{
  "classification": "synthetic analytic teaching study; no measurements; no confidence bands",
  "grid": {
    "r_min": 0,
    "r_max": 1,
    "step": 0.01,
    "rows": 101
  },
  "relations": {
    "remaining_kinetic_power_fraction": "1-r",
    "speed_ratio": "sqrt(1-r)",
    "momentum_flux_ratio": "sqrt(1-r)"
  },
  "derivation": "P=0.5*mass_flow*v^2; momentum_flux=mass_flow*v. Remove r*P_initial and solve for the remaining speed with the same mass flow.",
  "assumptions": [
    "One ideal uniform one-dimensional stream",
    "Fixed positive mass flow",
    "Before and after speeds and kinetic powers use the same fixed inertial frame, for example a nonaccelerating vehicle frame; kinetic power and the extracted fraction r depend on the chosen frame",
    "Fixed pressure condition; no change in pressure-thrust contribution is modeled",
    "Nonnegative extracted fraction of initial kinetic power",
    "No later heat addition or reacceleration"
  ],
  "limitations": [
    "Not net thrust, engine performance, or a scramjet prediction",
    "No inlet momentum subtraction, pressure-force calculation, compressibility, shocks, combustion, extraction hardware, drag, thermal balance, or losses",
    "Extracted kinetic power is not necessarily usable electrical power; conversion efficiency is unspecified",
    "The r=1 endpoint is a formal zero-speed limit and cannot represent positive fixed mass flow through a finite-area outlet at finite density",
    "The dimensional check values are arbitrary verification inputs, not vehicle specifications"
  ],
  "verification": {
    "passed": true,
    "checks": 506,
    "independent_method": "50-digit Decimal dimensional energy balance with arbitrary positive mass flow and initial speed, then independent momentum-flux reconstruction; endpoints and strict monotonicity"
  },
  "caption": "Removing a fraction r of the initial kinetic power of one ideal stream leaves power fraction 1-r and speed and momentum-flux fractions sqrt(1-r), under the stated fixed-flow assumptions. This analytic illustration does not predict net thrust or engine performance."
}