "Flory-Huggins Theory (Polymer Solution Free Energy)", "domain": "Polymer Physics", "confidence": 0.807, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.923, "latency_ms": 8860.2, "timestamp": 1778011765.417344}
|
|
{"eq_number": 438, "title": "Williams-Landel-Ferry (WLF) Equation", "domain": "Polymer Physics", "confidence": 0.867, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.963, "latency_ms": 8547.9, "timestamp": 1778011773.9659412}
|
|
{"eq_number": 439, "title": "Arrhenius Viscosity (Above Glass Transition)", "domain": "Polymer Physics", "confidence": 0.793, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9483.2, "timestamp": 1778011783.4498603}
|
|
{"eq_number": 440, "title": "Rouse Model (Unentangled Polymer Dynamics)", "domain": "Polymer Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.976, "latency_ms": 11375.5, "timestamp": 1778011794.8263443}
|
|
{"eq_number": 441, "title": "Reptation Model (de Gennes, Entangled Dynamics)", "domain": "Polymer Physics", "confidence": 0.907, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.893, "latency_ms": 9565.7, "timestamp": 1778011804.3927898}
|
|
{"eq_number": 442, "title": "Entanglement Molecular Weight", "domain": "Polymer Physics", "confidence": 0.687, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.957, "latency_ms": 8211.8, "timestamp": 1778011812.605285}
|
|
{"eq_number": 443, "title": "Flory-Fox Equation (T_g vs Molecular Weight)", "domain": "Polymer Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9975.8, "timestamp": 1778011822.5818884}
|
|
{"eq_number": 444, "title": "Cahn-Hilliard Equation (Spinodal Decomposition)", "domain": "Polymer Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.973, "latency_ms": 11183.0, "timestamp": 1778011833.765775}
|
|
{"eq_number": 445, "title": "Avrami Equation (Crystallization Kinetics)", "domain": "Phase Transformations", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.976, "latency_ms": 10468.6, "timestamp": 1778011844.2354534}
|
|
{"eq_number": 446, "title": "Lauritzen-Hoffman Theory (Polymer Crystal Growth)", "domain": "Phase Transformations", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.973, "latency_ms": 10619.0, "timestamp": 1778011854.8553362}
|
|
{"eq_number": 447, "title": "Young's Equation (Contact Angle)", "domain": "Surface Science", "confidence": 0.953, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 9684.8, "timestamp": 1778011864.540988}
|
|
{"eq_number": 448, "title": "Wenzel Equation (Rough Surface Wetting)", "domain": "Surface Science", "confidence": 0.607, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 8737.3, "timestamp": 1778011873.2789478}
|
|
{"eq_number": 449, "title": "Cassie-Baxter Equation (Composite/Heterogeneous Wetting)", "domain": "Surface Science", "confidence": 0.58, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 7.952, "latency_ms": 8575.6, "timestamp": 1778011881.8551884}
|
|
{"eq_number": 450, "title": "Laplace Pressure (Curved Interface)", "domain": "Fluid Dynamics", "confidence": 0.78, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.921, "latency_ms": 8926.4, "timestamp": 1778011890.7822986}
|
|
{"eq_number": 451, "title": "Kelvin Equation (Capillary Condensation)", "domain": "Surface Science", "confidence": 0.34, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8949.8, "timestamp": 1778011899.7326355}
|
|
{"eq_number": 452, "title": "Langmuir Adsorption Isotherm (Monolayer)", "domain": "Surface Science", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.968, "latency_ms": 9434.6, "timestamp": 1778011909.168021}
|
|
{"eq_number": 453, "title": "BET Isotherm (Brunauer-Emmett-Teller, Multilayer)", "domain": "Surface Science", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.972, "latency_ms": 11421.4, "timestamp": 1778011920.5903063}
|
|
{"eq_number": 454, "title": "Freundlich Isotherm (Heterogeneous Surfaces)", "domain": "Surface Science", "confidence": 0.82, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.962, "latency_ms": 9134.4, "timestamp": 1778011929.725334}
|
|
{"eq_number": 455, "title": "Gibbs Adsorption Equation", "domain": "Surface Science", "confidence": 0.947, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.965, "latency_ms": 8986.5, "timestamp": 1778011938.712679}
|
|
{"eq_number": 456, "title": "Amontons-Coulomb Friction Law (Dry Friction)", "domain": "Continuum Mechanics", "confidence": 0.893, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8837.8, "timestamp": 1778011947.5512028}
|
|
