brillouinKPoints_8
plain-language theorem explainer
The number of k-points in the first Brillouin zone of a cubic lattice equals 8, matching 2 raised to the spatial dimension. Solid-state physicists working from Recognition Science would cite this when confirming the lattice structure inside the solid-state certification. The proof is a direct decision procedure on the definition that sets the count to 2 cubed.
Claim. Let $N$ be the number of k-points in the first Brillouin zone of the cubic lattice. Then $N = 8$, where the count is given by $2^3$.
background
In the Recognition Science module on solid-state physics, the crystal lattice is identified with the 8-vertex cube Q₃. The number of k-points in the Brillouin zone is defined as 2 raised to the spatial dimension D = 3, yielding eight points. This follows the eight-tick octave structure in the forcing chain, where the period 2^3 produces the discrete sampling of the zone.
proof idea
This is a one-line wrapper that applies the decide tactic to the equality brillouinKPoints = 8, where the upstream definition sets brillouinKPoints to 2 ^ 3.
why it matters
This supplies the eight_kpoints field inside solidStatePhysicsCert, which certifies the five canonical solid-state phenomena from configDim D = 5. It instantiates the T7 eight-tick octave and T8 D = 3 from the unified forcing chain, confirming that the first Brillouin zone contains 2^3 points for the cubic lattice.
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