The Geometry of Logic: Stratified Univalence and the Chromatic Filtration on the Fargues-Fontaine Curve

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Authors: Antoni Piotr Kodzis
Cited by: 0

Abstract

We present a rigorous structural isomorphism between Stratified Univalence and Chromatic Homotopy Theory localized on the Fargues-Fontaine Curve. We resolve the Height Conjecture, proving that the n-th universe level U_n classifies formal group laws of height n, utilizing the classical definition of v_n in pi_*(BP). We further demonstrate that the Transfinite Jump corresponds to the adjunction of Drinfeld level structures, mirroring the Lubin-Tate deformation tower. Finally, we resolve the Bott Periodicity Conjecture, identifying v_n as the monodromy generator of the "Phantom" analytic glue, creating a stable period on the Logic Curve within the topos of Light Condensed Sets.

Fields of Study & Subjects

Homotopy and Cohomology in Algebraic Topology Algebraic Geometry and Number Theory Algebraic structures and combinatorial models

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
10 January 2026
Language
EN
Document type
Preprint