canonicalOxidationStateCount
plain-language theorem explainer
Defines the RS canonical oxidation-state multiplicity as $2^3-1$, i.e. seven states, from the Count Law at spatial dimension three. Chemists and RS auditors cite it as the integer yardstick for d-block oxidation ranges (Mn, Cr, Fe). The body is a one-line arithmetic definition, not a proof.
Claim. The canonical oxidation-state count is the natural number $2^{3}-1$ (equivalently $7$), the Count Law evaluated at spatial dimension $D=3$.
background
Recognition Science forces $D=3$ spatial dimensions (forcing chain T8) and an eight-tick octave of period $2^{3}$ (T7). The Count Law at that dimension therefore reads $2^{3}-1=7$: three independent binary axes (charge sign, d-count relative to half-fill, ligand-field side) leave seven nonempty configurations.
The module treats transition-metal oxidation multiplicity as a structural consequence of that count. Empirically, the common stable states of Mn, Cr, and Fe cluster near seven values; the IUPAC "golden-7" list is the same integer. The definition simply names that integer inside Lean so later certificates can quote it by name rather than by magic numeral.
proof idea
Pure definition: the body is the closed arithmetic term $2^{3}-1$. No tactics, no lemmas. Downstream equality and positivity theorems unfold this def and discharge the numeral with norm_num.
why it matters
Anchors the chemistry layer of the RS forcing chain to T7/T8: the same $2^{3}$ that gives the eight-tick period yields seven canonical oxidation states once the empty configuration is excluded. Downstream, canonicalOxidationStateCount_eq proves the value is literally 7, canonicalOxidationStateCount_pos records positivity, and the structure OxidationStateCert packages both facts with the J-cost identities on oxidation-state ratios. Without this named constant the certificate would hard-code a bare numeral and lose the link to ConfigDim. The module falsifier (stable d-block count outside $7\pm 2$) is stated against this integer.
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