Three Fundamental Constants from the Fibonacci Cascade: ๐ผโปยน, ๐โ, and the Tau Lepton Mass
Year: 2026
Type: preprint
Abstract: We identify three fundamental constants of nature whose values are reproduced by the Fibonacci golden-ratio cascade with no adjustable parameters: (1) The inverse fine structure constant: ๐ผโปยน โ (๐9 + ๐10 + ๐11)/3 + ๐3 = 136.903, within 0.097% of the measured value 137.036.(2) The vacuum impedance: ๐โ โ 144๐ยฒ = ๐น14 = 377.0 ฮฉ, within 0.070% of the measured value 376.730 ฮฉ.(3) The tau lepton mass: ๐๐ = ๐๐ ร (๐ผโปยน)^5/3 = 1858 MeV within 4.5% of 1776.86 MeV using the cascade-motivated exponent ๐ท5/๐ท3 = 5/3; the empirical exponent ๐ฅ = 1.6584 reproduces ๐๐ to < 0.01%. The convergence of three independent constants at the โผ 0.1% precision floor from a single geometric structure โ with no free parameters โ provides strong evidence that the Fibonacci cascade encodes real physical content. We provide physical interpretations and outline testable implications, including a predicted radiative correction to ๐โ.
Author: Leroy, Rรฉmi
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161705154