Why RSI matters.
Reaction Stability Index (RSI) is a single, bounded scalar that summarizes symbolic preference for any balanced reaction under declared scales and conditions. Alignments from reactants and products are pooled in rapidity space with stoichiometric weights, then mapped back through an outer tanh so results live in (-1, +1). For fixed stoichiometry and the symmetric contrast→alignment map, RSI preserves direction (Sign Lemma), is monotone in the contrast e, and is stable under common rescalings.
What RSI tells you (at a glance)
- Range & meaning: RSI in (-1, +1). RSI > 0 ⇒ products symbolically preferred; RSI < 0 ⇒ reactants preferred.
- Direction integrity: sign(RSI) follows sign(e) under the standard symmetric assignment.
- Monotone in contrast: increasing e increases RSI (fixed stoichiometry).
- Scale-robust: multiplying all coefficients by any k > 0 leaves RSI unchanged for any gamma ≥ 0.
- Streaming-friendly: you can build pathway-level preference by adding step contributions (rapidity + weights) and mapping back once.
Publish-with-results checklist
- Declare gamma, eps_a, eps_w in the manifest (values plus one-line definitions).
- Ensure all input alignments are clamped to |a| ≤ 1 − eps_a before any atanh call.
- Keep the contrast lens and study scales fixed within a study for auditability.
Plain ASCII formulas (copy-ready)
Balanced reaction (ASCII)
sum_i (m_i, a_i)_reactants -> sum_j (m_j, a_j)_products
Weights and rapidities
w = abs(m)^gamma # gamma >= 0 (default 1)
u = atanh_safe(a, eps_a) # with |a| <= 1 - eps_a (clamped)
Rapidity pools
U_r = sum_over_reactants( w_r * atanh_safe(a_r, eps_a) )
V_p = sum_over_products( w_p * atanh_safe(a_p, eps_a) )
Reactant-weight normalizer
W_r = sum_over_reactants( w_r )
W_r_safe = max( W_r, eps_w )
Reaction Stability Index (bounded preference)
RSI = tanh( ( V_p - U_r ) / W_r_safe )
Invariants and guarantees
|RSI| < 1 # outer tanh
V_p == U_r -> RSI = 0 # zero case
sign(RSI) = sign(e) # symmetric map, fixed stoichiometry
RSI increases as e increases # monotonicity
RSI invariant to scaling all coefficients by k > 0
Streaming: U_r, V_p, W_r are additive over species and steps
Collapse-safe: phi(m, a) = m leaves classical balances intact
Minimal notes (publish)
Manifest must include: gamma, eps_a, eps_w.
Clamp all a to |a| <= 1 - eps_a before atanh_safe(a, eps_a).
Navigation
Previous – Minimal Pseudocode (2.12)
Next – Contrast-to-Alignment Assignment (3.2)
Explore further
https://github.com/OMPSHUNYAYA/Symbolic-Mathematical-Chemistry
Parts of this release
Part 1 covers the core pipeline, invariants, empirical validations, and the reproducibility manifest; Part 2 contains canon tables, worked sets, software benches, CSV and JSON schemas, and detailed datasets.
Disclaimer (observation only)
This is an observation only, symbolic framework that provides bounded, table-free mappings for directionality and ranking. It is not a kinetics, safety, or hazard model and does not constitute operational guidance. Always follow lab safety protocols and regulatory requirements.
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