Integrate live-captured A/B/gamma params into framed_model; add CAP_ constants and parametric LUT helper

dsp/framed_model.hpp

@@ -10,7 +10,42 @@ struct DetectorBand {
     float level_scale = 1.0f;  // calibration: level = am * res * level_scale
 };
 
+// Live-captured BandConfig parameters from DSP snapshot (2026-08-20).
+// +0x180 (level LUT curve, FUN_180563a60): A = -24.0, B = +28.0, gamma = 1.0, flag = 0.
+// +0x188 (freq-range shaper, FUN_180563440): A = 16.0, B = 20000.0, gamma = 1.0, flag = 0.
+// These values are identical for both render_long.rpp and t1kq_only1_1000 configs.
+// The parametric LUT formula from FUN_180563a60 / FUN_180563440:
+//   t = clamp((x - A) / (B - A), 0.0, 1.0);
+//   val = A + (B - A) * t^gamma
+// With gamma=1: val = clamp(x, A, B)  [linear interpolation between A and B].
+// The x input is the mask-dependent dB-scaled value (mask * 8.6859 from 0x24c43e0).
+
+constexpr double CAP_A_LEVEL   = -24.0;
+constexpr double CAP_B_LEVEL   =  28.0;
+constexpr double CAP_GAMMA     =   1.0;
+
+constexpr double CAP_A_FREQ    =  16.0;
+constexpr double CAP_B_FREQ    = 20000.0;
+constexpr double CAP_GAMMA_FREQ =  1.0;
+
+// Helper: parametric LUT evaluation (gamma=1 path, linear interpolation)
+inline double lut_parametric(double x, double A, double B, double gamma) {
+    double t = (x - A) / (B - A);
+    if (t < 0.0) t = 0.0;
+    if (t > 1.0) t = 1.0;
+    if (gamma == 1.0) {
+        // linear: val = A + (B - A) * t = clamp(x, A, B)
+        return A + (B - A) * t;
+    }
+    // power-law path (gamma != 1)
+    double abs_t = std::abs(t);
+    double sign_t = (t >= 0.0) ? 1.0 : -1.0;
+    double pow_val = std::pow(std::max(abs_t, 1e-12), gamma);
+    return A + (B - A) * 0.5 * (1.0 + sign_t * pow_val);
+}
+
 // FramedDetector — C++ transcription of the real soothe2 mask-apply chain
+
 // (FUN_180529fe0 mono path, 0x5408b8==0), bit-exact structure.
 //
 // Per band, per bin (exact decomp /tmp/consumers_out.txt:638-1111):