causal_patch_angle
plain-language theorem explainer
The definition assigns the angular size of causally connected patches at the CMB the fixed value of 1 degree. Cosmologists comparing standard Big Bang predictions to Recognition Science models would cite this constant when quantifying the horizon discrepancy. The assignment is a direct numerical constant with no derivation or computation.
Claim. The angular size of causally connected patches at the cosmic microwave background is defined as $1^circ$.
background
The module COS-004 frames the horizon problem as the tension between CMB uniformity to 1 part in 10^5 and the causal disconnection of distant regions in standard cosmology. Recognition Science addresses this via the universal 8-tick clock, which enforces homogeneity as a ledger consistency condition without light-speed communication. The 8-tick octave (period 2^3) supplies intrinsic synchronization across the entire ledger.
proof idea
Direct constant definition that assigns the numerical value 1 (in degrees) with no lemmas or tactics applied.
why it matters
This definition anchors the quantitative statement of the horizon problem ahead of horizon_problem_stated and the contrast with standardInflation. It highlights the role of the 8-tick synchronization mechanism in providing homogeneity without causal contact, consistent with T7 of the forcing chain. The value sets up the count of roughly 10,000 disconnected patches on the full sky.
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