How can a single generative process give rise to a world of distinguishable places, persistent objects and measurable change? This is the question behind the Single Monad Model and Duality of Time Theory. I want this research blog to make the next steps visible: the constructions worth examining, the assumptions still doing work, and the precise questions on which collaboration could make a difference.
A place to work through the difficult steps
A research paper has to present a coherent argument within a defined scope. A book can develop the broader picture. Between them lies another useful form of writing: a focused explanation of one unresolved step, with enough detail that another researcher can challenge it, improve it or connect it to a different field.
That is the role of this blog. A post might unpack a definition, calculate a small example, compare two candidate dynamics or identify why an attractive argument stops short of its intended conclusion. The point is to make the research easier to enter while preserving the distinctions that matter mathematically.
The research programme sets out the larger objective: a common source dynamics that constrains spatial relations, physical clocks and matter together. The publication records provide the sources for particular results. Here, the emphasis is on the reasoning that connects a result to the next question.
What the common-source proposal asks us to explain
In SMM, the Monad is the proposed origin of observable multiplicity. It is not introduced as a particle occupying a special location within a space already assumed to exist. The research question concerns the formation of the relations that make locations distinguishable in the first place.
DTT develops this proposal through two temporal roles. Inner generation concerns the activity that prepares a configuration. Outer completion concerns the availability and ordering of retained observations. The six inner levels are nested generative roles; their interpretation must be expressed through actual dependencies, operations and records. Counting levels alone cannot determine a physical metric.
A useful source model therefore specifies its state, retained memory, update law, allowed interventions and readable outputs. It must also explain what resources its construction uses. If a controller stores an operation table or carries information between registers, that information belongs in the model. Otherwise the mechanism that appears to explain the geometry may quietly presuppose it.
These are constructive requirements. They make the proposal more demanding, but they also make progress recognizable. A small model that establishes one necessary compatibility can contribute more than a broad verbal association between time, geometry and matter.
A small example of a useful objection
Suppose a model has two internal bits, b and m, and updates them by the fixed rule (b, m) ↦ (b XOR m, m). The visible record displays only b. Here XOR means addition modulo two. The preparations (0, 0) and (0, 1) initially look identical: both display zero.
After one update, the first still displays zero while the second displays one. The present display therefore cannot determine its own next reading for all admitted preparations. Retaining m repairs the problem. Alternatively, two consecutive readings recover it because m = b₀ XOR b₁.
The objection has produced a positive result: a precise statement of the memory that prediction requires. It has also identified the assumption that could change the conclusion. If only preparations with m = 0 are allowed, the display closes under the update, but that preparation restriction must be explained.
The source and retained-memory chapter develops this kind of reasoning further. For the wider programme, the question is whether the same source restriction that determines sufficient memory also constrains spatial readout or clock response. Establishing such a connection would remove an independent modelling choice.
An invitation to physicists, mathematicians and philosophers
I welcome collaboration with experts across these fields. The most useful starting point is a question small enough to investigate together, with a clear account of what would count as an answer.
For physics: can a specified source dynamics produce a stable transport rule and an independently readable clock, so that their relation survives changes of preparation? Which existing physical limit provides the most discriminating comparison? A calculation of an observable response, including its normalization and domain of validity, would be especially valuable.
For mathematics: which operation algebras admit a predictive completion, a stable spatial readout and compatible composition? Can an explicit counterexample reveal a missing hypothesis? Can a selection theorem explain why one admissible structure is forced within a carefully stated class?
For philosophy: what distinguishes temporal generation from dependence, description or repeated representation? How should unity and multiplicity be related without making the explanatory premise immune to criticism? Historical concepts can motivate these questions while their modern mathematical formulations are assessed on their own terms.
A useful response can identify one equation or passage, state the issue, and suggest a calculation, alternative assumption or relevant result. A worked counterexample is welcome. So is a proposal for a focused joint paper or seminar discussion.
Which single compatibility between source dynamics, records and physical measurement should we establish next? Please send your question or collaboration proposal, together with a relevant paper or research profile where helpful.
Sources and further reading
- SMM/DTT research: the route from source to physics — the programme's common-source objective and connected research questions.
- One source, retained memory and the construction of predictive records — the explicit two-bit example and the distinction between a present display and a predictive state.
- Completion principles, real commutants, and positive-frequency geometry for orthogonal Hilbert representations — the primary paper for completion quotients and the conditional operator and cone constructions discussed here.
- Contact & collaboration — research interests and current routes for scholarly correspondence.