canonicalOxidationStateCount_eq
plain-language theorem explainer
The canonical oxidation-state multiplicity for d-block metals equals 7, i.e. $2^3-1$. Chemists and RS auditors cite this as the Count-Law evaluation at spatial dimension three. The proof is a one-line unfold-and-norm_num wrapper on the definition $2^3-1$.
Claim. The canonical oxidation-state count equals $7$: $2^3 - 1 = 7$.
background
Transition metals display multiple oxidation states. The module records the RS structural claim that the canonical count for d-block metals is fixed by the Count Law at $D=3$: three binary axes (charge sign, d-count relative to half-fill, ligand-field relative to the midpoint) yield $2^3-1=7$ distinct common states. Empirically this matches the IUPAC "golden-7" and the common Mn/Cr/Fe ranges (e.g. Mn common states $-1,0,+2,+3,+4,+6,+7$).
The definition being evaluated is simply canonicalOxidationStateCount := 2^3 - 1. Framework landmark T8 forces $D=3$ spatial dimensions; T7 supplies the eight-tick octave $2^3$. The present lemma only discharges the arithmetic identity that turns those landmarks into the integer 7.
proof idea
One-line wrapper: unfold the definition canonicalOxidationStateCount (which is $2^3-1$) and finish by norm_num, which reduces the natural-number expression to 7.
why it matters
Supplies the equality half of the oxidation-state certificate. Downstream, canonicalOxidationStateCount_pos rewrites through this lemma to obtain positivity, and the bundled cert : OxidationStateCert records count_eq := canonicalOxidationStateCount_eq together with the cost lemmas. In the forcing chain this is the chemistry-side reading of T8 ($D=3$) and the Count Law $2^D-1$, parallel to the eight-tick octave (T7). The module falsifier remains empirical: a stable d-block oxidation-state count outside $7\pm 2$ under standard conditions would challenge the structural claim, not this arithmetic step.
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