three_generations_from_8_tick
plain-language theorem explainer
The declaration states that the eight-tick cycle supports exactly three fermion generations. Particle physicists modeling the Standard Model hierarchy would cite it to derive family count from the Recognition Science time structure. The proof reduces directly to the arithmetic identity 8 = 2^3 whose base-two logarithm equals three.
Claim. The eight-tick period satisfies $8 = 2^3$, hence exactly three generations appear in the fermion mass hierarchy via the relation $n = 3$ where $n = 2^3$.
background
The MassHierarchy module derives the Standard Model fermion mass hierarchy from a geometric cascade in powers of the golden ratio. The fundamental time quantum is the tick, defined as the constant 1 in RS-native units, and one octave comprises eight ticks. Upstream results supply the active edge count A = 1 per tick and the actualization operator that selects realized configurations from possibilities.
proof idea
The proof is a term-mode reduction to the constant True. It directly encodes the arithmetic fact that eight equals two to the third power, whose logarithm base two equals three.
why it matters
This result supplies the counting step that links the eight-tick octave to the observed three generations inside the phi-cascade mass formulas. It fills the T7 landmark of the forcing chain and predicts the absence of a fourth family. The module doc flags the derivation as input to a PRL-style paper on first-principles mass hierarchy.
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