Block
plain-language theorem explainer
The Block inductive type enumerates the four orbital blocks s, p, d, f that index phi-tier rails in the periodic table model. Chemists applying the eight-tick neutrality condition to shell closures cite this enumeration when deriving block electron counts or rail energies. The declaration is a direct inductive definition equipped with decidable equality and representation.
Claim. Let $B$ be the inductive type with four constructors $s$, $p$, $d$, $f$.
background
The Periodic Table Engine maps the octave to an eight-tick ledger for chemistry. It uses phi-tier rails together with a fixed set of block offsets and an eight-window neutrality predicate that detects noble-gas closures at cumulative valence cost zero. No per-element tuning is allowed; the set of noble gases {2, 10, 18, 36, 54, 86} is forced by the neutrality condition alone.
proof idea
The declaration is the inductive definition of the Block type with constructors s, p, d, f, deriving DecidableEq and Repr.
why it matters
Block supplies the enumeration required by the Noble Gas Closure Theorem (P0-A0) and is referenced by blockElectronCount, blockFactor, BlockOffsets.default, and period_lengths_from_noble_gaps. It realizes the eight-tick octave (T7) inside the chemistry module and feeds the deterministic valence proxy that produces the observed noble-gas sequence without fitting.
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