SSM-AI – Appendix A — Gate Presets & Acceptance (A1–A3)

# Preset A — Steady (production default)
"gate": {
  "mode": "mul",
  "rho": 0.20,
  "g_min": 0.00,
  "eps_g": 1e-12,
  "weights": {"F":1.0,"D":1.0,"L":1.0,"E":1.0,"V":1.0,"Q":0.0},
  "safety_notch": {"enabled": false}
}

# Preset B — Safety-first (turbulence hardening)
"gate": {
  "mode": "mul",
  "rho": 0.30,
  "g_min": 0.20,
  "eps_g": 1e-12,
  "weights": {"F":1.5,"D":1.0,"L":1.0,"E":1.5,"V":0.5,"Q":0.5},
  "safety_notch": {"enabled": true, "s_thr": 0.80}
}

# Preset C — Incident mode (contain violations, preserve top-end signal)
"gate": {
  "mode": "u_scale",
  "rho": 0.50,
  "g_min": 0.10,
  "eps_g": 1e-12,
  "weights": {"F":1.5,"D":1.0,"L":1.5,"E":1.5,"V":0.5,"Q":0.5},
  "safety_notch": {"enabled": true, "s_thr": 0.70}
}

# Weighted mix of lane levels (all lanes in [0,1])
W   := wF+wD+wL+wE+wV+wQ
mix := (wF*F_t + wD*D_t + wL*L_t + wE*E_t + wV*V_t + wQ*Q_t) / max(W, eps_g)

# Instant gate and smoothed gate with floor
g_inst := clamp( 1 - mix , 0 , 1 )
g_t    := clamp( max(g_min, (1 - rho)*g_{t-1} + rho*g_inst ), 0, 1 )

# Cold-start convention for minis
# For first tick, set g_{t-1} := g_inst so g_t = g_inst at t=0 (calculator-fast).

# Vector V1 (calm-but-nonzero load)
Inputs: RSI = 0.70, lanes F=0.20, D=0.10, L=0.30, E=0.15, V=0.20, Q=0.00
Preset A (Steady):
  W=5.0
  mix=(0.20+0.10+0.30+0.15+0.20)/5=0.19
  g_t=1-0.19=0.81
  "mul" → RSI_env = 0.81 * 0.70 = 0.56700 → band A0
Preset C (Incident mode):
  same g_t=0.81
  "u_scale" → RSI_env = tanh( 0.81 * atanh(0.70) ) ≈ tanh(0.70251) ≈ 0.605998 → band A+

# Vector V2 (violation on F; notch active)
Inputs: RSI = 0.62, lanes F=0.85, D=0.10, L=0.10, E=0.05, V=0.10, Q=0.00
Preset B (Safety-first): weights {1.5,1.0,1.0,1.5,0.5,0.5} → W=6.0
  mix = (1.5*0.85 + 1.0*0.10 + 1.0*0.10 + 1.5*0.05 + 0.5*0.10 + 0.5*0.00)/6
      = (1.275 + 0.10 + 0.10 + 0.075 + 0.05 + 0.00)/6
      = 1.60/6 ≈ 0.266667
  g_inst ≈ 0.733333
  Notch: sev = max(F,D,E) = 0.85, s_thr=0.80
         g_sev := clamp( 1 - (0.85 - 0.80)/max(1 - 0.80, 1e-12) , 0 , 1 ) = 0.75
  g_inst := min(0.733333, 0.75) = 0.733333
  Cold-start → g_t = 0.733333
  "mul" → RSI_env = 0.733333 * 0.62 ≈ 0.454667 → band A0
  (If prior g_{t-1}=1: g_t ≈ 0.920000; 0.920000*0.62 ≈ 0.570400 → still A0)

# Vector V3 (calm conditions)
Inputs: RSI = 0.55, lanes all 0.05, Preset A:
  mix = (0.05*5)/5 = 0.05
  g_t = 0.95
  "mul" → RSI_env = 0.95 * 0.55 = 0.522500 → band A0