IndisputableMonolith.Core.URC
The Core.URC module supplies the foundational definitions for the Unified Recognition Calculus in Recognition Science. It introduces the basic objects from which the forcing chain T0-T8, the J-cost function, and the Recognition Composition Law are built. This is a definition module with no theorems or proofs.
claimThe module defines the Unified Recognition Calculus (URC) as the central structure containing the J-cost function $J(x) = (x + x^{-1})/2 - 1$ and the phi-ladder on which all subsequent derivations rest.
background
Recognition Science derives physics from a single functional equation. The URC module is the root of the Core domain and imports only Mathlib. It establishes notation for the J-cost, defectDist, and the self-similar fixed point phi that appears in T5 and T6 of the forcing chain. No upstream results exist because this module precedes all others.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
URC feeds the parent theorems in IndisputableMonolith.Foundation.UnifiedForcingChain, including the eight-tick octave and D=3. It supplies the base objects required for the mass formula, Berry threshold, and alpha band derivations that appear downstream.
scope and limits
- Does not contain any theorems or lemmas.
- Does not define the forcing chain steps T0-T8.
- Does not state the Recognition Composition Law.
- Does not introduce physical constants or the phi-ladder values.