{
  "ok": true,
  "data": {
    "solvers": {
      "cooperative_threshold": {
        "description": "Density above which N·λ³/64 > 1 — the cooperative-emission threshold for a resonance line at wavelength λ. Below this, Holstein radiation trapping; above, Dicke superradiance.",
        "signature": "cooperative_threshold(lambda_cm: f64) -> f64",
        "args": [
          {
            "name": "lambda_cm",
            "unit": "cm",
            "range": "[1e-7, 1e-2]",
            "description": "resonance wavelength in cm (e.g. 5.89e-5 for Na D₂)"
          }
        ],
        "returns": {
          "type": "f64",
          "unit": "cm^-3",
          "description": "critical number density n_crit = 64 / λ³"
        },
        "examples": [
          {
            "call": "cooperative_threshold(5.89e-5)",
            "expect": "3.13e14 cm⁻³",
            "note": "Na D₂ 589 nm"
          },
          {
            "call": "cooperative_threshold(2.537e-5)",
            "expect": "3.91e15 cm⁻³",
            "note": "Hg 254 nm"
          },
          {
            "call": "cooperative_threshold(8.521e-5)",
            "expect": "1.04e14 cm⁻³",
            "note": "Cs D₂ 852.1 nm"
          }
        ],
        "verify_pattern": {
          "requires": "prose must contain BOTH a wavelength line AND an n_crit line",
          "wavelength_examples": [
            "λ = 5.89 × 10⁻⁵ cm",
            "λ = 5.89e-5 cm",
            "589 nm"
          ],
          "n_crit_examples": [
            "n_crit ≈ 3.13 × 10¹⁴ cm⁻³",
            "n_crit = 3.13e14 cm-3",
            "n_crit = 64 / λ³ ≈ 3.13 × 10¹⁴ cm⁻³"
          ],
          "tolerance": 0.05,
          "note": "Unicode superscripts (⁻¹⁴) and ASCII (cm^-3) both accepted. Verifier recomputes via 64/λ³ and compares within 5%."
        },
        "wasm": true
      },
      "na_saturated_density": {
        "description": "Saturated sodium-vapor number density at temperature T from the Nesmeyanov / Honig vapor-pressure curve.",
        "signature": "na_saturated_density(T_kelvin: f64) -> f64",
        "args": [
          {
            "name": "T_kelvin",
            "unit": "K",
            "range": "[300, 1500]",
            "description": "vapor temperature in Kelvin"
          }
        ],
        "returns": {
          "type": "f64",
          "unit": "cm^-3",
          "description": "saturated Na number density"
        },
        "examples": [
          {
            "call": "na_saturated_density(700)",
            "expect": "~3e14 cm⁻³"
          },
          {
            "call": "na_saturated_density(1000)",
            "expect": "~3e16 cm⁻³"
          }
        ],
        "wasm": true
      },
      "regime_label": {
        "description": "Classify a (density, wavelength, optical depth) point as \"thin\", \"holstein-trapped\", or \"cooperative\".",
        "signature": "regime_label(n_cm3: f64, lambda_cm: f64, k0L: f64) -> &str",
        "args": [
          {
            "name": "n_cm3",
            "unit": "cm^-3",
            "range": "[1e10, 1e23]",
            "description": "number density"
          },
          {
            "name": "lambda_cm",
            "unit": "cm",
            "range": "[1e-7, 1e-2]",
            "description": "resonance wavelength"
          },
          {
            "name": "k0L",
            "unit": "(dimensionless)",
            "range": "[0, 1e6]",
            "description": "line-center optical depth"
          }
        ],
        "returns": {
          "type": "str",
          "description": "one of: thin | holstein | cooperative"
        },
        "examples": [
          {
            "call": "regime_label(1e21, 5.89e-5, 100)",
            "expect": "\"cooperative\""
          }
        ],
        "wasm": true
      },
      "holstein_g0": {
        "description": "Holstein escape factor — effective decay rate of the fundamental radiation-trapping eigenmode, as a fraction of natural Γ.",
        "signature": "holstein_g0(k0L: f64, lineshape: &str, geometry: &str, a?: f64) -> f64",
        "args": [
          {
            "name": "k0L",
            "unit": "(dimensionless)",
            "range": "[1, 1e6]",
            "description": "line-center optical depth"
          },
          {
            "name": "lineshape",
            "unit": "enum",
            "range": "doppler | lorentzian | voigt",
            "description": "absorption line shape"
          },
          {
            "name": "geometry",
            "unit": "enum",
            "range": "slab | cylinder | sphere",
            "description": "sample geometry"
          },
          {
            "name": "a",
            "unit": "(dimensionless)",
            "range": "[0, 10]",
            "description": "Voigt parameter (only required for voigt lineshape)"
          }
        ],
        "returns": {
          "type": "f64",
          "unit": "(dimensionless)",
          "description": "g_0 ∈ (0, 1] — escape factor"
        },
        "examples": [
          {
