cyDimension_eq_D
plain-language theorem explainer
The Calabi-Yau threefold dimension in the Recognition Science algebraic geometry construction equals 3. Researchers examining the Hodge connection between the recognition lattice Q₃ and Calabi-Yau threefolds cite this to align the dimension with the spatial value D. The proof is a direct reflexivity step on the explicit definition that assigns the integer 3.
Claim. The dimension of the Calabi-Yau threefold equals 3.
background
The module treats algebraic geometry as the study of varieties defined by polynomial equations, identifying the recognition lattice Q₃ as an algebraic variety over F₂. Five canonical objects (affine variety, projective variety, Calabi-Yau, K3 surface, elliptic curve) are introduced with configDim D = 5, and the Calabi-Yau case is singled out for its predicted mirror symmetry at D = 3. The upstream definition sets the Calabi-Yau dimension explicitly to the constant 3.
proof idea
One-line wrapper that applies reflexivity to the definition of the Calabi-Yau dimension.
why it matters
This supplies the concrete dimension value to algebraicGeometryCert, which records the five objects and the Calabi-Yau dimension. It realizes the T8 step of the forcing chain that fixes D = 3 spatial dimensions and supports the Calabi-Yau threefold connection for Q₃. No open questions are closed by this step.
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