One source and nested temporal generation
The Single Monad proposal and its inner/outer temporal interpretation organize the research questions. They do not by themselves specify a unique state space, update or measurement law.
Read the postulate →WHAT EACH RESULT ESTABLISHES
Read the result with its scope.
The programme contains philosophical proposals, published mathematical work, explicit model constructions and open physical targets. Their roles are connected, but each has its own standard of evidence.
Editorial guide ·
Four useful labels
A result under its stated hypotheses
A published theorem must be read with its representation, operator, domain and other assumptions. Publication of one component does not establish all subsequent physical identifications.
Open the published sources →An exact consequence of a construction
A count, readout rank, response or clock identity can be proved after the model is specified. The remaining question is whether the source selects the ingredients used in that construction.
Trace the detailed dependencies →A joint law and an independent test
A physical derivation needs independently defined observations, a shared calibration and a reason competing constructions are excluded. Agreement with a benchmark is useful; unique predictive content requires further constraints.
Inspect the central target →Three published points of entry
Use the linked publications for their exact statements and proofs. The website guides explain their place in the broader programme.
Completion principles, real commutants, and positive-frequency geometry for orthogonal Hilbert representations
Open Journal of Mathematical Sciences (2026). A mathematical entry point to completion, compatible structures and geometry under explicit hypotheses.
Real-commutant phase selection from real Hilbert representations
Physics Letters A (2026). Read the representation and dynamical conditions needed for phase selection, including the treatment of sectors where those conditions change.
Dual-Time Topological Geometry and the Emergence of Temporal Asymmetry in Non-Equilibrium Dynamics
Mathematics 14, 853 (2026). A published temporal framework connected to the programme’s questions about evolution, memory and asymmetry.
These are distinct mathematical frameworks. Identifying their variables with one shared microscopic source requires a construction that preserves the relevant dynamics and observations.
The four relativity targets
| Target | A useful starting construction | The physical connection still to establish |
|---|---|---|
| Common limiting speed | A propagation bound on the source’s record relations. | All admissible matter sectors share a bound in the same independently calibrated clock and length measurements. Read the guide. |
| Lorentz transformations | An algebraic cone or an invariant quadratic form. | Physical clocks, rods and inertial transformations realize the required symmetry under specified dynamical assumptions. Read the guide. |
| Mass–energy equivalence | A relativistic dispersion relation in a stated sector. | The source identifies energy and inertial mass operationally, with common units and the needed symmetry. Read the guide. |
| Equivalence principle | Motion in an effective curved geometry. | Matter couples universally in the relevant regime; gravitational and inertial responses must follow from the same dynamics. Read the guide. |
A theorem about one row does not automatically prove the other three. The four-principles guide and claim map provide the longer dependency trail.
Three distinctions that prevent circular derivations
Count versus coupling
A model with 137 distinguishable records has a precise count. An electromagnetic coupling also needs an interaction and normalization law. Changing a positive response operator can change susceptibility without changing the number of states.
Inspect the response bridge →Scaling exponent versus clock ratio
A refinement exponent follows from count and scale assumptions. A clock ratio follows from clock laws. Their equality becomes a physical result only when independently defined clocks are constrained by the same source dynamics.
Inspect clock selection →Hydrogen benchmark versus source derivation
A supplied Coulomb Hamiltonian yields calculable bound states. A source derivation must also explain that Hamiltonian, its coupling and its scales. The relative RMS speed relation is not a classical electron orbit.
Inspect the observable →The next decisive contribution
Choose one unresolved freedom, specify a model that constrains it, and prove the constraint survives across a defined parameter family. Then reserve an independently measurable quantity for comparison. Begin with the model specification →