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Preprint . 2026
License: CC BY
Data sources: ZENODO
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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VR-Audit: A Programme of Operational Audits of Classical Theorems

Authors: Reznik, Vitaly;

VR-Audit: A Programme of Operational Audits of Classical Theorems

Abstract

VR-Audit is an open-ended programme of operational audits of classical theorems of mathematics and the fifth work in the VR Cycle, its first applied one. It applies the two-register apparatus of VR-Forms: each audit establishes an operational corollary of a classical theorem through the transit pattern, in which the classical machinery is invoked as a black box in the formal register while operationality of the result is established separately, in the operational register, through wrapping predicates and explicit witness construction. The preprint accumulates the programme, each version superseding the previous as a complete record to date. Version 1.0.0 contains the first audit — the Hahn–Banach extension theorem for operational Hilbert spaces, proved via Riesz representation — exhibiting precisely where the classical tool is used and where the operational content is built. The accompanying machine-checked Lean 4 formalisation is published separately (DOI 10.5281/zenodo.20363739). Version 1.0.1 reframes the exposition to the cycle's no-ontology position — the empty set is taken as a nullary operation and "operational ontology" is renamed the operational universe/foundation — with no mathematics altered. The work was produced with AI assistance under Variant A (interactive parent-child architecture), human curator Vitaly Reznik, consistent with all works of the VR Cycle. Accompanying Lean 4 formalisation: DOI 10.5281/zenodo.20363739.

Keywords

computable analysis, Riesz representation, foundations of mathematics, two-register apparatus, mathlib, Hilbert space, Lean 4, constructive mathematics, transit pattern, functional analysis, Hahn–Banach theorem, operational mathematics, VR-Audit, formal verification, wrapping principle

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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!
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