Shunyaya Symbolic Mathematical Chemistry – Barrier-aware RSI (3.10)

# Qualitative barrier nudge in rapidity (no rates, observation-only).
# Falls back to standard RSI when no barrier info is present.

Ea_fwd   = forward activation (proxy)
Ea_back  = backward activation (proxy)
B_unit   > 0    # barrier scale (declare once)
beta     >= 0   # prior strength (small; declare once)
bcap     in (0,1]  # clamp for barrier contrast (policy default: 1)

# base rapidity difference from canonical RSI (§3.9)
u0 = ( V_p - U_r ) / max( W_r , eps_w )

# barrier contrast (dimensionless)
b = ( Ea_back - Ea_fwd ) / B_unit

u = u0 + beta * clip( b , -bcap , +bcap )

RSI_SBI = tanh( u )

INPUT:
  {reactants}, {products}
  gamma >= 0, E_unit > 0, c > 0
  B_unit > 0, beta >= 0, bcap in (0,1]
  eps_a > 0, eps_w > 0
  (optional) Ea_fwd, Ea_back

STEP 1: e = ( E_formed - E_broken ) / E_unit

STEP 2: a_r = tanh( -c * e )
         a_p = tanh( +c * e )
         a_r = clamp_a( a_r , eps_a )
         a_p = clamp_a( a_p , eps_a )

STEP 3: U_r = sum_r |m_r|^gamma * atanh_safe( a_r , eps_a )
         V_p = sum_p |m_p|^gamma * atanh_safe( a_p , eps_a )
         W_r = sum_r |m_r|^gamma
         W_r_safe = max( W_r , eps_w )

STEP 4: u0 = ( V_p - U_r ) / W_r_safe

STEP 5: if Ea_fwd and Ea_back available:
           b_raw = ( Ea_back - Ea_fwd ) / B_unit
           b_use = clip( b_raw , -bcap , +bcap )
           u = u0 + beta * b_use
         else:
           u = u0   # idempotent fallback

STEP 6: RSI_SBI = tanh( u )

OUTPUT:
  RSI_SBI in (-1, +1)
  RSI_SBI == RSI when beta = 0 or when no barrier data

# Idempotence:
beta = 0  => RSI_SBI == RSI

# Clamp barrier contrast:
b_use = clip( b , -bcap , +bcap )    # choose bcap in [0.5, 1]

# Sign-discipline (optional guard):
if abs(u0) >= tau_guard (e.g., 0.25) and sign(u0 + beta*b_use) != sign(u0):
   reduce beta so that abs(beta*b_use) <= abs(u0) - tau_guard

# Units:
#   e uses E_unit; barrier contrast uses B_unit. Keep both explicit in the manifest.

# Safety:
#   Observation-only; no rates or hazards introduced.

SBI adds a small, declared rapidity nudge toward the lower barrier, preserving boundedness, closure, and monotone response in e; it disappears cleanly when barrier data are absent.