The four-volume book programme
The 21 foundational topics develop the programme introduced in Chapter III of Duality of Time. Its postulate is developed in Chapter V. The companion volumes provide the philosophical origin, the broader symmetry programme and further presentations of the proposed temporal structure. The links below open the main site’s book records and reading guides.
Single Monad Model of the Cosmos
Volume I develops the relation between time, ever-renewed creation and the emergence of multiplicity from unity.
Duality of Time
Volume II provides the original major-problems programme in Chapter III and develops the temporal postulate in Chapter V.
Ultimate Symmetry
Volume III extends the discussion of temporal structure, symmetry and the physical and philosophical implications of the programme.
Time Chest
Volume IV provides a further presentation of the complex-time picture and its connections to matter, observation and cosmology.
A short entry point and the philosophical background
- DOT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics
A focused entry point into the postulate and its proposed physical consequences. Pair it with the first reading route.
- Ibn ‘Arabî — Time and Cosmology
The historical and philosophical context for the programme’s account of time, creation, unity and multiplicity.
- Complete books directory
Find the full set of book records, reading guides and available publication links on the main site.
Published mathematical papers
These papers develop mathematical structures relevant to the problems section. The associated site guides explain worked examples and how their hypotheses connect to the physical programme.
- Completion principles, real commutants, and positive-frequency geometry for orthogonal Hilbert representations
Mohamed Haj Yousef. Open Journal of Mathematical Sciences, 10, 996–1012 (2026). The paper develops a modular framework for completion and compatible operator structures. Read it with the completion guide, physical information and phase and composition.
- Real-Commutant Phase Selection from Real Hilbert Representations
Mohamed Haj Yousef. Physics Letters A, article 132085 (2026). The operator question concerns a compatible complex phase for real representations. The paper guide connects oriented evolution, stationary modes and composite-system questions.
- Dual-Time Topological Geometry and the Emergence of Temporal Asymmetry in Non-Equilibrium Dynamics
Mohamed Haj Yousef. Mathematics, 14(5), 853 (2026). The mathematical development links temporal geometry and memory-bearing reduced evolution. Read it alongside the temporal-asymmetry guide and the arrow-of-time article.
A result concerning a declared operator, quotient or memory equation gives a precise component of the programme. The problem articles identify the source interactions, physical calibrations and measurements that connect those components to the proposed physics.
Preprints connecting the physical proposals to current models
The following links open publication records or detailed guides that identify the manuscript and available source. Version information matters: a worked example should be read with the edition to which it refers.
- The Dynamic Formation of Spatial Dimensions in the Inner Levels of Time
A proposed route from nested temporal formation to spatial structure and relativistic behaviour. Connects to spatial dimensions, quantum gravity and vacuum energy.
- Deriving the Four Principles of Quantum Relativity from the Complex Temporal Dynamics of the Duality of Time Theory
A proposal connecting temporal structure to a limiting speed, Lorentz transformations, mass–energy relations and gravitational equivalence. Read with Lorentz symmetry and the common-clock target.
- Non-Commutative Geometric Foundations for the Emergence of Spatial Dimensions and Physical Structures from Complex-Time Spectral Triples
A proposed spectral framework linking temporal structure to dimensionality and physical excitations. Read with dimensional diagnostics and the matter spectrum.
- A Combinatorial–Geometric Derivation of the Fine-Structure Constant from Inner-Time Projection Dynamics in the Duality of Time Theory
A structural proposal developed alongside response and atomic examples. The normalized-coupling target explains the physical normalization to be calculated.
- The minimal magnetic-monopole proposal
A manuscript on the source and its proposed topological interpretation. Read with magnetic flux, charge and observable sectors.
- The discrete Yang–Mills mass-gap proposal
A detailed guide to the candidate spectral construction and the gap being investigated. Read alongside the physical and mathematical Yang–Mills problem.
- Discreteness and continuity as complementary spectral projections
A guide to the proposed relation between inner structure and continuous descriptions, relevant to resolution, retained information and limiting geometry.
Open the complete papers catalogue for publication records, source links and further reading guides.
Read the primary physics sources with the relevant problem
Each article links the proposed SMM/DTT mechanism to the particular phenomenon it seeks to explain. Its bibliography includes the primary theoretical or experimental sources used for that physical context.
- Bell correlations and quantum nonlocality
Use the original inequalities and experimental tests to distinguish joint correlations, factorization assumptions and operational signalling.
- Neutrino masses and mixing
Compare oscillation evidence, mixing analyses and absolute-mass measurements. They constrain different parts of a proposed spectrum.
- Mass generation
Relate proposed formation dynamics to the particle and field evidence that any effective description must reproduce.
- Yang–Mills theory and the mass gap
Consult the mathematical formulation of the problem as well as the candidate source construction.
- Homogeneity, expansion and perturbations
Read the cosmological proposals alongside the observations and model assumptions used to infer large-scale structure.
- Dark matter and dark energy
Keep clustering, lensing, background expansion and an inferred equation of state distinct when comparing models.
Use the source trail to develop a new result
Start with the article’s physical question and identify the exact source mechanism it proposes. Follow the book reference for the conceptual argument, the paper reference for the mathematical construction and the primary physics reference for the phenomenon being modelled. These readings contribute different parts of an explanation.
When extending a calculation, state the source version, assumptions, units and observable used. If a new choice is introduced—for example a detector, coupling, initial distribution or completion rule—explain how it relates to the original source. This makes the extension reproducible and gives other researchers a concrete place to contribute.
The research map identifies shared targets. The contact page provides correspondence details, research profiles and an invitation to collaborate in physics, mathematics and philosophy.