SWET - Spacetime Wave Emergence Theorem: A Speculative Theoretical Framework for the Emergence of Spacetime as an Oscillatory Phase Transition from a Pre-Spatial Substrate

We propose the Spacetime Wave Emergence Theorem (SWET), a speculative theoretical framework in which spacetime is not a fundamental substrate but an emergent structure arising from an underlying pre-spatial field Ω through a process formally analogous to a second-order phase transition. The emergence propagates as a wave — described by a scalar field Ψ(x,τ) obeying a modified Klein-Gordon equation with a double-well potential — rather than as a smooth, continuous expansion. The master equation unifies this emergence wave with Einstein's field equations, recovering General Relativity exactly in the limit Ψ = 1 (fully emerged spacetime). The framework proposes that cosmological and black hole event horizons are instances of the same physical boundary — the emergence frontier — and that Hawking radiation is the observable signature of pulse activity at that frontier. A testable prediction is derived: if spacetime expansion has oscillatory microstructure, the Cosmic Microwave Background (CMB) power spectrum should exhibit periodic modulation at low multipoles, consistent with anomalies already observed by the Planck satellite but not fully explained by standard inflation. Three undetermined constants (v_s, α, β) are identified as targets for future formalization. This paper is submitted as a speculative contribution for academic evaluation and does not claim mathematical completeness.