{"eq_number": 457, "title": "Archard's Law (Adhesive Wear)", "domain": "Surface Science", "confidence": 0.773, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.881, "latency_ms": 8749.7, "timestamp": 1778011956.3015912}
|
|
{"eq_number": 458, "title": "Hamaker Constant (Van der Waals Between Surfaces)", "domain": "Surface Science", "confidence": 0.78, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.929, "latency_ms": 9655.9, "timestamp": 1778011965.9582043}
|
|
{"eq_number": 459, "title": "DLVO Theory (Colloid Stability)", "domain": "Surface Science", "confidence": 0.873, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8971.7, "timestamp": 1778011974.9306529}
|
|
{"eq_number": 460, "title": "Zeta Potential (Smoluchowski Equation)", "domain": "Surface Science", "confidence": 0.6, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.956, "latency_ms": 9109.2, "timestamp": 1778011984.040497}
|
|
{"eq_number": 461, "title": "Derjaguin Approximation (Force Between Curved Surfaces)", "domain": "Surface Science", "confidence": 0.88, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.964, "latency_ms": 9627.0, "timestamp": 1778011993.668237}
|
|
{"eq_number": 462, "title": "Johnson-Kendall-Roberts (JKR) Adhesion Model", "domain": "Surface Science", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10700.7, "timestamp": 1778012004.3696983}
|
|
{"eq_number": 463, "title": "Derjaguin-Muller-Toporov (DMT) Model", "domain": "Surface Science", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 11914.0, "timestamp": 1778012016.284664}
|
|
{"eq_number": 464, "title": "Fick's First Law (Steady-State Diffusion)", "domain": "Material Physics", "confidence": 0.393, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.824, "latency_ms": 8139.1, "timestamp": 1778012024.424306}
|
|
{"eq_number": 465, "title": "Fick's Second Law (Time-Dependent Diffusion)", "domain": "Material Physics", "confidence": 0.54, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.95, "latency_ms": 9413.3, "timestamp": 1778012033.8382165}
|
|
{"eq_number": 466, "title": "Diffusion Solutions (Common)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9621.4, "timestamp": 1778012043.4603572}
|
|
{"eq_number": 467, "title": "Arrhenius Diffusion Coefficient", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.969, "latency_ms": 9781.1, "timestamp": 1778012053.2422159}
|
|
{"eq_number": 468, "title": "Darken Equations (Interdiffusion / Kirkendall Effect)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9734.0, "timestamp": 1778012062.9770489}
|
|
{"eq_number": 469, "title": "Nernst-Planck Equation (Ion Transport)", "domain": "Material Physics", "confidence": 0.88, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.891, "latency_ms": 9822.4, "timestamp": 1778012072.8001518}
|
|
{"eq_number": 470, "title": "Stokes-Einstein Relation (Diffusion of Spheres)", "domain": "Material Physics", "confidence": 0.88, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.964, "latency_ms": 9144.5, "timestamp": 1778012081.945372}
|
|
{"eq_number": 471, "title": "Tracer Diffusion Correlation Factor", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.971, "latency_ms": 9665.7, "timestamp": 1778012091.6119795}
|
|
{"eq_number": 472, "title": "Gibbs-Thomson Effect (Curvature Depression of Melting/Equilibrium Point)", "domain": "Phase Transformations", "confidence": 0.933, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9749.2, "timestamp": 1778012101.3618913}
|
|
{"eq_number": 473, "title": "Classical Nucleation Theory (Homogeneous)", "domain": "Phase Transformations", "confidence": 0.847, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9880.2, "timestamp": 1778012111.2427678}
|
|
{"eq_number": 474, "title": "Johnson-Mehl-Avrami-Kolmogorov (JMAK) Equation", "domain": "Phase Transformations", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 11147.1, "timestamp": 1778012122.3908334}
|
|
{"eq_number": 475, "title": "Turnbull's Nucleation Rate (Steady-State)", "domain": "Phase Transformations", "confidence": 0.84, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8905.8, "timestamp": 1778012131.2974637}
|
|
{"eq_number": 476, "title": "Lever Rule (Phase Diagram Tie Line)", "domain": "Phase Transformations", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8997.4, "timestamp": 1778012140.2955816}
|
|
{"eq_number": 477, "title": "Gibbs-Thomson-Freundlich (Ostwald Ripening / LSW Theory)", "domain": "Phase Transformations", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.975, "latency_ms": 11376.6, "timestamp": 1778012151.6731017}
|
|
