fix(divergence): guard reward-normalizer cold start; drop arctanh recovery

Welford variance-collapse divided by 1e-8 producing bit-exact +/−5e8 /
+−1.25e8 poisoned rewards into TD targets; guard skips normalization
until stats meaningful; tanh-inversion removal bounds log-prob path.

Fixes #60.

SAC_LSTM_Bot/src/SAC_LSTM_Bot/rewards.nim

@@ -69,8 +69,16 @@ proc update*(rn: var RewardNormalizer; r: float64) =
   rn.m2     += delta * delta2
 
 proc normalize*(rn: RewardNormalizer; r: float64): float64 =
-  ## Returns (r - mean) / (std + eps).
+  ## Returns (r - mean) / (std + eps) once statistics are meaningful
-  ## Cold start (n < 2): returns 0.0 to avoid NaN/inf.
+  ## (n >= 4 and spread well above zero). Before that, returns the RAW
-  if rn.n < 2: return 0.0
+  ## reward unchanged — Welford M2 collapses to exactly 0 when early raw
+  ## rewards are identical, and dividing by the 1e-8 floor then z-scores
+  ## the first differing reward to ~1e8, poisoning TD targets.
+  if rn.n < 4: return r
   let variance = rn.m2 / rn.n.float64  # ponytail: population var; switch to n-1 if bias matters
-  result = (r - rn.mean) / (sqrt(variance) + NormEps)
+  let stddev   = sqrt(variance)
+  if stddev <= 1e-3 * (abs(rn.mean) + 1.0): return r
+  # ponytail: warm-up pass-through ceiling — raw rewards bypass normalization
+  # until stats are meaningful; upgrade = persist Welford state in checkpoint
+  # if warm-up noise ever hurts learning.
+  result = (r - rn.mean) / (stddev + NormEps)

SAC_LSTM_Bot/src/SAC_LSTM_Bot/training.nim

@@ -200,10 +200,7 @@ proc squashedLogProb(mu, logStd, action: Tensor[float32]):
     tuple[logProb: float32;
           dLogProbDMu, dLogProbDLogStd: Tensor[float32]] =
   let std = logStd.map(proc(v: float32): float32 = exp(v))
-  # Recover pre-tanh z ≈ arctanh(action)
+  let z = mu  # deterministic reparam: action = tanh(mu), so z ≡ mu, diff ≡ 0
-  let z = action.map(proc(a: float32): float32 =
-    let ac = clamp(a, -1.0'f32 + 1e-6'f32, 1.0'f32 - 1e-6'f32)
-    0.5'f32 * ln((1.0'f32 + ac) / (1.0'f32 - ac)))
   result.dLogProbDMu     = newTensor[float32](4)
   result.dLogProbDLogStd = newTensor[float32](4)
   let twoPiLog = 0.5'f32 * ln(2.0'f32 * PI.float32)