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 venue trace), and the phase field closes with α_f = 2/120 derived as the minimum bosonic step, yielding the 8.4% Hubble tension.

v6 direction: integration of α = C(13/60) × Ω_Λ^(−1/60) = 0.00733 as Λ fine structure constant and Δ² = 4/R² as the Yang-Mills mass gap in the venue. Exploring how native 2D angular reception (θ, φ), 1D radial sampling (z), and 1D temporal flow (c) construct the human perception of 3D volume emergent from sampling structure, complementary to General Relativity's spacetime.

v6 notation: the phase position on the 120-domain, previously α, is now θ. The symbol α is reserved for its identity: the minimum step, α = 1/|I| = 1/60. The fine structure formula α = C(θ) × Ω⁻ᵅ reveals why physics named this coupling "α": the beginning, is one step of the end. α ∼ Ω⁻ᵅ

Endgame: awaiting Euclid DR1 (Oct 2026) for model validation. If confirmed, Mode Identity and supplemental material will be unified into thesis. The Waltz: Λ Note to Einstein's Field Equations

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