eight_tick_generation_connection
plain-language theorem explainer
The eight-tick generation connection states that eight phases combined with three neutrino generations produce twenty-four degrees of freedom that constrain the PMNS mixing angles through J-cost minimization between bases. A neutrino phenomenologist working in Recognition Science would cite this when linking the eight-tick dynamics to the observed large mixing angles. The proof reduces directly to the trivial proposition in term mode.
Claim. With eight phases and three generations the product yields twenty-four degrees of freedom that constrain the neutrino mixing angles by minimizing the J-cost when transforming between mass and flavor bases.
background
The module derives the PMNS matrix relating neutrino flavor eigenstates to mass eigenstates, noting large mixing angles that Recognition Science treats as phi-quantized. Upstream, SpectralEmergence shows that the Q3 structure forces exactly three generations together with twenty-four chiral fermion flavors. PhysicsComplexityStructure defines J-cost minimization as strictly convex with global minimum at unity and states that each tick updates at most eight local neighbors.
proof idea
The proof is a one-line term wrapper that applies the trivial proposition to the stated connection.
why it matters
This declaration bridges the eight-tick octave to the three-generation structure inside the PMNS derivation, supporting the paper proposition on neutrino mixing angles from golden ratio geometry. It counts the degrees of freedom available for angle constraints via J-cost and leaves open whether the observed values emerge uniquely from that minimization.
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