Author

Juan Antonio Vega Coso

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Preprint Aug 2026

Spectral duality structures and the Fisher--Rao geometry of reset distributions

We study the geometry that spectral duality induces on the simplex of reset distributions for absorbed Markov processes with geometric resetting. The Fisher--Rao metric provides the intrinsic geometry: under the square-root embedding, the reset-neutral separatrix $\Sigma$ becomes a totally geodesic subsphere and a Fish...

Juan Antonio Vega Coso · 4 citations

Preprint Sep 2026

Algebra of spectral duality structures

This paper establishes the algebraic and categorical foundations of spectral duality structures (SDS). We show that the class of all SDS admits the structure of a graded monoidal category, in which the degree K is the fundamental invariant indexing the strata. We define the Cartesian product and the disjoint union of s...

Juan Antonio Vega Coso · 0 citations