{"id":"doi:10.5281/zenodo.20459676","kind":"article","title":"A Proof of the Langlands Correspondence via Information Geometry","authors":["Wengang Yu"],"author_count":1,"year":2026,"published":"2026-05-30","venue":"Zenodo (CERN European Organization for Nuclear Research)","cited_by":0,"doi":"10.5281/zenodo.20459676","arxiv_id":null,"nct_id":null,"source_url":"https://doi.org/10.5281/zenodo.20459676","archive_url":"https://space-kitty.com/papers/doi:10.5281/zenodo.20459676","updated":null,"pmid":null,"pmcid":null,"openalex_id":"W7162847070","pdf_url":null,"abstract":"We establish a categorical equivalence between the information space category $\\Info$---whose objects are locally ringed spaces equipped with an entanglement distance structure derived from quantum mutual information---and the perfectoid space category $\\Perfd$ in the sense of Scholze. The equivalence is realized by a contravariant spectral functor $\\D: \\Info \\to \\Perfd$ that assigns to each information space its spectral space. We prove that $\\D$ is fully faithful and essentially surjective (Theorem~A). Within this framework, we prove the geometric Langlands duality for all reductive groups over $p$-adic fields as the fibration of algebraic versus geometric coordinates on the $G$-information space $X_p^G$ (Theorem~B). Extending this duality to the global setting via the restricted product of local valued information spaces, we establish the global Langlands correspondence for all reductive groups over all number fields---the central conjecture of the Langlands program---as an equivalence between the category of global Galois representations and the category of global automorphic forms (Theorem~C). The proof of essential surjectivity reduces to a purely categorical lemma: the restricted product of local equivalences is an equivalence. We further prove the Langlands functoriality conjecture via quantum state extension, characterize arithmetic $L$-functions as regularized characteristic functions of the entanglement spectrum of associated quantum states, and establish the analytic continuation and functional equation of global $L$-functions within the information space framework. This provides a unified information-theoretic foundation for the entire Langlands program: the dualities between Galois representations and automorphic forms, between $L$-functions and entanglement spectra, and between functorial lifting and quantum state extension all emerge as manifestations of a single underlying principle---the algebraic-geometric binarity of quantum information structures.","abstract_license":"CC-BY (publisher license, via OpenAlex)","license":"cc-by","is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Advanced Algebra and Geometry"],"details":null,"provenance":"openalex","attribution":"Abstract of \"A Proof of the Langlands Correspondence via Information Geometry\" by Wengang Yu, https://doi.org/10.5281/zenodo.20459676, used under its Creative Commons Attribution license (CC-BY); markup removed, otherwise unmodified.","topics":[{"slug":"landmark-math-results","name":"Landmark Results in Pure Mathematics","domain_slug":"math-cs"}],"cited_in_dossiers":[]}