Why this page. Two bond-basis, plain ASCII worked examples that illustrate strong, positive RSI and sign-preserving realization RSI_env = g_t * RSI. Numbers are illustrative; sign is the invariant. Use clamps and guards throughout.
6.3 Carbon oxidation to CO2
ReactionC + O2 -> CO2
Bond basis (kJ/mol)B_O=O = 498, B_C=O ~ 805
Inputs (study constants for this example)E_unit = 100, c = 0.5, gamma = 1
Tally (contrast)
E_broken = 1*(B_O=O)
= 498
E_formed = 2*(B_C=O)
= 2*805
= 1610
e = (E_formed - E_broken) / E_unit
= (1610 - 498) / 100
= 11.12
Alignment assignment (symmetric, bounded)
a_r = tanh(-c*e) = tanh(-0.5 * 11.12) = tanh(-5.56) ~ -0.99997037
a_p = tanh(+c*e) = tanh(+5.56) ~ +0.99997037
# guard before any atanh:
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( w_r * atanh_safe(a_r, eps_a) ) = 2 * (-5.56) = -11.12
V_p = sum_p( w_p * atanh_safe(a_p, eps_a) ) = 1 * (+5.56) = +5.56
RSI = tanh( (V_p - U_r) / W_r_safe )
= tanh( (5.56 - (-11.12)) / max(2, eps_w) )
= tanh( 8.34 )
~ +0.99999989
Verdict
Essentially fully favored; bounded (|RSI| < 1). sign(e) is positive and equals sign(RSI). If a condition gate is applied, publish RSI_env = g_t * RSI with 0 <= g_t <= 1; the gate modulates magnitude only and preserves sign.
Data reference
See Appendix D for dataset identifiers, versions, and licence terms relevant to this example.
6.4 CO oxidation to CO2
Reaction2 CO + O2 -> 2 CO2
Bond basis (kJ/mol)B_C#O (in CO) ~ 1072, B_O=O = 498, B_C=O ~ 805
Inputs (study constants for this example)E_unit = 100, c = 0.5, gamma = 1
Tally (contrast)
E_broken = 2*(B_C#O in CO) + 1*(B_O=O)
= 2*1072 + 498
= 2144 + 498
= 2642
E_formed = 4*(B_C=O)
= 4*805
= 3220
e = (E_formed - E_broken) / E_unit
= (3220 - 2642) / 100
= 5.78
Alignment assignment (symmetric, bounded)
a_r = tanh(-c*e) = tanh(-0.5 * 5.78) = tanh(-2.89) ~ -0.99384159
a_p = tanh(+c*e) = tanh(+2.89) ~ +0.99384159
# guard before any atanh:
a_r = clamp_a(a_r, eps_a)
a_p = clamp_a(a_p, eps_a)
RSI computation (stoichiometric weights)
W_r = |2| + |1| = 3
U_r = sum_r( w_r * atanh_safe(a_r, eps_a) ) = 3 * (-2.89) = -8.67
V_p = sum_p( w_p * atanh_safe(a_p, eps_a) ) = 2 * (+2.89) = +5.78
RSI = tanh( (V_p - U_r) / W_r_safe )
= tanh( (5.78 - (-8.67)) / max(3, eps_w) )
= tanh( 4.8166667 )
~ +0.99986899
Verdict
Strongly favored; bounded (|RSI| < 1). sign(e) is positive and equals sign(RSI). If a condition gate is applied, publish RSI_env = g_t * RSI with 0 <= g_t <= 1; the gate modulates magnitude only and preserves sign.
Data reference
See Appendix D for dataset identifiers, versions, and licence terms relevant to this example.
Navigation
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Next — Thermal NO formation (disfavored); Weak-acid dissociation (6.5, 6.6)
Disclaimer (observation-only). All formulas and results are observation-only—not predictive or operational—and require peer validation and governance before any deployment.
SHUNYAYA 