IndisputableMonolith.RecogSpec.PhiSelectionCore
The PhiSelectionCore module states the selection criterion φ² = φ + 1 with φ > 0. Modules testing alternative constants cite it to demonstrate uniqueness of φ. The module is purely definitional with no proofs or derivations.
claimThe selection criterion requires a positive real number φ satisfying the equation φ² = φ + 1.
background
This module belongs to the RecogSpec domain and introduces the φ selection criterion as the core condition φ² = φ + 1 with φ > 0. It operates in the setting of the Recognition Science forcing chain where T6 identifies φ as the self-similar fixed point. The criterion is the mathematical object referenced by sibling definitions such as PhiSelection.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The criterion supplies the equation used by the Alternatives module to show that e, π, √2, √3 and √5 fail the selection, proving φ is the only positive real satisfying x² = x + 1 and addressing the numerology objection.
scope and limits
- Does not derive the criterion from the Recognition Composition Law.
- Does not prove existence or uniqueness of φ.
- Does not connect the criterion to physical constants or the phi-ladder.
- Does not address alternative selection equations.