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