IndisputableMonolith.Chemistry.OxidationStateFromConfigDim
At spatial dimension D = 3 the configuration count law forces exactly 2^3 - 1 = 7 canonical oxidation states. Chemists and RS periodic-table work cite this as the discrete spine for accessible oxidation numbers. The module defines the count, a non-negative cost peaked at the expected state, and a certificate package; equalities are short algebraic identities from the eight-tick octave.
claimIn $D = 3$ spatial dimensions the canonical oxidation-state count is $2^3 - 1 = 7$. An oxidation-state cost is non-negative and attains its expected minimum at that count; a certificate packages the count identity and positivity.
background
Recognition Science fixes spatial dimension by the forcing chain: T7 supplies the eight-tick octave (period $2^3$), and T8 forces $D = 3$. The same binary counting that yields eight ticks yields $2^D - 1$ nontrivial configuration labels once the zero (closed-shell) state is excluded.
This chemistry module imports the RS constants and the J-cost infrastructure. It treats oxidation number as a discrete label on that configuration space rather than an empirical valence table. The sibling objects are a pure count canonicalOxidationStateCount, an equality pinning it to 7, positivity, a cost functional on candidate states, and a small certificate record that packages the identities for downstream use.
proof idea
The spine is definitional plus short equalities: the count is set to $2^3 - 1$, the equality lemma is rfl or a one-line arithmetic reduction, and positivity is immediate from the numeral. The cost is built from the imported Cost layer so non-negativity and the on-target minimum are inherited or reduced by rewriting. The certificate is an inhabited structure bundling those facts; no deep analysis or external chemistry data is required.
why it matters in Recognition Science
Downstream, OxidationStatesDerived (Phase 8B of the periodic-table closure plan) imports this module as the proved count-law spine and installs chemistry-facing target tables for accessible oxidation states, beginning with Fe and Mn. Without a forced integer count tied to $D = 3$ and the eight-tick octave, those targets would be free parameters. The module therefore closes the discrete half of the oxidation-state story before element-specific ladders and costs are attached. It sits on the T7/T8 landmarks rather than on empirical valence rules.
scope and limits
- Does not predict which of the 7 states a given element realizes.
- Does not derive numerical ionization energies or redox potentials.
- Does not treat f-block or exotic high-pressure oxidation chemistry.
- Does not replace empirical Pourbaix or Latimer diagrams.
- Does not vary D; the count is fixed at the forced D = 3.