Mode Identity Theory: Modal Realization on Brane Topology

We present Mode Identity Theory, a framework in which matter is wave and cosmological observables emerge as modal realizations on brane topology. The core equation A =_(Ω,n,θ) B identifies observable A with brane waveform B through scale hierarchy Ω, dimensional index n, and phase θ. The scaling law A/A_P = C · Ω^(−n/2) with C(θ) = 2 sin²(1.5θ) is consistent with Λ, H₀, and a₀ across 61 orders of magnitude. Surface modes (n = 2) reference Ω_Λ, the de Sitter horizon scale fixed by boundary conditions. Edge modes (n = 1) reference Ω_H, the current Hubble horizon scale, which evolves with cosmic expansion. Phase angles are not free parameters but emerge at Fibonacci values from mode stability on the non-orientable manifold. Falsification criteria are specified.