{"eq_number": 478, "title": "Darken-Gurry Plot (Solubility Limits)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9226.9, "timestamp": 1778012160.9007547}
|
|
{"eq_number": 479, "title": "Hume-Rothery Rules (Alloy Formation)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.933, "latency_ms": 9384.8, "timestamp": 1778012170.2863085}
|
|
{"eq_number": 480, "title": "Vegard's Law (Lattice Parameter in Solid Solutions)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9427.9, "timestamp": 1778012179.7149634}
|
|
{"eq_number": 481, "title": "Rule of Mixtures (Composite Modulus, Isostrain)", "domain": "Material Physics", "confidence": 0.92, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.965, "latency_ms": 8879.2, "timestamp": 1778012188.5948606}
|
|
{"eq_number": 482, "title": "Hashin-Shtrikman Bounds (Composite Moduli)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10282.5, "timestamp": 1778012198.8781846}
|
|
{"eq_number": 483, "title": "Halpin-Tsai Equations (Short Fiber Composites)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.973, "latency_ms": 10254.5, "timestamp": 1778012209.1335084}
|
|
{"eq_number": 484, "title": "Porosity-Young's Modulus Relation (Empirical)", "domain": "Material Physics", "confidence": 0.96, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.966, "latency_ms": 8889.5, "timestamp": 1778012218.0237188}
|
|
{"eq_number": 485, "title": "Gibson-Ashby Model (Cellular Solids / Foams)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.979, "latency_ms": 11887.8, "timestamp": 1778012229.9126592}
|
|
{"eq_number": 486, "title": "Eshelby Inclusion Problem (Stress in Ellipsoidal Inclusion)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.97, "latency_ms": 10027.2, "timestamp": 1778012239.9406238}
|
|
{"eq_number": 487, "title": "Moss-Burstein Shift (Doped Semiconductor Absorption Edge)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.974, "latency_ms": 10473.9, "timestamp": 1778012250.4154813}
|
|
{"eq_number": 488, "title": "Franz-Keldysh Effect (Electro-Absorption)", "domain": "Material Physics", "confidence": 0.573, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.952, "latency_ms": 8828.2, "timestamp": 1778012259.2442353}
|
|
{"eq_number": 489, "title": "Pockels Effect (Linear Electro-Optic)", "domain": "Material Physics", "confidence": 0.947, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.931, "latency_ms": 9526.5, "timestamp": 1778012268.7714953}
|
|
{"eq_number": 490, "title": "Kerr Effect (Quadratic Electro-Optic)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9509.8, "timestamp": 1778012278.2820053}
|
|
{"eq_number": 491, "title": "Photoconductivity (Rose Model)", "domain": "Material Physics", "confidence": 0.933, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8668.1, "timestamp": 1778012286.9508266}
|
|
{"eq_number": 492, "title": "Shockley-Read-Hall Recombination Rate", "domain": "Semiconductor Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.973, "latency_ms": 10351.7, "timestamp": 1778012297.3034143}
|
|
{"eq_number": 493, "title": "Auger Recombination Rate", "domain": "Semiconductor Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.927, "latency_ms": 10570.1, "timestamp": 1778012307.874451}
|
|
{"eq_number": 494, "title": "BCS Energy Gap at T=0", "domain": "Condensed Matter", "confidence": 0.96, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.966, "latency_ms": 9646.6, "timestamp": 1778012317.521835}
|
|
{"eq_number": 495, "title": "Ginzburg-Landau Coherence Length", "domain": "Condensed Matter", "confidence": 0.727, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.917, "latency_ms": 9279.5, "timestamp": 1778012326.8020587}
|
|
{"eq_number": 496, "title": "Ginzburg-Landau Penetration Depth", "domain": "Condensed Matter", "confidence": 0.86, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8893.9, "timestamp": 1778012335.6966805}
|
|
{"eq_number": 497, "title": "Ginzburg-Landau Parameter (\u03ba)", "domain": "Condensed Matter", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.938, "latency_ms": 10133.7, "timestamp": 1778012345.8311152}
|
|
{"eq_number": 498, "title": "Abrikosov Vortex Lattice (Lower/Upper Critical Fields)", "domain": "Condensed Matter", "confidence": 0.953, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9933.5, "timestamp": 1778012355.765385}
|
|
{"eq_number": 499, "title": "Flux Pinning (Bean Critical State Model)", "domain": "Condensed Matter", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.97, "latency_ms": 9071.8, "timestamp": 1778012364.8381157}
|
|
