Why this page. A plain ASCII bond-basis worked example showing sign and boundedness of RSI, plus a transparent catalyst prior and condition gate g_t. Numbers are illustrative; sign is the invariant. Use clamps and guards throughout.
Reaction
C2H4 + H2 -> C2H6
Bond basis (kJ/mol, illustrative)
B_C=C = 614, B_C-C = 348, B_H-H = 436, B_C-H = 413
Inputs (study constants for this example)
E_unit = 100, c = 0.5, gamma = 1
Tally (contrast)
E_broken = 1 * B_C=C + 1 * B_H-H
= 614 + 436
= 1050
E_formed = 1 * B_C-C + 2 * B_C-H
= 348 + 2 * 413
= 1174
e = (E_formed - E_broken) / E_unit
= (1174 - 1050) / 100
= +1.24
Alignment assignment (symmetric, bounded)
a_r = tanh(-c * e) = tanh(-0.5 * 1.24) = tanh(-0.62) ~ -0.55112803
a_p = tanh(+c * e) = tanh(+0.62) ~ +0.55112803
# clamp before any atanh (guard):
a_r = clamp_a(a_r, eps_a)
a_p = clamp_a(a_p, eps_a)
RSI computation (stoichiometric weights)
W_r = |1| + |1| = 2
U_r = sum_r( |m_r|^gamma * atanh_safe(a_r, eps_a) ) = 2 * (-0.62000000) = -1.24000000
V_p = sum_p( |m_p|^gamma * atanh_safe(a_p, eps_a) ) = 1 * (+0.62000000) = +0.62000000
RSI = tanh( (V_p - U_r) / W_r_safe )
= tanh( (0.62 - (-1.24)) / 2 )
= tanh( 0.93 )
~ +0.73059390
Optional catalyst prior (CPI on product path, transparent, small)
delta_u = alpha * Index = 0.20 * 0.80 = +0.16 # apply to product term only
V_p' = 0.62 + 0.16 = 0.78
s' = (0.78 - (-1.24)) / 2 = 1.01
RSI' = tanh(1.01) ~ +0.76576202
Verdict. Favored (moderate); sign(e) > 0 aligns with sign(RSI) > 0. A small, declared prior increases magnitude but preserves boundedness and transparency.
Gate note (illustrative)
If g_t = 0.80 -> RSI_env ~ 0.80 * 0.73059390 = 0.58447512
If g_t = 0.30 -> RSI_env ~ 0.30 * 0.73059390 = 0.21917817
Data posture. Illustrative bond basis for sign and magnitude sketch; publish actual lens/tables and any priors if used.
Navigation
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Disclaimer (observation-only). All formulas and results are observation-only—not predictive or operational—and require peer validation and governance before any deployment.
SHUNYAYA 