number_of_patches
plain-language theorem explainer
The number_of_patches definition supplies the count of independent causal regions on the sky as 129600. Cosmologists examining the horizon problem in Recognition Science would cite this figure to quantify the uniformity puzzle in the CMB. It arises from a direct arithmetic calculation of 360 squared without invoking further lemmas.
Claim. The number of causal patches on the celestial sphere is $N = (360/1)^2 = 129600$.
background
The Cosmology.HorizonProblem module frames the horizon problem as the observed CMB uniformity to 1 part in 10^5 despite regions that never shared a causal past in standard Big Bang cosmology. Recognition Science supplies an alternative via the universal 8-tick clock that enforces homogeneity as a ledger consistency condition. Upstream results include the fundamental period T from Breath1024, the active-edge count A from IntegrationGap and Masses.Anchor, and the actualization operator A from Modal.Actualization that selects minimal-J configurations.
proof idea
The definition is a one-line arithmetic expression that directly evaluates (360/1)^2 in natural numbers. No lemmas from the depends_on list are invoked; the computation relies only on basic division and multiplication.
why it matters
This definition quantifies the scale of the horizon problem inside the RS 8-tick synchronization framework (T7), preparing the ground for cost-minimization arguments such as homogeneous_minimizes_cost. It complements the standard inflation solution by offering intrinsic synchronization without exponential expansion. The declaration touches the open question of how the universal clock produces the observed 10^{-5} correlations.
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