fermion_states_eq_aut
plain-language theorem explainer
The equality shows that the total number of fermion states, counting chirality, equals the order of the automorphism group of the three-dimensional hypercube. Researchers deriving the Standard Model from discrete geometry would cite this to equate the cube's symmetries with the 48 fermionic degrees of freedom. The proof reduces to a direct numerical check confirming both sides equal 48.
Claim. The total number of chiral fermion states equals the order of the automorphism group of the three-dimensional hypercube, given by $2^3 times 3! = 48$.
background
The module starts from the forced dimension D=3 and constructs the binary cube Q3 with eight vertices. It shows that the combinatorial structure simultaneously produces the gauge group dimensions, three generations from face pairs, and exactly 24 chiral fermion flavors, which double to 48 states when chirality is included. The key numerical identity is that this count matches the size of the cube's symmetry group.
proof idea
The proof is a one-line wrapper that applies native_decide to evaluate the numerical equality between the total fermion state count and the automorphism order for dimension 3.
why it matters
This result supplies the numerical match required by the master theorem spectral_emergence, which certifies that the full Standard Model structure plus a consciousness ground state follows from D=3 with zero free parameters. It realizes the self-consistency loop in which the eight-tick octave and phi-ladder mass hierarchy emerge from the same cube whose automorphism group accounts for all 48 chiral fermion states.
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