not_1_2_signature
plain-language theorem explainer
Recognition Science forces exactly three spatial dimensions from the T8 step of the unified chain, so the spatial dimension cannot equal two. Researchers deriving Lorentzian geometry from J-cost minimization would cite this when confirming the dimensional count in spacetime emergence. The proof is a direct simplification that unfolds the constant definitions to reach an immediate contradiction.
Claim. $¬(D = 2)$ where $D$ is the number of spatial dimensions, defined to equal the physical dimension constant set to three.
background
The module derives the complete structure of 4D Lorentzian spacetime from the J-cost functional and the T0–T8 forcing chain. Spatial dimension is introduced as the count of axes whose metric coefficient is positive, fixed by the requirement that J''(1) = 1 together with the self-similar fixed point φ. D_physical is the upstream definition that sets this count to three; spatial_dim simply aliases that constant.
proof idea
The proof is a one-line wrapper that applies the simp tactic to the definitions of spatial_dim and D_physical, reducing the claim directly to the falsehood 3 = 2.
why it matters
The result closes the exclusion of two-dimensional spatial geometry inside the central theorem of the module, which states that spacetime metric signature (−,+,+,+) is forced by RCL, J-uniqueness, the eight-tick octave, and D = 3. It feeds the sibling derivations of spacetime_dim_eq_four and lorentzian_signature by guaranteeing the spatial count required for the positive-definite spatial block.
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