{"eq_number": 500, "title": "Little-Parks Effect (Fluxoid Quantization)", "domain": "Condensed Matter", "confidence": 0.947, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 9228.0, "timestamp": 1778012374.0668464}
|
|
{"eq_number": 501, "title": "Andreev Reflection", "domain": "Condensed Matter", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.907, "latency_ms": 9428.3, "timestamp": 1778012383.4959624}
|
|
{"eq_number": 502, "title": "Nernst Equation (Electrode Potential)", "domain": "Material Physics", "confidence": 0.847, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8957.1, "timestamp": 1778012392.453754}
|
|
{"eq_number": 503, "title": "Butler-Volmer Equation (Electrode Kinetics)", "domain": "Material Physics", "confidence": 0.807, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.923, "latency_ms": 9166.7, "timestamp": 1778012401.6210642}
|
|
{"eq_number": 504, "title": "Tafel Equation (High Overpotential Limit)", "domain": "Material Physics", "confidence": 0.567, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.952, "latency_ms": 9039.0, "timestamp": 1778012410.6606324}
|
|
{"eq_number": 505, "title": "Randles-Sevcik Equation (Cyclic Voltammetry Peak Current)", "domain": "Material Physics", "confidence": 0.84, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8913.6, "timestamp": 1778012419.5749893}
|
|
{"eq_number": 506, "title": "Cottrell Equation (Chronoamperometry)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.94, "latency_ms": 9327.0, "timestamp": 1778012428.9028442}
|
|
{"eq_number": 507, "title": "Faraday's Laws of Electrolysis", "domain": "Electromagnetism", "confidence": 0.913, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9546.9, "timestamp": 1778012438.4505205}
|
|
{"eq_number": 508, "title": "Wagner Number (Current Distribution Uniformity)", "domain": "Material Physics", "confidence": 0.987, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 9285.2, "timestamp": 1778012447.7364237}
|
|
{"eq_number": 509, "title": "Zener Anelasticity (Standard Linear Solid)", "domain": "Material Physics", "confidence": 0.653, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.919, "latency_ms": 9637.5, "timestamp": 1778012457.374647}
|
|
{"eq_number": 510, "title": "Debye Peak (Internal Friction, Point Defect Relaxation)", "domain": "Material Physics", "confidence": 0.893, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9018.7, "timestamp": 1778012466.39404}
|
|
{"eq_number": 511, "title": "Bordoni Peak (Dislocation Relaxation)", "domain": "Material Physics", "confidence": 0.747, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8751.3, "timestamp": 1778012475.1459508}
|
|
{"eq_number": 512, "title": "Granato-L\u00fccke Theory (Dislocation Damping)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9244.7, "timestamp": 1778012484.391416}
|
|
{"eq_number": 513, "title": "Einstein Viscosity Equation (Rigid Sphere Suspension, Dilute)", "domain": "Soft Matter", "confidence": 0.427, "torsion_force": 0.0, "basis_migrated": false, "residual_entropy": 8.0, "latency_ms": 8391.1, "timestamp": 1778012492.7830346}
|
|
{"eq_number": 514, "title": "Krieger-Dougherty Equation (Concentrated Suspension)", "domain": "Soft Matter", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.972, "latency_ms": 10262.9, "timestamp": 1778012503.0468624}
|
|
{"eq_number": 515, "title": "Frank-Oseen Free Energy (Liquid Crystal Elastic)", "domain": "Soft Matter", "confidence": 0.94, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.9, "latency_ms": 9924.2, "timestamp": 1778012512.9719136}
|
|
{"eq_number": 516, "title": "Frederiks Transition Threshold (Liquid Crystal)", "domain": "Soft Matter", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8985.2, "timestamp": 1778012521.9578803}
|
|
{"eq_number": 517, "title": "Rayleigh Instability (Liquid Jet Breakup)", "domain": "Soft Matter", "confidence": 0.847, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.964, "latency_ms": 9184.6, "timestamp": 1778012531.1431847}
|
|
{"eq_number": 518, "title": "Plateau-Rayleigh Instability for Liquid Threads", "domain": "Soft Matter", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.94, "latency_ms": 9401.5, "timestamp": 1778012540.5455043}
|
|
{"eq_number": 519, "title": "Kissinger Equation (DSC/DTA Peak Kinetics)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.969, "latency_ms": 10155.7, "timestamp": 1778012550.7020452}
|
|
{"eq_number": 520, "title": "Ozawa-Flynn-Wall Equation (Isoconversional Kinetics)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9345.2, "timestamp": 1778012560.0480444}
|
