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    "caption": "Exponential decay of a constant-width unstable population in its rest-frame lifetime convention.",
    "example": "example-11"
  },
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    "caption": "Malus law for 10 W linearly polarized light and an ideal analyzer.",
    "example": "example-14"
  },
  "quantum-computing": {
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    "caption": "Apply Ry(\u03b8) to |0\u3009; ideal measurement gives sin\u00b2(\u03b8/2), without noise.",
    "example": "example-03"
  },
  "microelectronics": {
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    "caption": "Ideal Shockley diode: IS=1 pA, ideality one, VT=25.85 mV; series resistance and breakdown excluded.",
    "example": "example-07"
  },
  "computer-chip-design": {
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    "caption": "P=\u03b1CV\u00b2f with \u03b1=0.2, C=10 pF, f=1 GHz; no leakage term.",
    "example": "example-07"
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    "caption": "Earth point-mass circular speed. Radius is from Earth\u2019s centre, not altitude.",
    "example": "example-02"
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    "caption": "Ideal cosine projection for 40.83 W normal-incidence power; no shadowing or thermal change.",
    "example": "example-07"
  },
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    "caption": "Tsiolkovsky equation for Isp=300 s; excludes drag, gravity and steering losses.",
    "example": "example-02"
  },
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    "caption": "Planar two-link robot with l1=l2=0.5 m; zero determinant marks a position singularity.",
    "example": "example-20"
  },
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    "caption": "Independent radioactive decay with a constant decay probability per unit time.",
    "example": "example-09"
  },
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    "caption": "5 V step applied to an initially uncharged RC circuit with \u03c4=0.1 s.",
    "example": "example-11"
  },
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    "caption": "20 mA active and 0.1 mA sleep; wakeup energy and converter losses omitted.",
    "example": "example-18"
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    "caption": "Stable M/M/1 queue with service rate 100/s; time includes service and waiting.",
    "example": "example-17"
  },
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    "caption": "Real reference impedance, single-mode line; matching does not establish radiation efficiency.",
    "example": "example-07"
  },
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    "caption": "Shannon AWGN capacity with bandwidth 1 MHz; an upper bound rather than practical throughput.",
    "example": "example-12"
  },
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    "caption": "L=2 m, A=100 mm\u00b2, E=200 GPa; small-strain uniform axial elastic loading.",
    "example": "example-03"
  },
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    "caption": "Steady fully developed laminar circular-pipe Poiseuille flow, no slip.",
    "example": "example-13"
  },
  "heat-transfer": {
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    "y_label": "Body temperature (\u00b0C)",
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    ],
    "caption": "Lumped body: T0=100\u00b0C, ambient 20\u00b0C, \u03c4=900 s; small Biot number required.",
    "example": "example-13"
  },
  "chemical-kinetics": {
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    "y_label": "Reactant concentration (mol/L)",
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    "caption": "First-order loss: c0=2 mol/L, k=0.1 s\u207b\u00b9 at constant volume and temperature.",
    "example": "example-02"
  },
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    "caption": "Open-loop first-order model G(s)=2/(0.5s+1), zero initial state and unit input step.",
    "example": "example-02"
  },
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    "caption": "Convex objective f=(x\u22123)\u00b2+2; unique unconstrained minimum at (3,2).",
    "example": "example-01"
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    "caption": "Constant failure hazard \u03bb=10\u207b\u2075 per hour; nonrepairable mission survival.",
    "example": "example-01"
  },
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    "caption": "Single-energy attenuation coefficient \u03bc=0.2 cm\u207b\u00b9; scattering buildup is omitted.",
    "example": "example-10"
  },
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    "caption": "Fickian random-walk length \u221a(2Dt), D=10\u207b\u00b9\u2070 m\u00b2/s; not a finite-body concentration profile.",
    "example": "example-06"
  },
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    "example": "example-17"
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    "caption": "Solar Hohmann transfer from a circular 1 AU orbit to a larger circular orbit. No planetary escape or capture time is included.",
    "example": "example-12"
  },
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    "caption": "Two equal 1 m\u00b2 surfaces with emissivity 0.8 and mutual view factor one. Gebhart reflections give K=\u03c3(2/3).",
    "example": "example-16"
  },
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    "caption": "Green strain E11=(\u03bb\u00b2\u22121)/2 for uniaxial stretch; this is a strain measure, not a stress law.",
    "example": "example-03"
  },
  "plastic-viscoelastic-deformation": {
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    "y_label": "Maxwell stress (MPa)",
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    "caption": "A held strain produces initial stress 1 MPa and Maxwell relaxation time 10 s.",
    "example": "example-13"
  },
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    "caption": "Ideal-gas normal-shock benchmark with \u03b3=1.4. Constant-gamma limitations apply at high enthalpy.",
    "example": "example-14"
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    "caption": "Constant CT=0.005, wetted area 150 m\u00b2 and water density 1025 kg/m\u00b3. Actual CT is not generally constant.",
    "example": "example-14"
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    "example": "example-06"
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    "caption": "No-wind drag and rolling resistance for the stated 1500 kg vehicle; no drivetrain or accessory losses.",
    "example": "example-03"
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    "caption": "Calorically perfect air-standard Otto cycle, \u03b3=1.4; not measured brake efficiency.",
    "example": "example-08"
  },
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    "caption": "DC-equivalent linear motor with kt=0.5 N m/A; saturation and thermal limits excluded.",
    "example": "example-09"
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    "caption": "Fixed free-stream density 0.02 kg/m\u00b3. Density changes with altitude in a real flight.",
    "example": "example-06"
  },
  "atomic-physics": {
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    "caption": "Hydrogen 1s radial probability density 4(r/a0)\u00b2exp(\u22122r/a0); maximum at r=a0 and integral one.",
    "example": "example-12"
  },
  "particle-unification": {
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      15.122246251032058,
      15.125020779239538,
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    "caption": "Illustrative one-loop running with b=\u22127 and \u03b1\u207b\u00b9(\u03bc0)=10. This is not a demonstrated unification crossing.",
    "example": "example-17"
  },
  "statistics": {
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    "y_label": "Standard normal probability density",
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    "caption": "Standard normal density; probabilities are areas under the curve, not density values at a point.",
    "example": "example-06"
  },
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    "caption": "Output standard deviation 2 in the output variable\u2019s units. Simulation error shrinks as N\u207b\u00b9/\u00b2; physical spread does not.",
    "example": "example-13"
  },
  "statistical-physics": {
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    "caption": "Two nondegenerate classical canonical states with energies zero and \u0394. The Fermi-like algebra does not make this a Fermi gas.",
    "example": "example-06"
  },
  "quantum-statistical-physics": {
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    "caption": "Ideal Fermi\u2013Dirac occupation per single-particle state at nonzero temperature.",
    "example": "example-02"
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    "caption": "Poisson mission survival for a defined component failure process; input rate needs validated environment and damage models.",
    "example": "example-18"
  }
}