This contribution proposes, from first principles, a resolution of the Riemann Hypothesis: all non-trivial zeros of the zeta function lie on the critical line Re (s) = 1/2. It rests on two previously developed frameworks — the Nitescence Theorem (resolution of undecidability through canonical structural ascension) and the Theory of Cymalogy (an undulatory reading of analytic objects). The starting point is philosophical: number is not primitively quantitative but intrinsically geometric. The passage from 1 to 2 requires a 0 understood as a frame rather than as nothingness; the pair 0, 1 is then the first geometric datum, and the whole of arithmetic unfolds from a spatial act of distinction. Since, in cymalogy, a geometric structure carries a temporal and undulatory one, the zeros of zeta appear as the points of perfect destructive interference between the additive and multiplicative organisations of the integers — realisable only on the self-dual axis fixed by the functional equation, namely the critical line. A deliberately speculative and strictly principial proposal, making no appeal to empirical or observational corroboration, shared in the spirit of open science. Keywords: Riemann Hypothesis • zeta function • analytic number theory • non-trivial zeros • critical line • causal geometry • metageometric projection • structural ascension • proof theory • mathematical logic • ordinal analysis • Peano Arithmetic • independence results • mathematical physics • prime distribution • Cymalogy • Nitescence Theorem • structuralism • ontology of mathematics • wave interference • self-duality • Open Science.
Xavier J. Régent (Wed,) studied this question.