Publication and edition
- Author
- Mohamed Haj Yousef
- Status
- Published journal article
- Version
- Version of record
- Venue or repository
- Open Journal of Mathematical Sciences
- Year
- 2026
- Published
- 2026-07-22
- Volume
- 10
- Pages
- 996–1012
- DOI
- 10.30538/oms2026.0328
Publisher article record supplies received, revised, accepted and publication dates, volume and pagination.
- Primary publication record
- Full text supplied by the source — Publisher PDF retrieved; 17 pages.
- Resolve the DOI
Question and construction
The paper organizes a mathematical route from completed histories to observable quotients, symmetry-compatible phase and spectral geometry. Its central operator results characterize compatible complex structures through a real commutant and select a positive-frequency structure from an oriented orthogonal flow. Further modules examine composition, record distances and a cone bound.
Scope of the result
The proofs concern the stated quotient, Hilbert-space and operator hypotheses. The cone statement additionally uses supplied length, delay and Euclidean readout data. It does not independently determine a universal physical clock, three spatial dimensions or the numerical speed of light.
Guide to a published modular framework, with independently worked finite examples. The cone bound is conditional on supplied displacement and delay observables; a common physical calibration is a further construction.
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Citation
Haj Yousef, M. (2026). Completion principles, real commutants, and positive-frequency geometry for orthogonal Hilbert representations. Open Journal of Mathematical Sciences, 10, 996–1012. https://doi.org/10.30538/oms2026.0328
Source and version notes
Publisher record and opening full text checked. This catalogue summary is not an independent verification of every proof.