not_1_4_signature
plain-language theorem explainer
Recognition Science forces the spatial dimension to three via the T8 step of the unified forcing chain, so the only RS-compatible spatial count is three and the metric signature cannot be (1,4). Researchers deriving emergent Lorentzian geometry from the J-cost functional cite this when confirming that spacetime dimension four arises strictly as one temporal octave plus three spatial axes. The proof is a one-line term simplification that unfolds spatial_dim against the constant supplied by D_physical.
Claim. The spatial dimension of the physical world satisfies $d_s = 3$, hence $d_s ≠ 4$.
background
The SpacetimeEmergence module derives the complete 4D Lorentzian structure (metric signature (−,+,+,+), light cone, arrow of time) as a theorem of J-cost minimization under the T0–T8 forcing chain. Spatial metric positivity follows from J''(1) = 1 while the temporal direction is singled out by the 8-tick recognition operator; dimension counting is completed by T8 (D = 3 spatial) together with the octave period. D_physical is the upstream definition that fixes the spatial dimension of the physical world to the constant 3 and asserts RS-compatibility.
proof idea
Term-mode proof consisting of a single simp application. The tactic unfolds the definition of spatial_dim and substitutes the constant value of D_physical, reducing the negated equality to four directly to falsehood.
why it matters
The declaration supplies SE-010, the uniqueness of the (1,3) signature, inside the central theorem of the module. It closes the spatial count from T8, guaranteeing that total spacetime dimension is exactly four with the required Lorentzian signature and thereby supporting all downstream derivations of the light cone, proper time, and E² = p² + m² with zero free parameters.
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