| _version_ | 1866901364852916224 |
|---|---|
| author | Seguin, Guillaume André Louis |
| author_facet | Seguin, Guillaume André Louis |
| contents | <p>Time has historically been treated as a continuous parameter with arbitrarily fine resolution.</p> <p>This assumption, older than modern analysis and never critically examined, is incompatible</p> <p>with the existence of a non-trivial time flow. We show that time possesses a two-component</p> <p>structure : a continuous support manifold ensuring order and orientation, and a finite minimal</p> <p>resolution h0 required to prevent the collapse of the derivative. This resolution is not imposed</p> <p>externally; it emerges from the octonionic associator and defines a geometric cutoff that</p> <p>cannot be removed by refinement.</p> <p>The operational realization of this structure is provided by the bilateral right-acting</p> <p>quaternionic Laplace transform (QLT). The QLT converts the geometric cutoff induced by</p> <p>octonionic non-associativity into the fundamental cycle time h0, which bounds the admissible</p> <p>spectral domain to [−1/h0, 1/h0]. Most importantly, the QLT acts as a causal selector : it</p> <p>resolves the two algebraically valid but causally incompatible branches of the octonionic</p> <p>associator, choosing the one consistent with global causal coherence.</p> <p>We prove a necessity-and-sufficiency theorem : any mathematical framework satisfying</p> <p>the minimal topological, metric, and operational requirements for a non-trivial time flow is</p> <p>uniquely isomorphic to the qdRIS structure. Conversely, qdRIS satisfies all such requirements.</p> <p>Thus,qdRISisnotanalternativemodelbuttheminimalcompletionofthestandardframework</p> <p>once the infinite-resolution assumption is removed. In this corrected setting, the analytic</p> <p>pathologies of the classical framework arise from the infinite-resolution assumption rather</p> <p>than intrinsic mathematical difficulty. Part II examines the consequences of this structural</p> <p>correction for several major open problems.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18439223 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Time, Resolution, and Causal Selection: The Structural Foundations of qdRIS Seguin, Guillaume André Louis q-dRIS Mathematical physics Theoretical physics General relativity Quantum physics Quantum gravity Standard model Octonions Octonionic associator Minimal time resolution Quaternionic laplace transform Quaternions Non associativity Spectral cutoff Observability fundamental cycle time Causal coherence <p>Time has historically been treated as a continuous parameter with arbitrarily fine resolution.</p> <p>This assumption, older than modern analysis and never critically examined, is incompatible</p> <p>with the existence of a non-trivial time flow. We show that time possesses a two-component</p> <p>structure : a continuous support manifold ensuring order and orientation, and a finite minimal</p> <p>resolution h0 required to prevent the collapse of the derivative. This resolution is not imposed</p> <p>externally; it emerges from the octonionic associator and defines a geometric cutoff that</p> <p>cannot be removed by refinement.</p> <p>The operational realization of this structure is provided by the bilateral right-acting</p> <p>quaternionic Laplace transform (QLT). The QLT converts the geometric cutoff induced by</p> <p>octonionic non-associativity into the fundamental cycle time h0, which bounds the admissible</p> <p>spectral domain to [−1/h0, 1/h0]. Most importantly, the QLT acts as a causal selector : it</p> <p>resolves the two algebraically valid but causally incompatible branches of the octonionic</p> <p>associator, choosing the one consistent with global causal coherence.</p> <p>We prove a necessity-and-sufficiency theorem : any mathematical framework satisfying</p> <p>the minimal topological, metric, and operational requirements for a non-trivial time flow is</p> <p>uniquely isomorphic to the qdRIS structure. Conversely, qdRIS satisfies all such requirements.</p> <p>Thus,qdRISisnotanalternativemodelbuttheminimalcompletionofthestandardframework</p> <p>once the infinite-resolution assumption is removed. In this corrected setting, the analytic</p> <p>pathologies of the classical framework arise from the infinite-resolution assumption rather</p> <p>than intrinsic mathematical difficulty. Part II examines the consequences of this structural</p> <p>correction for several major open problems.</p> |
| title | Time, Resolution, and Causal Selection: The Structural Foundations of qdRIS |
| topic | q-dRIS Mathematical physics Theoretical physics General relativity Quantum physics Quantum gravity Standard model Octonions Octonionic associator Minimal time resolution Quaternionic laplace transform Quaternions Non associativity Spectral cutoff Observability fundamental cycle time Causal coherence |
| url | https://doi.org/10.5281/zenodo.18439223 |