IndisputableMonolith.URCAdapters.TcGrowth
The module URCAdapters.TcGrowth supplies adapter definitions that apply binary scales and φ-exponential wrappers to model Tc growth. Researchers extending the Recognition Science phi-ladder to critical or time-dependent phenomena would cite it when linking growth to the forcing chain. The module structure is a property declaration followed by a theorem that the property holds, built directly on the imported Scales constructions.
claimThe module defines the Tc growth property $P_{Tc}$ together with the theorem asserting that $P_{Tc}$ holds, where both are constructed from binary scales and φ-exponential wrappers satisfying the recognition composition law.
background
The module sits in the URCAdapters domain and imports binary scales and φ-exponential wrappers from RecogSpec.Scales. These wrappers encode the self-similar fixed point φ forced at step T6 of the unified forcing chain, together with the eight-tick octave and the recognition composition law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y).
proof idea
This is a definition module, no proofs. The structure consists of the declaration of tc_growth_prop followed by the theorem tc_growth_holds that directly applies the upstream binary-scale and φ-exponential constructions.
why it matters in Recognition Science
The module supplies the adapter layer that feeds Tc growth into the larger URC framework, supporting downstream use of the phi-ladder mass formula and the constants G = φ^5/π and α^{-1} in (137.030, 137.039). It closes the interface between the Scales module and physical growth models in the eight-tick octave.
scope and limits
- Does not derive φ or the forcing chain steps independently.
- Does not extend beyond binary scales.
- Does not contain numerical evaluations or simulations.
- Does not address non-exponential or multi-dimensional growth.