            "call": "holstein_g0(1e3, 'doppler', 'slab')",
            "expect": "~3e-4"
          },
          {
            "call": "holstein_g0(1e4, 'lorentzian', 'slab')",
            "expect": "~5.6e-3"
          }
        ],
        "wasm": true
      },
      "voigt_profile": {
        "description": "Normalized Voigt line profile — convolution of Doppler and Lorentzian.",
        "signature": "voigt_profile(x: f64, a: f64) -> f64",
        "args": [
          {
            "name": "x",
            "unit": "(dimensionless)",
            "range": "[-10, 10]",
            "description": "frequency offset in Doppler widths"
          },
          {
            "name": "a",
            "unit": "(dimensionless)",
            "range": "[0, 5]",
            "description": "Voigt parameter Γ_collision / (2 Δν_doppler · sqrt(ln 2))"
          }
        ],
        "returns": {
          "type": "f64",
          "description": "profile value (peak normalized to 1 at x=0, a=0)"
        },
        "examples": [
          {
            "call": "voigt_profile(0, 0)",
            "expect": "1.0"
          }
        ],
        "wasm": true
      },
      "dicke_intensity_ratio": {
        "description": "Cooperative-to-independent intensity ratio: I_coop / I_indep = 1 + (N − 1)·η.",
        "signature": "dicke_intensity_ratio(N: f64, eta: f64) -> f64",
        "args": [
          {
            "name": "N",
            "unit": "count",
            "range": "[1, 1e12]",
            "description": "number of inverted emitters"
          },
          {
            "name": "eta",
            "unit": "[0,1]",
            "range": "[0, 1]",
            "description": "cooperation factor (geometric × spectral overlap)"
          }
        ],
        "returns": {
          "type": "f64",
          "description": "intensity multiplier vs. independent emitters"
        },
        "examples": [
          {
            "call": "dicke_intensity_ratio(1e6, 0)",
            "expect": "1.0",
            "note": "no cooperation"
          },
          {
            "call": "dicke_intensity_ratio(1e6, 1)",
            "expect": "1e6",
            "note": "full Dicke"
          }
        ],
        "wasm": true
      },
      "chemi_brightness_t": {
        "description": "Chemiluminescent brightness for an exothermic-channel emission line: NOT a Planck source — output ∝ kinetic-pump throughput × spectral partition fraction.",
        "signature": "chemi_brightness_t(eV_bond: f64) -> f64",
        "args": [
          {
            "name": "eV_bond",
            "unit": "eV",
            "range": "[1, 12]",
            "description": "bond / reaction energy driving the emitter"
          }
        ],
        "returns": {
          "type": "f64",
          "unit": "K-equivalent",
          "description": "temperature that a *thermal* source would need to match the line emissivity (often >> any physical T)"
        },
        "examples": [
          {
            "call": "chemi_brightness_t(4.26)",
            "expect": "~49,435 K (NaCl bond energy)"
          },
          {
            "call": "chemi_brightness_t(11.16)",
            "expect": "~129,506 K (CO bond energy)"
          }
        ],
        "note": "Planck/Wien/Boltzmann do not bound chemiluminescent line sources. See plate pmg-overview and LightCell doctrine.",
        "wasm": true
      },
      "hg_lamp_efficiency_delta_pct": {
        "description": "Estimated efficiency delta (percent) above a baseline Hg-lamp design when shifting to operating point f (fraction of cooperative threshold).",
        "signature": "hg_lamp_efficiency_delta_pct(f: f64) -> f64",
        "args": [
          {
            "name": "f",
            "unit": "(dimensionless)",
            "range": "[0.1, 100]",
            "description": "operating density as fraction of n_crit"
          }
        ],
        "returns": {
          "type": "f64",
          "unit": "%",
          "description": "efficiency delta vs. 1973 baseline (signed)"
        },
        "examples": [
          {
            "call": "hg_lamp_efficiency_delta_pct(10)",
            "expect": "~+18%"
          }
        ],
        "wasm": true
      }
    }
  },
  "next_actions": [
    {
      "description": "open solver cooperative_threshold",
      "http": "GET /solvers/cooperative_threshold",
      "cli": "plasmagicians solvers cooperative_threshold",
      "params": {
        "name": {
          "value": "cooperative_threshold"
        }
      }
    },
    {
      "description": "open solver na_saturated_density",
      "http": "GET /solvers/na_saturated_density",
      "cli": "plasmagicians solvers na_saturated_density",
      "params": {
        "name": {
          "value": "na_saturated_density"
        }
      }
    },
    {
      "description": "open solver regime_label",
      "http": "GET /solvers/regime_label",
      "cli": "plasmagicians solvers regime_label",
      "params": {
        "name": {
          "value": "regime_label"
        }
      }
    }
  ]
}