temporal_dim
plain-language theorem explainer
Recognition Science fixes the temporal dimension count at exactly one, identified with the advance of the eight-tick recognition cycle. Workers deriving Lorentzian geometry from J-cost minimization cite this assignment when assembling the metric signature and arrow of time. The declaration is a direct constant definition justified by the T7 step of the forcing chain.
Claim. The number of temporal dimensions equals $1$.
background
The module derives the full 4D Lorentzian structure from the J-cost functional and the T0–T8 chain. J(x) = (x + x^{-1})/2 − 1 is strictly convex with unique minimum at x = 1; the eight-tick operator decreases cost along the temporal direction while spatial directions carry positive curvature from J''(1) = 1. The local setting states that spacetime itself is a theorem of cost minimization, with c = 1 as a tautology and no free parameters.
proof idea
Direct definition assigning the natural number 1, matching the octave advance stated in the module documentation.
why it matters
This supplies the temporal component required by downstream results including arrow_of_time, lorentzian_signature, and spacetime_dim. It completes the central theorem of the module: 1 temporal dimension from the 8-tick cycle (T7) plus 3 spatial dimensions (T8) produces η = diag(−1, +1, +1, +1). It touches the interface between the temporal forcing step and the spatial dimension count.
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