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2025
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| Online Access: | https://doi.org/10.5281/zenodo.17830979 |
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| _version_ | 1866901187377233920 |
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| author | wu, dafeng |
| author_facet | wu, dafeng |
| contents | <div>Based on the recently established L-function generation framework starting from distin</div> <div>guishability and scale-inversion symmetry [13], we present a physics-based proof of the Gen</div> <div>eralized Riemann Hypothesis (GRH). In this framework, a unitary representation ρ : A → U(n)</div> <div>not only generates an L-function L(s, ρ) via the total distinguishability energy Eρ(s), but also</div> <div>rigidly corresponds to an SU(n) gauge theory whose coupling constant αG −1 is locked onto</div> <div>the arithmetic invariant</div> <div></div> <div> L</div> <div>0</div> <div>L(1 (1,ρG)</div> <div>,ρG</div> <div>)</div> <div></div> <div></div> <div></div> <div>. We demonstrate: If L(s, ρ) possesses a zero s0 not on the</div> <div>critical line < (s) = 1/2, then the corresponding gauge coupling αG, via the locking formula,</div> <div>would become either complex or singular (infinite). Such a coupling would simultaneously</div> <div>violate the two foundational pillars of quantum field theory–unitarity (probability conserva</div> <div>tion) and causality (microscopic locality). Since the observable physical world–specifically, the</div> <div>Standard Model described by the specific direct sum ρSM–must be both unitary and causal,</div> <div>all relevant L-functions must have their zeros on the critical line. This argument relies solely</div> <div>on the intrinsic physical correspondence of the generative framework, thereby establishing</div> <div>the validity of GRH for all classical L-functions (Dirichlet, automorphic, motivic) as a direct</div> <div>corollary of quantum physical consistency</div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17830979 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Physical Proof of the Generalized Riemann Hypothesis: Unitarity as the Origin of the Critical Line from the Distinguishability–Gauge Correspondence wu, dafeng <div>Based on the recently established L-function generation framework starting from distin</div> <div>guishability and scale-inversion symmetry [13], we present a physics-based proof of the Gen</div> <div>eralized Riemann Hypothesis (GRH). In this framework, a unitary representation ρ : A → U(n)</div> <div>not only generates an L-function L(s, ρ) via the total distinguishability energy Eρ(s), but also</div> <div>rigidly corresponds to an SU(n) gauge theory whose coupling constant αG −1 is locked onto</div> <div>the arithmetic invariant</div> <div></div> <div> L</div> <div>0</div> <div>L(1 (1,ρG)</div> <div>,ρG</div> <div>)</div> <div></div> <div></div> <div></div> <div>. We demonstrate: If L(s, ρ) possesses a zero s0 not on the</div> <div>critical line < (s) = 1/2, then the corresponding gauge coupling αG, via the locking formula,</div> <div>would become either complex or singular (infinite). Such a coupling would simultaneously</div> <div>violate the two foundational pillars of quantum field theory–unitarity (probability conserva</div> <div>tion) and causality (microscopic locality). Since the observable physical world–specifically, the</div> <div>Standard Model described by the specific direct sum ρSM–must be both unitary and causal,</div> <div>all relevant L-functions must have their zeros on the critical line. This argument relies solely</div> <div>on the intrinsic physical correspondence of the generative framework, thereby establishing</div> <div>the validity of GRH for all classical L-functions (Dirichlet, automorphic, motivic) as a direct</div> <div>corollary of quantum physical consistency</div> |
| title | A Physical Proof of the Generalized Riemann Hypothesis: Unitarity as the Origin of the Critical Line from the Distinguishability–Gauge Correspondence |
| url | https://doi.org/10.5281/zenodo.17830979 |