Always Now: Möbius Geometry and the Universal Manifold - A Recursive Geometric Model of Time and Physical Constants

Always Now: Möbius Geometry and the Universal Manifold presents a mathematically unified framework in which time, physical constants, number theory, and particle structure emerge from a single recursive geometric substrate defined by the constants π, φ, and e. Building on the Resolution Gap RG=ln⁡φ/ln⁡π\mathrm{RG} = \ln \varphi / \ln \piRG=lnφ/lnπ, this work demonstrates that fundamental constants, prime number distributions, and selected particle mass ratios occupy a statistically privileged corridor within a twisted logarithmic manifold. The geometry of this manifold is shown to possess non-trivial holonomy, equivalent to a Möbius topology, where forward evolution and global closure coexist through a constant geometric twist. Four independently developed frameworks — Shadow Path Geometry, Still Point prime threading, Recursive Vacuum Theory, and cross-framework RG quantization — are mapped into a single coordinate system, revealing that primes, constants, and particles are standing-wave structures on the same recursive φ–π–e geometry. Monte-Carlo and Bayesian validation confirm that the observed clustering within the RG corridor is far beyond chance under multiple null models. The resulting structure provides a geometrically grounded model of time, scale, and physical emergence without introducing arbitrary fitting parameters. This paper serves as a synthetic convergence point for the ENSO research program, providing a mathematically explicit geometry in which number, physics, and temporal structure become manifestations of a single universal manifold. For further information about the ENSO Framework, please contact Eric Needham: ensotheory1@gmail.com