What question did this study set out to answer?

This research aims to connect a specific Kervaire manifold to fundamental physical theories and predictions.

March 28, 2026Open Access

The Last Kervaire Manifold as a Physical Origin: From Gödel Incompleteness Oscillation to Riemann Zeros Spectrum

Key Points

This research aims to connect a specific Kervaire manifold to fundamental physical theories and predictions.
Deriving physical parameters from a unique 126-dimensional Kervaire manifold.
Using arithmetic conditions related to the Heegner point τ₁₆₃.
Establishing links between mathematical axioms and physical models like general relativity.
Predicting a universal power-law tail in the CMB small-scale power spectrum.
Observing periodic modulations in cosmic expansion history.
Identifying discrete features in gravitational wave backgrounds, all parameter-free and testable.

Abstract

This mathematical foundation expands physical principles to a unique last 126-dimensional smooth closed manifold with Kervaire invariant one, serving as the underlying space for a self-projective topological system subject to the following arithmetic condition. The complex structure modulus is locked at the Heegner point ₁₆₃, yielding arithmetic invariants that determine all physical parameters. From five axioms we derive the standard model and general relativity as projections, and obtain a spectral density for the chaotic background that is the unique fixed point of a Fourier self-projection equation, relying on the Riemann hypothesis, making it testable. Testable predictions include a universal power-law tail in the CMB small-scale power spectrum, periodic modulations in the expansion history, and discrete features in the stochastic gravitational wave background. All predictions are parameter-free and accessible to current or near-future observations.

The Last Kervaire Manifold as a Physical Origin: From Gödel Incompleteness Oscillation to Riemann Zeros Spectrum

Key Points

Abstract

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