spatial_dim
Defines the spatial dimension count as exactly 3, the value forced by the T8 step of the Recognition Science forcing chain. Researchers deriving Lorentzian geometry from J-cost minimization would reference this when establishing the (1,3) metric signature. The definition is a direct alias for the upstream D_physical constant.
claimThe number of spatial dimensions is $D=3$, as required by the T8 step of the Recognition Science forcing chain.
background
Recognition Science derives the full structure of 4D Lorentzian spacetime from the J-cost functional and the T0–T8 forcing chain. The module shows that the metric signature (−,+,+,+), light cones, and arrow of time arise as theorems of cost minimization rather than background postulates. Spatial curvature is positive definite because J''(1)=1, while the temporal direction is the unique cost-reducing axis set by the 8-tick recognition operator.
proof idea
One-line definition that aliases the upstream D_physical value.
why it matters in Recognition Science
This supplies the spatial count required by the downstream theorems that establish the unique Lorentzian signature (1,3). It implements the T8 step of the forcing chain and feeds directly into lorentzian_signature, signature_unique, spacetime_dim, and SpacetimeEmergenceCert. The parent results close the derivation of η = diag(−1,+1,+1,+1) with zero free parameters.
scope and limits
- Does not derive the value 3 from the J-cost equation inside this module.
- Does not address non-integer or variable dimensions.
- Does not compute dynamical evolution of the dimension count.
formal statement (Lean)
65def spatial_dim : ℕ := D_physical
proof body
Definition body.
66
67/-- Total spacetime dimension: temporal + spatial. -/