Generation
plain-language theorem explainer
BiologyRealization sets Generation to the natural numbers to model unbounded reproductive steps in a lightweight biological carrier. Researchers extending universal forcing to biology cite this when composing ledger entries across generational scales. The declaration is a direct abbreviation with no proof obligations or lemmas.
Claim. Generation is defined to be the type of natural numbers, $Generation := ℕ$.
background
The module supplies a lightweight biological realization in which the carrier is the generation count and the reproductive step functions as generator. This setting imports from SpectralEmergence, CKM, ThreeGenerations, and RSLedger, where Generation is instead realized as Fin 3 or as an inductive type with three constructors (first, second, third) tied to parity patterns across dimensions. Upstream results establish that the three-generation structure follows from D = 3 via cube face pairs and ledger torsion.
proof idea
The declaration is a direct abbreviation to the built-in Nat type; no lemmas are applied and no tactics are used.
why it matters
This definition supplies the carrier for biologyCost and biologyCost_self in the same module and feeds into downstream statements such as three_generations_from_dimension and closure_populates_next. It extends the forcing chain (T0–T8) and RCL to biology by permitting arbitrary generation counts on the phi-ladder, while the physics modules enforce the three-generation limit from D = 3. It touches the open interface between biological realizations and the eight-tick octave.
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