QSG-000-001: QSG Global-Research-Roadmap
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| Format: | Recurso digital |
| Langue: | russe |
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Zenodo
2026
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| _version_ | 1866901250125070336 |
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| author | MONAKHOV, EVGENIY |
| author_facet | MONAKHOV, EVGENIY |
| contents | <div>This document presents a global research roadmap for Quantum Spectral Geometry (QSG), an operator-spectral research program aimed at developing a common mathematical language for spectra, spectral measures, geometry, symmetries, topology, arithmetic structures, composite systems, and dynamical regimes.</div> <div> </div> <div>Unlike the QSG Manifesto, which fixes the conceptual foundations of the program, this roadmap describes the staged development of the theory. It outlines the transition from operator primitives and minimal carrier classes to local spectral densities, induced geometry, Dirac and multicomponent constructions, Hodge and topological sectors, symmetry and positivity structures, arithmetic-spectral functionals, tensor and multilayer systems, computational infrastructure, and eventual integration with existing mathematical and physical formalisms.</div> <div> </div> <div>The document does not claim to provide a completed axiomatic system or a finished physical theory. Its purpose is to organize the long-term development of QSG as a disciplined research program: to identify dependencies between sectors, distinguish foundational and advanced stages, specify the types of results required at each level, and clarify the criteria by which the value of the emerging operator-spectral language should be evaluated.</div> <div> </div> <div>The roadmap is intended both as an internal planning document for the QSG Notes series and as an entry point for specialists interested in contributing to particular sectors of the program, including functional analysis, spectral geometry, noncommutative geometry, global analysis, analytic number theory, mathematical physics, and computational spectral methods.</div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19884351 |
| institution | Zenodo |
| language | rus |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | QSG-000-001: QSG Global-Research-Roadmap MONAKHOV, EVGENIY Quantum Spectral Geometry QSG operator theory spectral geometry self-adjoint operators spectral measures functional calculus local spectral density induced geometry Hodge theory noncommutative geometry analytic number theory arithmetic spectral structures tensor systems composite carriers mathematical physics computational spectral methods research roadmap <div>This document presents a global research roadmap for Quantum Spectral Geometry (QSG), an operator-spectral research program aimed at developing a common mathematical language for spectra, spectral measures, geometry, symmetries, topology, arithmetic structures, composite systems, and dynamical regimes.</div> <div> </div> <div>Unlike the QSG Manifesto, which fixes the conceptual foundations of the program, this roadmap describes the staged development of the theory. It outlines the transition from operator primitives and minimal carrier classes to local spectral densities, induced geometry, Dirac and multicomponent constructions, Hodge and topological sectors, symmetry and positivity structures, arithmetic-spectral functionals, tensor and multilayer systems, computational infrastructure, and eventual integration with existing mathematical and physical formalisms.</div> <div> </div> <div>The document does not claim to provide a completed axiomatic system or a finished physical theory. Its purpose is to organize the long-term development of QSG as a disciplined research program: to identify dependencies between sectors, distinguish foundational and advanced stages, specify the types of results required at each level, and clarify the criteria by which the value of the emerging operator-spectral language should be evaluated.</div> <div> </div> <div>The roadmap is intended both as an internal planning document for the QSG Notes series and as an entry point for specialists interested in contributing to particular sectors of the program, including functional analysis, spectral geometry, noncommutative geometry, global analysis, analytic number theory, mathematical physics, and computational spectral methods.</div> |
| title | QSG-000-001: QSG Global-Research-Roadmap |
| topic | Quantum Spectral Geometry QSG operator theory spectral geometry self-adjoint operators spectral measures functional calculus local spectral density induced geometry Hodge theory noncommutative geometry analytic number theory arithmetic spectral structures tensor systems composite carriers mathematical physics computational spectral methods research roadmap |
| url | https://doi.org/10.5281/zenodo.19884351 |