Dynatology 00: Ontology and Scope
Date: 24 October 2026 Status: canonical investigation ontology; not a physical theory or claim of new mathematics
Definition
Dynatology is the study of structured possibility under admissibility, transformation, realization and observation.
Its minimal object is
| Symbol | Role | Governing question |
|---|---|---|
| \(X\) | ambient carrier or possibility space | What alternatives are represented? |
| \(A\subseteq X\) | admissible region or admissibility predicate | Which alternatives satisfy the declared physical constraints? |
| \(T\) | allowed transformations, controls or interventions | Which admissible states can be connected? |
| \(J\) | objective, order, action or selection functional | Why is one admissible outcome preferred? |
| \(\rho\) | realization, restriction or quotient map | What becomes the effective physical carrier? |
| \(L\) | dynamics on the realized carrier | How does the realized state evolve? |
| \(D\) | detector, record or observational interface | Which distinctions are empirically available? |
| \(I\) | invariants, scars and recovery data | What survives or reveals the discarded alternatives? |
| \(R\) | scale and composition maps | Does the construction persist when systems or resolutions change? |
Not every investigation has every component. A missing component must be marked undefined, open or not applicable, never silently replaced by zero.
The nine questions
The tuple produces a fixed sequence:
These questions define different proof obligations.
Four nested regions
The ontology distinguishes four commonly conflated sets:
- Possible means represented in the declared carrier.
- Admissible means consistent with stated algebraic, causal, positive, gauge, boundary and resource constraints.
- Viable means at least one allowed evolution remains admissible over the required duration.
- Reachable means an allowed control or endogenous trajectory actually connects the initial condition to the target.
An optimum outside \(Q_{\rm reachable}\) is not a physical selection. A reachable state outside \(A_{\rm admissible}\) is not a valid realization.
Selection is not assumed
Writing physics as an optimization problem is meaningful only when \(J\) has provenance. It may arise from:
- an action or free energy;
- a stability or spectral criterion;
- entropy production or thermodynamic work;
- inference or control cost;
- boundary consistency;
- a variational principle; or
- a partial order rather than a scalar objective.
Admissibility alone supplies a feasible region, not its preferred point. Symmetry alone supplies an orbit, not its selected representative. If no physical \(J\) or selection dynamics is known, the selection coordinate remains open.
Realization and observation are distinct quotients
The physical reduction \(\rho\) and detector map \(D\) need not coincide:
A detector can impose an observational quotient even when the microscopic carrier remains resolved. Consequently:
This distinction is central to the quotient-scar calculus.
For a directed typed relation set, the free realization prior to quotient is the typed two-rail carrier
Its positive Gram kernel retains source, target and type. The map identifying the two rails and summing the type channels is a concrete realization quotient \(\rho_{\rm support}\); it produces the ordinary Laplacian and may erase direction and semantic type before any detector acts. Dynatology must therefore allow realization loss and detector loss to occur at different stages.
Dynatological defects
The programme tracks failures of expected commutation:
Dynamical closure defect
When \(\Omega_L\neq0\), hidden elimination generally produces memory, fluctuating forces or initial-condition dependence.
Observational sufficiency defect
Distinct states \(x,y\) are detector-equivalent when their record laws agree:
This is a limitation of the declared experiment, not evidence that \(x=y\).
Composition defect
Its interpretation is carrier-specific: it may measure path-dependent coarse-graining, fitted basis drift, hysteresis or a genuine anomaly.
Selection defect
If the optimum of \(J\) is an orbit or manifold rather than a point, the proposed selector is incomplete. A second relational datum may reduce the degeneracy; it must not be smuggled into the objective after the fact.
Relationship to the exceptional ambient picture
The corpus may use \(E_8\), the magic square, Jordan algebras, Freudenthal systems and related representation structures as ambient architectures for \(X\). Dynatology does not promote that availability into a physical background claim.
The physical burden remains the complete descent:
Every arrow must specify its carrier, action, normalization and evidence.
One-line doctrine
Physics describes realized processes; dynatology audits the structured passage from possibility to realization and the evidence left by alternatives.