{
  "codex": "The Physics Codex",
  "source_url": "https://thecodex.expert/physics/",
  "schema_version": "1.0",
  "last_updated": "2026-07-05",
  "status": "in progress — 13 named equation forms live across 6 concept/equation pages plus 1 simulation",
  "total_planned_equations": 570,
  "total_published_equations": 13,
  "equations": [
    {
      "name": "Newton's Second Law (constant mass)",
      "page_url": "https://thecodex.expert/physics/equations/newtons-second-law/",
      "latex": "F = ma",
      "variables": [
        {"symbol": "F", "name": "Net force", "unit": "N"},
        {"symbol": "m", "name": "Mass", "unit": "kg"},
        {"symbol": "a", "name": "Acceleration", "unit": "m/s^2"}
      ],
      "conditions": "Inertial reference frame; constant mass; non-relativistic speeds (v << c)",
      "source": "Newton, I. (1687). Principia Mathematica, Book I, Law II.",
      "domain": "classical-mechanics",
      "confidence": "high"
    },
    {
      "name": "Newton's Second Law (general, momentum form)",
      "page_url": "https://thecodex.expert/physics/equations/newtons-second-law/",
      "latex": "F = dp/dt",
      "variables": [
        {"symbol": "F", "name": "Net force", "unit": "N"},
        {"symbol": "p", "name": "Momentum", "unit": "kg m/s"},
        {"symbol": "t", "name": "Time", "unit": "s"}
      ],
      "conditions": "Valid for variable-mass systems and, with relativistic momentum, at any speed",
      "source": "Newton, I. (1687). Principia Mathematica, Book I, Law II.",
      "domain": "classical-mechanics",
      "confidence": "high"
    },
    {
      "name": "Linear Momentum",
      "page_url": "https://thecodex.expert/physics/classical-mechanics/linear-momentum/",
      "latex": "p = mv",
      "variables": [
        {"symbol": "p", "name": "Momentum", "unit": "kg m/s"},
        {"symbol": "m", "name": "Mass", "unit": "kg"},
        {"symbol": "v", "name": "Velocity", "unit": "m/s"}
      ],
      "conditions": "Non-relativistic speeds (v << c)",
      "source": "Newton, I. (1687). Principia Mathematica, Book I, Definition II.",
      "domain": "classical-mechanics",
      "confidence": "high"
    },
    {
      "name": "Gauss's Law",
      "page_url": "https://thecodex.expert/physics/equations/maxwells-equations/",
      "latex": "\\nabla \\cdot E = \\rho / \\varepsilon_0",
      "variables": [
        {"symbol": "E", "name": "Electric field", "unit": "V/m"},
        {"symbol": "\\rho", "name": "Charge density", "unit": "C/m^3"},
        {"symbol": "\\varepsilon_0", "name": "Vacuum permittivity", "unit": "F/m"}
      ],
      "conditions": "Vacuum or dielectric media (with substituted permittivity)",
      "source": "Maxwell, J.C. (1865). Philosophical Transactions of the Royal Society of London, 155.",
      "domain": "electromagnetism",
      "confidence": "high"
    },
    {
      "name": "Gauss's Law for Magnetism",
      "page_url": "https://thecodex.expert/physics/equations/maxwells-equations/",
      "latex": "\\nabla \\cdot B = 0",
      "variables": [
        {"symbol": "B", "name": "Magnetic field", "unit": "T"}
      ],
      "conditions": "Holds universally; no magnetic monopole observed",
      "source": "Maxwell, J.C. (1865).",
      "domain": "electromagnetism",
      "confidence": "high"
    },
    {
      "name": "Faraday's Law of Induction",
      "page_url": "https://thecodex.expert/physics/equations/maxwells-equations/",
      "latex": "\\nabla \\times E = -\\partial B/\\partial t",
      "variables": [
        {"symbol": "E", "name": "Electric field", "unit": "V/m"},
        {"symbol": "B", "name": "Magnetic field", "unit": "T"}
      ],
      "conditions": "Classical (non-quantum) electromagnetism",
      "source": "Maxwell, J.C. (1865).",
      "domain": "electromagnetism",
      "confidence": "high"
    },
    {
      "name": "Ampère-Maxwell Law",
      "page_url": "https://thecodex.expert/physics/equations/maxwells-equations/",
      "latex": "\\nabla \\times B = \\mu_0 J + \\mu_0 \\varepsilon_0 (\\partial E/\\partial t)",
      "variables": [
        {"symbol": "B", "name": "Magnetic field", "unit": "T"},
        {"symbol": "J", "name": "Current density", "unit": "A/m^2"},
        {"symbol": "\\mu_0", "name": "Vacuum permeability", "unit": "N/A^2"}