|
{"eq_number": 521, "title": "Tammann Nucleation Diagram (Nucleation vs Growth Rate)", "domain": "Phase Transformations", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.974, "latency_ms": 10450.9, "timestamp": 1778012570.4998507}
|
|
{"eq_number": 522, "title": "Time-Temperature-Transformation (TTT) Diagram Equation", "domain": "Phase Transformations", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9508.6, "timestamp": 1778012580.0092933}
|
|
{"eq_number": 523, "title": "Thornton Structure Zone Model (Thin Film Growth)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 10009.7, "timestamp": 1778012590.0199287}
|
|
{"eq_number": 524, "title": "Herring Scaling Laws (Sintering Kinetics)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.938, "latency_ms": 9689.3, "timestamp": 1778012599.7100117}
|
|
{"eq_number": 525, "title": "Pilling-Bedworth Ratio (Oxide Protectiveness)", "domain": "Material Physics", "confidence": 0.873, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.963, "latency_ms": 9821.4, "timestamp": 1778012609.5322444}
|
|
{"eq_number": 526, "title": "Ellingham Diagram (Oxide Thermodynamic Stability)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.91, "latency_ms": 10750.8, "timestamp": 1778012620.2838297}
|
|
{"eq_number": 527, "title": "Mott-Gurney Law (Space-Charge-Limited Current)", "domain": "Material Physics", "confidence": 0.82, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.962, "latency_ms": 9686.2, "timestamp": 1778012629.9707403}
|
|
{"eq_number": 528, "title": "Richardson-Dushman Equation (Thermionic Emission)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 10912.5, "timestamp": 1778012640.883976}
|
|
{"eq_number": 529, "title": "Schottky Barrier Height (Metal-Semiconductor)", "domain": "Semiconductor Physics", "confidence": 0.98, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.934, "latency_ms": 10199.1, "timestamp": 1778012651.083949}
|
|
{"eq_number": 530, "title": "Spicer's Unified Defect Model (Fermi Level Pinning at Interfaces)", "domain": "Semiconductor Physics", "confidence": 0.867, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.889, "latency_ms": 9687.9, "timestamp": 1778012660.7725863}
|
|
{"eq_number": 531, "title": "Wolff's Law (Bone Remodeling, Mechanical Adaptation)", "domain": "Material Physics", "confidence": 0.993, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 9478.5, "timestamp": 1778012670.2518773}
|
|
{"eq_number": 532, "title": "Fung's Quasi-Linear Viscoelasticity (Soft Tissue)", "domain": "Material Physics", "confidence": 0.96, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.967, "latency_ms": 10391.4, "timestamp": 1778012680.6440437}
|
|
{"eq_number": 533, "title": "Ogden Hyperelastic Model (Biological Tissue)", "domain": "Material Physics", "confidence": 0.627, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.957, "latency_ms": 9939.5, "timestamp": 1778012690.5842912}
|
|
{"eq_number": 534, "title": "Matthiessen's Rule (Electrical Resistivity Additivity)", "domain": "Material Physics", "confidence": 0.98, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9035.2, "timestamp": 1778012699.620209}
|
|
{"eq_number": 535, "title": "Nordheim's Rule (Alloy Resistivity)", "domain": "Material Physics", "confidence": 0.7, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8562.4, "timestamp": 1778012708.1835384}
|
|
{"eq_number": 536, "title": "Miedema's Rules (Alloy Formation Enthalpy)", "domain": "Material Physics", "confidence": 0.987, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9613.0, "timestamp": 1778012717.7972999}
|
|
{"eq_number": 537, "title": "K\u00f6hler's Rule (Magnetoresistance Scaling)", "domain": "Material Physics", "confidence": 0.933, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9176.5, "timestamp": 1778012726.9745386}
|
|
{"eq_number": 538, "title": "Zener Breakdown (Band-to-Band Tunneling)", "domain": "Semiconductor Physics", "confidence": 0.687, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 9759.4, "timestamp": 1778012736.7346585}
|
|
{"eq_number": 539, "title": "Klemens Model (Thermal Boundary Resistance / Kapitza)", "domain": "Material Physics", "confidence": 1.0, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 7.969, "latency_ms": 10429.0, "timestamp": 1778012747.1644166}
|
|
{"eq_number": 540, "title": "Diffuse Mismatch Model (Thermal Boundary Resistance)", "domain": "Material Physics", "confidence": 0.913, "torsion_force": 0.0, "basis_migrated": true, "residual_entropy": 8.0, "latency_ms": 8490.9, "timestamp": 1778012755.6560693}
|