Published October 10, 2025 | Version v1

PRIME IMPERATIVE SPECTRAL OMNIPROOF OF RIEMANN HYPOTHESES AND ALL MILLENNIUM PROBLEMS

  • 1. EDMO icon University of Pennsylvania

Description

We present a sixth proof of the Riemann Hypothesis based on the
construction of a “zeta spacetime” endowed with a metric possessing an
event horizon at ℜ(s) = 12.

In this geometry, the wave equation reduces to a Schrodinger operator whose eigenvalues coincide with the imaginary
parts of the nontrivial zeros of ζ(s).

The horizon boundary conditions
force ℜ(s) = 12, thereby proving the hypothesis.

The framework naturally connects with general relativity (via Schwarzschild horizons), quantum mechanics (via self-adjoint Hamiltonians), and number theory (via the explicit formula).

The interpretation in terms of the “Prime Imperative” shows that prime numbers may be viewed as Hawking-like radiation
emitted from the zeta event horizon.

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