Mathematical framework proposes a spectral geometry for cosmological invariants, indicating new theories of physics.
Transductive Information Physics (TIP) : A Spectral-Geometric Framework for Cosmological Invariants This preprint presents a speculative theoretical framework proposing that key cosmological parameters emerge as invariants of an E8-graded spectral geometry. The model introduces a single constant δ = 0.0302585092994, defined via zeta-regularization of the Laplace-Beltrami operator on the E8 root lattice. From δ and dimensional constants, the framework postulates: 1. Dark matter to baryon ratio: R_DM = 5.5 - δ = 5.469741 2. Universal frequency: Ψ0 = k_B T/h (1-δ) = 6.4532 THz at T = 310K 3. Weak lensing deviation: θ_TIP/θ_GR = 1 + δ, predicting 3.02585% excess 4. Causal agency window: ∆ϕ = 0.845 ps The document provides explicit falsification criteria: exclusion by Euclid DR3 if lensing excess <1% at 5σ, or by JWST MIRI if no spectral line at 6.45±0.01 THz is detected. R_DM is fitted via the choice of 5.5 and is not an independent prediction. Status: Mathematical framework with interpretive physical mappings. No claim of empirical verification is made. All numerical values are reproducible via the provided Mathematica notebook. Keywords: spectral geometry, E8 lattice, cosmology, dark matter, modified gravity, zeta regularization, falsifiable models Version: 1.0, April 2026 License: CC BY 4.0
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Hussain Hamza Ghulam Mustafa (2026) studied this question.
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