A Proof of the Riemann Hypothesis: Persistent Presence of Multiplicative Identity and the Identity Repositioning of the Critical Half-Scale 1/2 in GHT

This preprint re-audits the Riemann Hypothesis within the GHT foundation of mathematics. In standard notation, the target is ξ(ρ)=0 ⇒ Re ρ=1/2. The paper treats multiplication as the root identity: Prime, Euler factors, Dirichlet/Möbius structure, analytic continuation, completion, reflection, and the objectification of zeros are analyzed as mature manifestations in which multiplicative provenance remains traceable. The central GHT distinction is among identity, role, and mature role-reading. For a fixed multiplicative relation mq=N, role exchange corresponds in normalized exponent language to σ ↔ 1−σ; the complete complementary unit is 1 and the critical half-scale is 1/2. The paper formulates the mature presence of the complete multiplicative self-dual identity at the critical half-scale and calls the resulting closure identity repositioning. The theoretical argument is supplemented by finite executable checks and a systematic adversarial audit, including perturbation tests, provenance tracing, regression tests, mutation tests, symmetry masks, finite-sampling escape tests, forged-genealogy tests, and role-sensitivity tests. This is Paper II of the GHT Foundations of Mathematics Series.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-26
DOI
https://doi.org/10.5281/zenodo.23663854
Citations
1
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

A Proof of the Riemann Hypothesis: Persistent Presence of Multiplicative Identity and the Identity Repositioning of the Critical Half-Scale 1/2 in GHT

Yifei Ren
1 citations
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

A Proof of the Riemann Hypothesis: Persistent Presence of Multiplicative Identity and the Identity Repositioning of the Critical Half-Scale 1/2 in GHT

Yifei Ren
preprint en
1 citations

Abstract

This preprint re-audits the Riemann Hypothesis within the GHT foundation of mathematics. In standard notation, the target is ξ(ρ)=0 ⇒ Re ρ=1/2. The paper treats multiplication as the root identity: Prime, Euler factors, Dirichlet/Möbius structure, analytic continuation, completion, reflection, and the objectification of zeros are analyzed as mature manifestations in which multiplicative provenance remains traceable. The central GHT distinction is among identity, role, and mature role-reading. For a fixed multiplicative relation mq=N, role exchange corresponds in normalized exponent language to σ ↔ 1−σ; the complete complementary unit is 1 and the critical half-scale is 1/2. The paper formulates the mature presence of the complete multiplicative self-dual identity at the critical half-scale and calls the resulting closure identity repositioning. The theoretical argument is supplemented by finite executable checks and a systematic adversarial audit, including perturbation tests, provenance tracing, regression tests, mutation tests, symmetry masks, finite-sampling escape tests, forged-genealogy tests, and role-sensitivity tests. This is Paper II of the GHT Foundations of Mathematics Series.

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
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