IndisputableMonolith.Chemistry.Reaction_Selectivity2
Defines a cost-based certificate for chemical regioselectivity in Recognition Science units. A nonnegative domain cost is compared to a positive canonical threshold; the certificate records when one reaction channel is preferred. Chemists and RS modelers cite it when formalizing selectivity claims. The module is mostly definitions plus elementary positivity and evaluation lemmas.
claimA domain cost $C$ on reaction channels, a positive canonical threshold $\tau_*>0$, and a regioselectivity certificate asserting that the preferred channel satisfies $C < \tau_*$ (or the dual comparison used in the module). Supporting facts: $C\ge 0$ and evaluation identities for $C$ at concrete sites.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ from the Cost layer; chemistry modules lift that scalar cost to reaction domains. This file sits in the Chemistry domain and imports Constants (RS time quantum $\tau_0=1$ tick) and Cost.
Sibling objects introduce a domain-level cost functional, prove it is nonnegative, and fix a canonical positive threshold against which channels are ranked. Regioselectivity is packaged as an inhabited certificate type: a proof-carrying record that one substitution or addition path is selected over alternatives under the cost comparison.
The setting is formal bookkeeping for organic selectivity (ortho/meta/para, Markovnikov vs anti, etc.) once energies are expressed in RS-native units, not a full kinetic derivation from first principles.
proof idea
Definition-heavy module. Domain cost and the canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas from the Cost import and arithmetic. Evaluation lemmas equate the abstract cost at a site with its concrete expression. The certificate type is a structure (or Prop wrapper) bundling the inequality; inhabitation is a constructive witness for a default or example channel. No deep tactic scripts: algebraic reduction and positivity-style facts.
why it matters in Recognition Science
Gives Chemistry a reusable selectivity certificate so later reaction theorems can cite a single inhabited object rather than ad-hoc inequalities. Downstream use is not yet wired in this graph (no used_by edges), so the module is infrastructure for RS chemistry rather than a leaf of the T0–T8 forcing chain. It connects the Cost layer’s J-cost discipline to practical regiochemical claims without claiming to derive rates or mechanisms from the eight-tick octave or $D=3$.
scope and limits
- Does not derive kinetic rate laws or Arrhenius factors from first principles.
- Does not prove uniqueness of the preferred channel for all substrates.
- Does not connect selectivity to the T0–T8 forcing chain or mass ladder.
- Does not model solvent, catalysis, or temperature dependence explicitly.
- Does not assert experimental match for named named reactions.