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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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The CRM Signature of Berkovich Motives: How Scholze's Independence of l Confirms the Archimedean Obstruction Thesis (Paper 101 of the Constructive Reverse Mathematics Series)

Authors: Lee, Paul Chun-Kit;

The CRM Signature of Berkovich Motives: How Scholze's Independence of l Confirms the Archimedean Obstruction Thesis (Paper 101 of the Constructive Reverse Mathematics Series)

Abstract

Description:Paper 101 of the Constructive Reverse Mathematics (CRM) Series. We perform a CRM audit of Scholze's Berkovich motivic proof of independence of l for local Langlands parameters (2024-2026). The classical approach requires the isomorphism iota: Q_l-bar ~ C, routing through the Archimedean place at cost CLASS. Scholze's motivic strategy achieves CRM signature WKL, strictly below CLASS, by constructing the Langlands parameterization natively in a universal motivic coefficient system. Four main results: (A) CRM Signature = WKL after parasitic WLPO excision. Decomposition: 3 BISH + 3 WKL = 6 structural components (50% constructive). (B) Logical Independence: WKL < CLASS proves the motivic proof cannot inherit CLASS from Fargues-Scholze. (C) Seven CRM Discoveries from partial Lean 4 formalization and definitional audit (831 lines, 0 sorry). (D) Motivic descent is a fourth mode of de-omniscientising descent. The seven discoveries: (1) Berkovich Type 3 points require WLPO; Huber adic spaces achieve WKL. (2) Non-Archimedean completion preserves Q-valued groups (BISH). (3) Perfectoid tilting = WKL. (4) Quasicategorical horn fillers are parasitically CLASS. (5) Arc-topology cost collapses from CLASS to WKL for countable p-adic algebras. (6) Universe impredicativity is orthogonal to logical cost. (7) Derived functors via functorial resolutions are BISH. This is the first CRM analysis of frontier arithmetic geometry produced independently of the CRM program, confirming the Archimedean Obstruction Thesis (Paper 98). Keywords: constructive reverse mathematics, Berkovich motives, independence of l, local Langlands, CRM audit, Weak Konig's Lemma, Archimedean obstruction, motivic descent, Scholze, Fargues-Fontaine curve, perfectoid spaces, Lean 4, formal verification License: Creative Commons Attribution 4.0 International (CC BY 4.0) Upload type: publication Publication type: article DOI: 10.5281/zenodo.18869076 Related identifiers:- Paper 98 (Motivic CRM Architecture): 10.5281/zenodo.18828345- Paper 76 (CRMLint): 10.5281/zenodo.18779362- Format guide: 10.5281/zenodo.18765700- Scholze, Berkovich motives: arXiv:2412.03382- Scholze, Motivic geometrization: arXiv:2501.07944

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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