preprintOpen MINDMar 15, 2026GREEN OA

The Riemann Hypothesis: A Gauge-Theoretic Proof via Even Dominance and Spectral Stability

LGLukas Geiger

Schwarzwald-Baar Klinikum

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Abstract

Three-part research series establishing the Riemann Hypothesis via Connes' spectral program and the Weil quadratic form. v1.1 Changelog (from v1.0): Lemma B upgraded: Parity-split spectral gap bound (fully analytical). Even-index modes: gap ~ 2√λ. Odd-index modes: gap ~ 4π²(j²-1)√λ/L², with matched coupling suppression. Lemma C reformulated: Sector-difference control replaces the global ||R0K||

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Topics & keywords

Topics
Keywords
  • Lemma (botany)
  • Spectral gap
  • Quadratic equation
  • Series (stratigraphy)
  • Riemann hypothesis
  • Eigenfunction
  • Parity (physics)
  • Stability (learning theory)
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