From Absolute Space to Angular Phase: An Extended Classical Mechanics (ECM) Reassessment of the Physics–Mathematics Relationship in Gravitational Theory and the Genesis of Manifested Reality

This monograph re-examines the epistemological relationship between physics and mathematics, tracing the historical development of gravitational theory from Newtonian mechanics through Einstein's general relativity, and evaluates the empirical standing of the spacetime concept. It is argued that physics, as an empirical science, holds precedence over mathematical abstraction: nature remains the ultimate arbiter of physical truth, and no formalism, however elegant, survives contradiction by verifiable experiment. The historical record is reviewed — the role of non-Euclidean geometry, Marcel Grossmann's mathematical mediation, Einstein's "hole argument," the Einstein–Hilbert correspondence of 1915, and Newton's independent invention of calculus — to show that physics and mathematics interact as two halves of a continuous synthesis. Building on this foundation, the monograph presents the Extended Classical Mechanics (ECM) framework: a non-relativistic, physical-first model in which manifested reality emerges from a non-zero, vibrating point origin through a Pre-Planck phase state (λₚₕₐₛₑ₍ₓ∘₎ < ℓᴘ₍ₓ∘₎) into an angularly complete universe (≥ 360°), governed by a transformation engine Tₓ∘ = x°/360° f₀. Within this model, phenomena conventionally attributed to spacetime curvature — gravitational redshift, time dilation, and the invariance of c — are reinterpreted as localized frequency modulations and angular phase alignments constrained by the conservation mechanics of the sub-Planckian origin. Version 1.1 additionally develops the Planck anchoring of the framework, the accumulated-phase formalism (x° = 360° f Δt), a phase-modulated orbital derivation of Mercury’s anomalous perihelion advance, and a weak-field limiting-case recovery of Newtonian gravity through the phase-displacement field.