Which physical constants are derived from phi?

permalink: https://pith.science/recognition/ask/which-physical-constants-are-derived-from-phi-c5ad380f · first asked 2026-05-24 · browse all asks

confidence: low in recognition cached

φ is forced by self-similarity in a discrete ledger with J-cost phi_forced. Uniqueness among positive self-similar ratios is proved by phi_unique_self_similar and phi_unique_positive. From φ the coherence quantum is derived as E_coh := φ^{-5} E_coh_pos and the minimum non-trivial cost as J_bit := ln(φ) J_bit_pos. The supplied slice contains no derivations of standard physical constants (c, ħ, G, α, masses) from φ.

cited recognition theorems

PhiForcing.phi_forced Establishes φ is forced by self-similarity in discrete ledger.
PhiForcing.phi_unique_self_similar Proves uniqueness of φ as the positive self-similar ratio.
PhiEmergence.phi_unique_positive Proves φ is the unique positive solution to r² = r + 1.
PhiForcing.E_coh_pos Establishes positivity of E_coh derived directly from φ.
PhiForcing.J_bit_pos Establishes positivity of J_bit derived directly from φ.

outside recognition

Aspects Recognition does not yet address:

Derivations of c, ħ, G, α or particle masses from φ
Any theorem identifying E_coh with ħ or J_bit with a standard constant
Theorems for alpha inverse or mass scaling from φ

recognition modules consulted

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.