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Claim

The 𝔽₁ Square with an Intersection Theory

integration_instructionsResearch softwarekeyboard_double_arrow_right Software 06 Jun 2026Publisher:Zenodo
Authors: Flom, Alex;
Code repository: https://github.com/afflom/F1/tree/v0.17.0

doi: 10.5281/zenodo.20667237 , 10.5281/zenodo.20570841 , 10.5281/zenodo.20705758 , 10.5281/zenodo.20619686 , 10.5281/zenodo.20740196 , 10.5281/zenodo.20665732 , 10.5281/zenodo.20619087 , 10.5281/zenodo.20669546 , 10.5281/zenodo.20679615 , 10.5281/zenodo.20571263 , 10.5281/zenodo.20574813 , 10.5281/zenodo.20581942 , 10.5281/zenodo.20603919 , 10.5281/zenodo.20570842 , 10.5281/zenodo.20573219 , 10.5281/zenodo.20572542 , 10.5281/zenodo.20571847 , 10.5281/zenodo.20571586 , 10.5281/zenodo.20573984 , 10.5281/zenodo.20571432 , 10.5281/zenodo.20572140 , 10.5281/zenodo.20572960 , 10.5281/zenodo.20572768 , 10.5281/zenodo.20575748 , 10.5281/zenodo.20573726

The 𝔽₁ Square with an Intersection Theory

Abstract

An active research program formalizing the arithmetic surface Spec ℤ ×_{𝔽₁} Spec ℤ together with the Hodge-index positivity whose truth is the Riemann Hypothesis. It pairs a Lean 4 formalization — extending the UOR-Foundation library — that encodes the construction's honest epistemic status (verified and classical results carry their established status; the RH crux is encoded as not-asserted, never as proven) with research documents that specify the target object, the candidate-construction gap, the named obstructions, and a checkable verification ladder.

If you use this software, please cite it as below.

Keywords

intersection theory, Connes-Consani, formalization, arithmetic site, tropical geometry, Lean 4, characteristic one, Hodge index theorem, Riemann Hypothesis, F1 geometry, field with one element

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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
Average
Average