What this page defines.
How a single energetic contrast is mapped, symmetrically and bounded, to reactant and product alignments. The map is collapse-safe, sign-consistent with the contrast, and uses a global slope so the study remains auditable. Exactly one lens is chosen per study and kept fixed.
Practical notes
- Default lens (formation/bonds): build contrast from bonds formed vs. broken, then map with a single slope c to reactant/product alignments.
- Sign convention: use
E_formed - E_brokenso forward-favored formation yieldse > 0. - Scales: choose
E_unitso|e|is O(1) (e.g., 100 kJ/mol); publishE_unitandc. - Bounds: clamp each alignment to the open interval using the study’s
eps_a. - Direction vs. magnitude: only sign(e) sets direction (see Sign Lemma); magnitudes of
aand RSI depend onE_unitandc. - Data sources: if bond energies come from tables or estimates, cite source and version in the manifest.
- Alternatives: other lenses are allowed (thermo/redox/kinetic etc.); pick exactly one per study and publish it.
Plain ASCII formulas (copy-ready)
Default bond/formation lens
E_broken = sum_over_bonds_broken(B_bond)
E_formed = sum_over_bonds_formed(B_bond)
e = ( E_formed - E_broken ) / E_unit # E_unit > 0
a_react = tanh( -c * e ) # c > 0
a_prod = tanh( +c * e )
# clamp to keep |a| <= 1 - eps_a
a_react = clamp_a( a_react , eps_a )
a_prod = clamp_a( a_prod , eps_a )
Scope and guards
# One lens per study; keep fixed. Alternatives listed in 4.1.
# Sign convention: E_formed - E_broken -> forward-favored => e > 0
# Scales: choose E_unit so |e| ~ O(1); c is the global slope
# Clamp policy: enforce |a| <= 1 - eps_a after mapping
# Direction vs magnitude: only sign(e) controls sign(RSI); magnitudes depend on E_unit and c
# Data sources: record bond tables/estimates (name, version) in the manifest
# Publish: E_unit, c, eps_a, lens name, and data sources
Navigation
Previous – RSI Overview & Definition (3, 3.1)
Next – Sign Lemma & Monotonicity (3.3, 3.4)
SHUNYAYA 