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| Format: | Recurso digital |
| Language: | English |
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2025
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| Online Access: | https://doi.org/10.5281/zenodo.17339936 |
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| _version_ | 1866901350100500480 |
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| author | Yuanjian, Li |
| author_facet | Yuanjian, Li |
| contents | <p>We present a mathematically rigorous, axiomatic formulation of a candidate unified field framework based on measure-valued dynamics on a spectral manifold. Time is treated as the weak derivative of a family of Radon probability measures \(\{\mu_t\}_{t\in\mathbb R}\) and matter fields are encoded by operator-valued measures \(M_t\) on a separable Hilbert space \(\mathcal H\). A single dynamical operator \(\mathcal G\) --- the \emph{universal gravitational generator} --- drives the joint evolution<br>\[<br>\frac{d}{dt}(\mu_t,M_t)=\mathcal G(\mu_t,M_t).<br>\]<br>We (i) give a concise, rigorous axiom system (Axiom I–X) and discuss necessity/weakenability of each axiom; (ii) prove a uniqueness theorem for \(\mathcal G\) within the adopted axiomatic framework (with full statements of technical lemmas used); (iii) construct a computable \(3\times3\) Hermitian toy model for \(\mathcal G\) and demonstrate explicitly how spectral invariants map to Yukawa-like couplings; (iv) derive several concrete observational predictions (CMB non-Gaussianity signatures, Higgs/Yukawa perturbations, black-hole information-retrieval timescales, cold-atom interferometry signals) along with back-of-the-envelope estimates; and (v) provide a methodological discussion and research program to advance the framework toward empirical falsification. All proofs are given under clearly stated axioms; empirical claims are presented as testable predictions.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17339936 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Axiomatization and Spectral Completion of a Unified Field Framework Yuanjian, Li <p>We present a mathematically rigorous, axiomatic formulation of a candidate unified field framework based on measure-valued dynamics on a spectral manifold. Time is treated as the weak derivative of a family of Radon probability measures \(\{\mu_t\}_{t\in\mathbb R}\) and matter fields are encoded by operator-valued measures \(M_t\) on a separable Hilbert space \(\mathcal H\). A single dynamical operator \(\mathcal G\) --- the \emph{universal gravitational generator} --- drives the joint evolution<br>\[<br>\frac{d}{dt}(\mu_t,M_t)=\mathcal G(\mu_t,M_t).<br>\]<br>We (i) give a concise, rigorous axiom system (Axiom I–X) and discuss necessity/weakenability of each axiom; (ii) prove a uniqueness theorem for \(\mathcal G\) within the adopted axiomatic framework (with full statements of technical lemmas used); (iii) construct a computable \(3\times3\) Hermitian toy model for \(\mathcal G\) and demonstrate explicitly how spectral invariants map to Yukawa-like couplings; (iv) derive several concrete observational predictions (CMB non-Gaussianity signatures, Higgs/Yukawa perturbations, black-hole information-retrieval timescales, cold-atom interferometry signals) along with back-of-the-envelope estimates; and (v) provide a methodological discussion and research program to advance the framework toward empirical falsification. All proofs are given under clearly stated axioms; empirical claims are presented as testable predictions.</p> |
| title | The Axiomatization and Spectral Completion of a Unified Field Framework |
| url | https://doi.org/10.5281/zenodo.17339936 |