What this page covers.
How to read the magnitude of the bounded preference index in practice, and a minimal, copy-ready algorithm to compute it for a single balanced reaction under fixed conditions.
Reading the magnitude (practical guidance)
|RSI|~0.0 .. 0.2→ weak preference (sensitive to the calm gateg_tand any declared priors).|RSI|~0.2 .. 0.6→ moderate preference (robust at highg_t; edge-lift can invert at lowg_t).|RSI|>0.6→ strong preference (inversion requires extreme edge conditions).
Notes:
- These cutlines are heuristic; programs may publish stricter policy bands for green/amber/red decisions.
- Always report whether the calm gate was applied;
RSI_env = g_t * RSIis smaller in magnitude but never flips the sign ofRSI(sinceg_t >= 0). - When communicating results, include
{E_unit, c, gamma, eps_a, eps_w}from the manifest so readers can reproduce magnitudes.
Plain ASCII (copy-ready)
Minimal algorithm (per reaction, fixed conditions)
INPUT:
stoichiometric lists {reactants}, {products}
gamma >= 0
E_unit > 0
c > 0
eps_a > 0
eps_w > 0
STEP 1: tally energetic contrast
e = (E_formed - E_broken) / E_unit
STEP 2: symmetric, bounded alignments
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: guarded rapidity pools (weights w = |m|^gamma)
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: bounded preference
RSI = tanh( ( V_p - U_r ) / W_r_safe )
OUTPUT:
RSI in (-1, +1) with sign(RSI) = sign(e)
# Condition-aware use (optional):
# replace RSI by RSI_env = g_t * RSI in downstream ranking, with 0 <= g_t <= 1.
Reminder (interpretation bands)
|RSI| in [0.0, 0.2) -> weak preference
|RSI| in [0.2, 0.6) -> moderate preference
|RSI| in [0.6, 1.0) -> strong preference
Navigation
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