Structure
plain-language theorem explainer
The declaration introduces an inductive type enumerating the three primary crystal lattices used in Recognition Science chemistry: body-centered cubic, face-centered cubic, and hexagonal close-packed. Material scientists applying the eight-tick ledger or phi-stability predictions would cite this type when computing coordination numbers or energy scales. It is a direct inductive definition that supplies the constructors together with Repr and DecidableEq instances.
Claim. Let $S$ be the inductive type whose constructors are BCC (body-centered cubic), FCC (face-centered cubic), and HCP (hexagonal close-packed).
background
The module sets out Crystal Structure Stability (CM-001) in which BCC, FCC, and HCP emerge from RS principles. BCC coordination number 8 directly reflects the 8-tick ledger period, while FCC and HCP realize close packing at coordination 12 with ideal HCP c/a ratio near phi. The upstream result from UniversalForcingSelfReference.for records structural properties required of a meta-realization instance, stating that a MetaRealizationCert captures all such properties that would be needed.
proof idea
The declaration is an inductive definition that enumerates the three constructors and attaches the derived Repr and DecidableEq instances; no tactics or lemmas are applied.
why it matters
This type is the common domain for downstream definitions such as coordination (BCC maps to 8, FCC and HCP to 12), eightTickCoherence (perfect match only for BCC), and energyScale (lower values for close-packed structures). It realizes the CM-001 predictions that link directly to the T7 eight-tick octave and supports the forcing-chain derivation of chemistry without extra hypotheses.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.