Mode Identity Theory: Modal Realization on Nested Topology

Mode Identity Theory (MIT) proposes that matter is wave, and cosmological observables emerge as modal samples on a bounded, non-orientable topology. The framework inverts standard assumptions: waves exist and observation samples them; particles are realizations of that return. From one topological postulate, S¹ = ∂(Möbius) ↪ S³, a single scaling law emerges with no free parameters; it recovers Λ, H₀, and a₀ across 61 orders of magnitude. Five anomalies resolve under one geometric structure: CMB large-angle departures, the a₀ ≈ cH₀ coincidence, the cosmological constant problem, the cosmic coincidence, and null dark matter detection. Two distinct predictions separate MIT from alternatives: a₀(z) ∝ H(z): the MOND scale evolves with expansion Λ remains constant: the apparent w(z) evolution is an inference artifact Both predictions are testable now. Falsification criteria are pre-registered; Euclid DR1 (October 2026) provides the decisive test. v5 update: every component of the scaling law now traces explicitly to the topology postulate, including the 120-grid (irreducibility), Fibonacci wells (Hurwitz stability), observer position (UV↔IR fixed point), and manifold assignments (epoch-dependence). The Λ prediction sharpens via a 3/2 dimensional conversion (2D surface eigenvalue → 3D bulk trace), and the phase field closes with α_f = 2/120 derived as the minimum bosonic step, yielding the 8.4% Hubble tension. Endgame: awaiting Euclid DR1 (Oct 2026) for model validation. If confirmed, MIT and supplemental material will be unified into thesis.