IndisputableMonolith.Core.URC
The Core.URC module establishes the foundational definitions for the unified recognition core in the Recognition Science framework. Researchers deriving all physics from one functional equation via the T0-T8 forcing chain would cite it as the entry point. It imports only Mathlib and contains definitions with no proofs.
claimThe module defines the core objects of the unified recognition calculus, including the J-cost $J(x) = (x + x^{-1})/2 - 1$ and the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$.
background
This module sits in the Core domain and supplies the initial theoretical setting for Recognition Science by importing Mathlib. It introduces the basic notation and objects that later modules use to build the forcing chain from T0 to T8, the phi-ladder, and the eight-tick octave. No upstream results are referenced, positioning the module as the root of the dependency graph.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module feeds the parent theorems in IndisputableMonolith.Foundation.UnifiedForcingChain that derive T5 J-uniqueness, T7 eight-tick octave, T8 D=3, and the constants c=1, hbar=phi^{-5}, G=phi^5/pi. It fills the base step for the single functional equation that generates all subsequent physics results.
scope and limits
- Does not contain any theorems or proofs.
- Does not depend on any other Recognition Science modules.
- Does not export any named declarations visible in the head list.