ECM Confidence: Planck-Scale Frequency-Length Invariance

This note presents a compact foundational consistency relation within Extended Classical Mechanics (ECM), ℓᴘ/tᴘ = ℓᴘfᴘ = c = λf and interprets it as a universal frequency–length invariant manifestation law. The relation links Planck-scale quantities (Planck length ℓᴘ, Planck time tᴘ, and Planck frequency fᴘ) with the classical wave identity λf = c, thereby establishing continuity between primordial manifestation and observable physical reality. Within ECM, this equivalence supports the principle that frequency is primary, while velocity and spatial manifestation emerge from frequency–length coupling. The result suggests that the same invariant propagation law governs both the earliest phase-dependent emergence of physical existence and all later manifested wave phenomena, providing a unified physical basis for scale continuity from the Planck domain to atomic and cosmological domains. Accordingly, ECM interprets universal propagation not merely as a spacetime property, but as a deeper frequency-governed law of manifestation. ℓᴘ/tᴘ = ℓᴘfᴘ = c = λf This compact relation represents a foundational consistency condition in Extended Classical Mechanics (ECM), linking Planck-scale emergence, classical wave mechanics, and universal propagation under a single invariant law.