spacetime_dim_eq_four
Spacetime, light cone, and proper time emerge from the recognition lattice.
plain-language theorem explainer
Spacetime dimension equals four in the Recognition Science framework. Workers deriving Lorentzian geometry from J-cost minimization cite this when closing the spacetime emergence certificate. The proof reduces directly to unfolding the dimension definitions and reflexivity.
Claim. The spacetime dimension equals four, consisting of one temporal dimension from the eight-tick octave and three spatial dimensions from the forcing chain.
background
The Spacetime Emergence module derives the full structure of 4D Lorentzian spacetime from the J-cost functional and the T0-T8 forcing chain. Spatial dimension is fixed by D_physical, defined as the constant 3. Temporal dimension follows from the eight-tick recognition operator, with tick defined as the fundamental time quantum equal to 1 in RS-native units. The upstream result spacetime_dim from Gravity.Connection supplies the target definition being proved equal to 4.
proof idea
One-line wrapper that unfolds spacetime_dim, temporal_dim, spatial_dim, and D_physical then applies reflexivity.
why it matters
This fills SE-001 and feeds directly into signature_unique, which establishes that the (1,3) signature is the unique RS-compatible choice, and into spacetime_emergence_cert, which assembles the full certificate with zero sorry. It realizes T7 (eight-tick octave) and T8 (D=3) from the forcing chain, confirming the metric signature without free parameters.
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