IndisputableMonolith.Pipelines
The Pipelines module supplies concrete definitions for the golden ratio and pipeline functions central to Recognition Science. It defines phi as a real number, along with coeff, partialSum, F, f_gap, deltaKappa, and alphaInvPrediction. These enable numerical evaluations on the phi-ladder and constant derivations. The module serves as a base layer for mass and alpha calculations in the framework.
claimThe module defines the golden ratio as the concrete real number $phi = (1 + sqrt(5))/2$ and introduces pipeline objects coeff, partialSum, $F$, $f_{gap}$, $delta kappa$, and the prediction for $alpha^{-1}$.
background
Recognition Science derives all physics from one functional equation. The golden ratio phi emerges as the self-similar fixed point in the forcing chain T0 to T8, with constants fixed in RS-native units where c=1, hbar=phi^{-5}, and G=phi^5/pi. This module supplies a concrete embedding of phi into the reals together with auxiliary pipeline functions for the phi-ladder and gap computations.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The definitions feed parent results on the phi-ladder mass formula and alpha inverse predictions within (137.030, 137.039). They supply the yardstick and gap functions used in rung calculations and support the Recognition Composition Law together with the eight-tick octave structure.
scope and limits
- Does not include theorem statements or proofs.
- Does not depend on any other modules besides Mathlib.
- Does not expose any hypothesis interfaces or open questions.