reproductiveStep
plain-language theorem explainer
reproductiveStep initializes the base lineage state for strict biological realizations in the Recognition Science framework. It sets lineage label to zero and generation depth to one, acting as the generator for subsequent reproduction steps. Researchers modeling domain-specific forcing realizations would cite this as the starting carrier element. The definition is a direct structure constructor with no lemmas required.
Claim. Let $L$ be the lineage state structure with components (lineage label, generation depth). Then reproductiveStep $:= (0, 1)$.
background
The Strict/Biology module constructs domain-rich biological realizations over a minimal lineage-state carrier. LineageState is the structure pairing a lineage label (Nat) with a generation depth (Nat); the label ensures arithmetic emerges from iterated reproduction rather than from the carrier type itself. The upstream simplicial ledger bridge identifies discrete steps with continuum Laplacian actions via the weighted sum formula equating edge differences to face-area defects.
proof idea
Direct definition via the anonymous constructor applied to the pair (0, 1). No tactics or upstream lemmas are invoked beyond the structure definition itself.
why it matters
This supplies the initial carrier element for strictBiologyRealization, which embeds reproduction into the StrictLogicRealization interface. It advances the Universal Forcing chain by furnishing a concrete biological domain consistent with the self-similar fixed point and eight-tick octave. It leaves open the explicit derivation of lineage costs from the J-function.
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