Start here: a guide to SMM and DTT
Complete printable guide with equations, references and the figures used in the web edition.
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Downloads & reusable material
Find the available paper PDFs, book previews, and original vector figures in one place.
The complete course handbook
50 illustrated pages containing all twelve English lessons, learning objectives, prerequisites, 24 exercises with complete worked answers, source links and further reading. The PDF is a dated course snapshot; the online lessons remain independently editable.
Download the course handbook (PDF) · Study online · الدورة العربية
Eight printable foundation guides
Read the complete English foundations offline, including the 60-entry glossary, 26 FAQ answers and eight reading routes. The PDFs reproduce the foundation content as captured for this edition; the web guides remain available for subsequent updates.
The Single Monad Model: source, multiplicity, and records
Complete printable guide with equations, references and the figures used in the web edition.
Duality of Time: generation, completion, and physical clocks
Complete printable guide with equations, references and the figures used in the web edition.
The duality-of-time postulate: from statement to model
Complete printable guide with equations, references and the figures used in the web edition.
SMM/DTT research: the route from source to physics
Complete printable guide with equations, references and the figures used in the web edition.
Reading paths through SMM and DTT
Complete printable guide with equations, references and the figures used in the web edition.
SMM/DTT glossary: 60 connected definitions
Complete printable guide with equations, references and the figures used in the web edition.
SMM/DTT questions and answers
Complete printable guide with equations, references and the figures used in the web edition.
All 78 explanatory figures
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Publication citations
These records identify the three published papers. Each keeps its DOI and publication details; the accompanying reading guide explains the result and its scope.
All three citations · BibTeX · All three citations · plain text
Completion principles, real commutants, and positive-frequency geometry for orthogonal Hilbert representations
Mohamed Haj Yousef (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
Real-commutant phase selection from real Hilbert representations
Mohamed Haj Yousef (2026). Real-commutant phase selection from real Hilbert representations. Physics Letters A, 594, Article 132085. https://doi.org/10.1016/j.physleta.2026.132085
Dual-Time Topological Geometry and the Emergence of Temporal Asymmetry in Non-Equilibrium Dynamics
Mohamed Haj Yousef (2026). Dual-Time Topological Geometry and the Emergence of Temporal Asymmetry in Non-Equilibrium Dynamics. Mathematics, 14(5), Article 853. https://doi.org/10.3390/math14050853
The download collection points to public source files and to the diagrams included with this website. Each paper keeps its DOI or source page alongside the download so that the version and publication context remain visible.
Working manuscripts referenced in the article atlas are not automatically public downloads. Where only an exact draft filename is available, the source register records that fact. Public paper files open from their existing locations, and the reusable figure set opens locally within the website.
Published paper PDFs
Open Journal of Mathematical Sciences
2026 · Vol.10 · pp.996–1012
2026 · Vol.10 · pp.996–1012
Completion principles, real commutants, and positive-frequency geometry for orthogonal Hilbert representations
Completion, compatible complex structures, and the conditions behind positive-frequency geometry.
Physics Letters A
2026 · Vol.594 · 132085
2026 · Vol.594 · 132085
Real-Commutant Phase Selection from Real Hilbert Representations
How real representations and their commutants constrain the selection of quantum phase.
Mathematics
2026 · Vol.14 · 853
2026 · Vol.14 · 853
Dual-Time Topological Geometry and the Emergence of Temporal Asymmetry in Non-Equilibrium Dynamics
A dual-time geometric approach to temporal asymmetry and reduced dynamics.
Seventy-eight explanatory vector diagrams
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Keep following the question.
The glossary explains the vocabulary; the reading paths connect the ideas; the source register points to the original arguments.
Complete publication citation list
Download thirteen source-checked citations (plain text). Each entry identifies publication status and the cited version.