      ],
      "conditions": "Classical electromagnetism; displacement current term added by Maxwell 1861-1862",
      "source": "Maxwell, J.C. (1865).",
      "domain": "electromagnetism",
      "confidence": "high"
    },
    {
      "name": "Time-Dependent Schrödinger Equation",
      "page_url": "https://thecodex.expert/physics/equations/schrodinger-equation/",
      "latex": "i\\hbar \\frac{\\partial \\Psi}{\\partial t} = \\hat{H}\\Psi",
      "variables": [
        {"symbol": "\\hbar", "name": "Reduced Planck constant", "unit": "J s"},
        {"symbol": "\\Psi", "name": "Wavefunction", "unit": "system-dependent"},
        {"symbol": "\\hat{H}", "name": "Hamiltonian operator", "unit": "J"}
      ],
      "conditions": "Non-relativistic quantum systems (v << c)",
      "source": "Schrödinger, E. (1926). Annalen der Physik, 384(4), 361-376.",
      "domain": "quantum-mechanics",
      "confidence": "high"
    },
    {
      "name": "Time-Independent Schrödinger Equation",
      "page_url": "https://thecodex.expert/physics/equations/schrodinger-equation/",
      "latex": "\\hat{H}\\psi = E\\psi",
      "variables": [
        {"symbol": "\\psi", "name": "Spatial wavefunction", "unit": "system-dependent"},
        {"symbol": "E", "name": "Energy eigenvalue", "unit": "J"}
      ],
      "conditions": "Time-independent Hamiltonian; stationary states only",
      "source": "Schrödinger, E. (1926).",
      "domain": "quantum-mechanics",
      "confidence": "high"
    },
    {
      "name": "De Broglie Relation",
      "page_url": "https://thecodex.expert/physics/quantum-mechanics/wave-particle-duality/",
      "latex": "\\lambda = h/p",
      "variables": [
        {"symbol": "\\lambda", "name": "De Broglie wavelength", "unit": "m"},
        {"symbol": "h", "name": "Planck constant", "unit": "J Hz^-1"},
        {"symbol": "p", "name": "Momentum", "unit": "kg m/s"}
      ],
      "conditions": "Applies to any particle with momentum p",
      "source": "De Broglie, L. (1924). Doctoral thesis, Sorbonne.",
      "domain": "quantum-mechanics",
      "confidence": "high"
    },
    {
      "name": "Heisenberg Uncertainty Principle (position-momentum)",
      "page_url": "https://thecodex.expert/physics/quantum-mechanics/uncertainty-principle/",
      "latex": "\\Delta x \\cdot \\Delta p \\geq \\hbar/2",
      "variables": [
        {"symbol": "\\Delta x", "name": "Position uncertainty", "unit": "m"},
        {"symbol": "\\Delta p", "name": "Momentum uncertainty", "unit": "kg m/s"},
        {"symbol": "\\hbar", "name": "Reduced Planck constant", "unit": "J s"}
      ],
      "conditions": "General result for any quantum state; equality for Gaussian minimum-uncertainty wave packets",
      "source": "Heisenberg, W. (1927). Zeitschrift für Physik, 43(3-4), 172-198.",
      "domain": "quantum-mechanics",
      "confidence": "high"
    },
    {
      "name": "Born Rule (position space)",
      "page_url": "https://thecodex.expert/physics/quantum-mechanics/born-interpretation/",
      "latex": "P(x) = |\\Psi(x,t)|^2",
      "variables": [
        {"symbol": "P(x)", "name": "Probability density", "unit": "m^-1 (1D case)"},
        {"symbol": "\\Psi(x,t)", "name": "Wavefunction", "unit": "m^-1/2 (1D case)"}
      ],
      "conditions": "Wavefunction must be normalised over all space",
      "source": "Born, M. (1926). Zeitschrift für Physik, 37(12), 863-867.",
      "domain": "quantum-mechanics",
      "confidence": "high"
    },
    {
      "name": "Einstein Photoelectric Equation",
      "page_url": "https://thecodex.expert/physics/simulations/photoelectric-effect/",
      "latex": "KE_{max} = hf - \\Phi",
      "variables": [
        {"symbol": "KE_max", "name": "Maximum kinetic energy of ejected electron", "unit": "eV"},
        {"symbol": "h", "name": "Planck constant", "unit": "eV s"},
        {"symbol": "f", "name": "Light frequency", "unit": "Hz"},
        {"symbol": "\\Phi", "name": "Work function of material", "unit": "eV"}
      ],
      "conditions": "Valid when hf > Phi (photoemission threshold exceeded)",
      "source": "Einstein, A. (1905). Annalen der Physik, 17(6), 132-148.",
      "domain": "quantum-mechanics",
      "confidence": "high"
    }
  ]
}