total_fermion_states
plain-language theorem explainer
The definition computes total fermion states as twice the chiral fermion flavor count, producing the integer 48 when D equals 3. Particle physicists matching geometric symmetries of the binary cube Q3 to Standard Model degrees of freedom would cite this count. It is a direct arithmetic doubling of the upstream fermion_flavors result to incorporate chirality.
Claim. The total number of fermion states, including chirality doubling, equals $2$ times the chiral fermion flavor count, where the flavor count is computed as $3$ colors times $3$ generations times $2$ chiralities for quarks plus $1$ times $3$ times $2$ for leptons.
background
In the SpectralEmergence module the binary cube Q3 arises directly from the forced datum D=3 (T8), yielding 8 vertices. The sibling definition fermion_flavors computes the chiral count as quarks plus leptons, with quarks given by SpectralSector.dim .color times face_pairs 3 times 2 and leptons by SpectralSector.dim .hypercharge times face_pairs 3 times 2, producing 24. The module_doc states that this structure simultaneously forces the gauge group SU(3) times SU(2) times U(1), exactly 3 generations from face-pair count, and |Aut(Q3)|=48 total fermionic degrees of freedom.
proof idea
One-line definition that applies the arithmetic doubling 2 * to the output of fermion_flavors.
why it matters
This definition supplies the left-hand side of the downstream theorem fermion_states_eq_aut, which equates it to aut_order 3 and thereby confirms that the symmetry group of Q3 is the fermion state space. It closes the counting loop begun in the module_doc from T8 (D=3) through the eight-tick octave (T7) and phi forcing (T6) to the observed 48 states. The SpectralEmergenceCert structure then packages the same count as one of its verified fields.
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