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A Phase-Geometric Framework with Fixed Planck Length, Mathematical Subdivided Coordinates, and Cyclic Cosmic Evolution: Extended Classical Mechanics

Extended Classical Mechanics (ECM) presents a phase-, frequency-, energy-, and propagation-based framework for describing physical emergence from an initial zero-length potential-energy state. The formulation retains the Planck length ℓₚ = 1.616255 × 10⁻³⁵ m as a fixed physical r...

Propagation-State Transformation Matrix in Extended Classical Mechanics

Version 1.2 The propagation-state formalism recently introduced within the framework of Extended Classical Mechanics (ECM) provides an alternative physical interpretation of the relativistic Doppler effect by distinguishing the normalized propagation state from the observed propa...

Core Operational Relations of Extended Classical Mechanics (ECM)

Extended Classical Mechanics (ECM) formulates a unified operational framework in which time, frequency, energy, mass, and force are represented as physically connected manifestations of phase-dependent transformation rather than as independent quantities. The framework begins wit...