{
  "_comment": [
    "Concretization of the FRET-spec predicates as numerical halfspaces.",
    "This file is the single source of truth — all reach-analysis code loads",
    "from here, and any future predicate changes happen here first.",
    "",
    "Each predicate in fret-pipeline/pwr_hybrid_3.json (t_avg_above_min,",
    "t_avg_in_range, p_above_crit, inv1_holds, inv2_holds) lives here as a",
    "polytope over the 10-state vector x = [n, C1..C6, T_f, T_c, T_cold].",
    "A polytope is {x : A_poly * x <= b_poly}, with units noted per entry."
  ],
  "_units": {
    "temperatures": "degrees Celsius (SI, internal model units)",
    "n": "normalized power, 1.0 = full power",
    "_display_note": "Figures and prints show Fahrenheit; predicates stored in C."
  },
  "references": {
    "T_c0": "308.35 °C — full-power avg coolant (from pke_params.m)",
    "T_f0": "328.35 °C — full-power fuel",
    "T_cold0": "290.0 °C — full-power cold leg",
    "T_standby": "275.02 °C — hot standby T_avg, defined as T_c0 - 33.33 C (= T_c0 - 60 F)"
  },
  "derived": {
    "T_standby_offset_F": -60.0,
    "T_standby_offset_C": -33.333333333,
    "t_avg_in_range_halfwidth_F": 5.0,
    "t_avg_in_range_halfwidth_C": 2.777777,
    "t_avg_above_min_margin_F": 10.0,
    "t_avg_above_min_margin_C": 5.555555,
    "p_above_crit_threshold_n": 1.0e-4
  },
  "predicates": {
    "t_avg_above_min": {
      "meaning": "Coolant has been warmed above a cold-start threshold; shutdown may transition to heatup.",
      "concretization": "T_c >= T_standby + 5.556 C  (= hot-standby + 10 F margin)",
      "halfspaces": [
        { "state_index": 9, "coeff": -1.0, "rhs_expr": "-(T_standby + 5.556)",
          "comment": "-T_c <= -(T_standby+5.556) i.e. T_c >= T_standby+5.556" }
      ]
    },
    "t_avg_in_range": {
      "meaning": "Average coolant temperature is inside the operating band.",
      "concretization": "|T_c - T_c0| <= 2.778 C  (= 5 F tech-spec-like deadband)",
      "halfspaces": [
        { "state_index": 9, "coeff":  1.0, "rhs_expr": "T_c0 + 2.778" },
        { "state_index": 9, "coeff": -1.0, "rhs_expr": "-(T_c0 - 2.778)" }
      ]
    },
    "p_above_crit": {
      "meaning": "Reactor power is in the 'power range' instrumentation regime, above source/intermediate.",
      "concretization": "n >= 1e-4  (0.01% of rated)",
      "halfspaces": [
        { "state_index": 1, "coeff": -1.0, "rhs_expr": "-1.0e-4",
          "comment": "n >= 1e-4" }
      ]
    },
    "inv1_holds": {
      "meaning": "Heatup safety invariant — fuel not overheated, coolant subcooled, ramp rate nominal.",
      "concretization": "(T_f <= 1200 C) AND (T_cold >= T_standby - 10 C) AND (dT_avg/dt <= 28 C/hr placeholder)",
      "halfspaces": [
        { "state_index": 8, "coeff":  1.0, "rhs_expr": "1200.0",
          "comment": "T_f <= 1200 C (fuel design limit; placeholder)" },
        { "state_index": 10, "coeff": -1.0, "rhs_expr": "-(T_standby - 10.0)",
          "comment": "T_cold >= T_standby - 10 (minimal subcooling proxy)" }
      ],
      "_status": "PLACEHOLDER — ramp-rate constraint not expressible as a state halfspace without augmentation; DNBR not modeled."
    },
    "inv2_holds": {
      "meaning": "Operation safety invariant — power range, T_avg band, coolant subcooling.",
      "concretization": "(n in [0.2, 1.1]) AND (T_c in [T_c0 - 8.33, T_c0 + 8.33] C) AND (T_cold in [T_cold0 - 20, T_cold0 + 10] C)",
      "halfspaces": [
        { "state_index": 1, "coeff":  1.0, "rhs_expr": "1.1",       "comment": "n <= 1.1" },
        { "state_index": 1, "coeff": -1.0, "rhs_expr": "-0.2",      "comment": "n >= 0.2" },
        { "state_index": 9, "coeff":  1.0, "rhs_expr": "T_c0 + 8.33", "comment": "T_c <= T_c0 + 15 F" },
        { "state_index": 9, "coeff": -1.0, "rhs_expr": "-(T_c0 - 8.33)", "comment": "T_c >= T_c0 - 15 F" },
        { "state_index": 10, "coeff":  1.0, "rhs_expr": "T_cold0 + 10", "comment": "T_cold <= T_cold0 + 10" },
        { "state_index": 10, "coeff": -1.0, "rhs_expr": "-(T_cold0 - 20)", "comment": "T_cold >= T_cold0 - 20" }
      ],
      "_status": "PLACEHOLDER — DNBR not modeled; bands chosen to match typical PWR tech-spec deadbands but not calibrated against a specific plant."
    }
  },
  "_placeholder_warning": [
    "The halfspace numbers for inv1_holds and inv2_holds are engineering",
    "placeholders, not derived from a specific plant's tech specs or DNBR",
    "correlation.  They are the authors' best guess at the shape such",
    "invariants should take and should be revised before the thesis defense.",
    "The t_avg_* and p_above_crit predicates are defensible for the demo."
  ]
}