DPΦ adopts a controlled vocabulary to underscore its unique, process-oriented ontology. Legacy terms such as trajectory, outcome, or collapse are deliberately avoided because of their association with the block universe or Copenhagen interpretations.

Core Concepts

Actualization: The general, ongoing process of reality unfolding through irreversible system instantiation.

Coherence: The persistence of stable patterns and structures through repeated re-actualization guided by minimal informational cost.

Coherence Stall: The cessation of actualization due to high Constraint Load (C), where the number of accessible configurations drops to near zero (Lock-In). This is distinct from CPA Freeze.

Configuration / Manifestation: The definite, resolved instantiation of a system (ϕnow,S ) after a CPA instance.

Constraint Load (C): A dimensionless, information-theoretic measure of the lawful restrictions on a system. It quantifies the deficit between the maximum possible entropy and the actual entropy: C ≡ (Smax − Sactual)/kB . 17

Continuous Present Actualization (CPA): The core ontological concept of DPΦ, describing reality as a process that unfolds through an order-continuous and irreversible, localized cascade of actualization instances.

Continuum of Potential: The state of an unmeasured system, representing the full range of lawfully constrained possibilities (described by the wavefunction or partition function) that exists as a holistic field prior to a CPA instance.

CPA Cascade: The large-scale, propagating sequence of interconnected, localized actualization instances that constitutes the unfolding of reality.

CPA + Constraint (CPA + C): The designation for the physically-derived formulation. It describes the baseline CPA Rate being modulated by Constraint Load (C).

CPA Freeze / Suspended Actualization: The high-density or high-constraint limit where ωCPA → 0, causing cessation of actualization. It replaces gravitational singularities and provides a physical cutoff in quantum regimes.

CPA Lock-In: The finite threshold (analogous to glass transition temperature Tg) where Constraint Load (C) maximizes, causing actualization to stabilize into a persistent configuration. This replaces the non-physical VFT singularity, T0.

CPA Rate (ωCPA): The local pace of actualization, governed by the CPA + C Rate Law.

CPA + C Rate Law: The local rate of actualization is not constant but is governed by the fundamental informational cost of instantiation. In physical systems, this cost is modulated by Energy Density (ρE ) and Constraint Load (C). This scaling relation is universal and describes the viscosity divergence in glass formers (VFT), coherence thresholds in AI, and optical scaling in cosmology.

CPA Rate Gradient (CRG): The spatial gradient of the CPA Rate (∇ωCP A), defined by Energy Density (ρE ) variations. It is the slope of the temporal landscape that drives gravitational motion.

CPA Timescale (τCPA): The characteristic duration of an actualization instance, defined as the inverse of the local CPA Rate: τCPA ≡ 1/ωCPA.

Energy-Density Gravity (EDG): The manifestation of gravity as a system’s alignment with a CRG graded by Energy Density (ρE ).

Holistic Actualization: The property that all coupled degrees of freedom within a constrained system actualize simultaneously as a single configuration. It provides the ontological basis for quantum entanglement.

Inertial Path: The persistence of a system’s configuration by maintaining alignment with a uniform CRG, requiring ∆C = 0.

Instance: A single, unique, abstract unit of the actualization process. Whereas a CPA configuration describes a physical occurrence, an instance refers to a specific instantiation.

Instantiation: The act of manifesting a definite configuration from potential. The process through which an instance occurs; the transition from possibility to actualized presence.

Local Constraints (L): The set of all local physical variables that influence a CPA 18 instantiation, primarily the local Energy Density (ρE ) and the Constraint Load (C).

Optical Conformal Factor Ω(a): A standard geometric construction in GR that rescales null intervals while preserving causal structure. In DPΦ, it represents the accumulated actualization density along a photon’s path.

Principle of Efficient Actualization: The consequence of PMAC stating that a system’s evolution follows the path that extremizes the total CPA Rate over time (path of least resistance).

Principle of Minimal Actualization Cost (PMAC): The foundational, empirically validated principle stating that the rate of actualization is inversely proportional to its informational cost (Constraint Load C).

Interface Principles

These principles connect DPΦ’s process dynamics to the mathematical language of general relativity (GR):

Principle of Consistent Time (Clock Law): An interface principle stating that the local CPA Rate must be proportional to the flow of proper time in GR: g00 = (ωCPA/ω∞)2.

Principle of Entropic Correspondence: A bridge principle connecting the CPA process to macroscopic thermodynamics, positing that the rate of entropy growth is proportional to the CPA Rate: dS/dt = κS ωCPA.

Principle of Light Propagation (Null-Closure Law): An interface principle ensuring that the path of light in DPΦ’s temporal landscape is consistent with null geodesics in GR. 19

Index of Mathematical Notation

Symbol Units Meaning

A[r] — (Action) Action functional for efficient actualization

β — Dimensionless closure exponent (cosmological model)

C, CQ — Constraint Load (classical and quantum)

CRG s —1m−1 CPA Rate Gradient (∇ωCPA)

E∗, ρ∗ J, J m —3 Reference energy and density scales

g00 — Time component of metric (GR interface)

γ — Dimensionless coupling constant in Rate Law

κ N s — Proportionality constant (inertial force model)

κS J/K — Proportionality constant (entropic correspondence)

L — Set of local constraints (ρE , C)

Ω(a) — Accumulated cosmic lapse function

ϕnow,S — Definite configuration of system S after CPA instance

Φ J kg — 1 Newtonian gravitational potential (weak field)

Φeff J kg —1 Efficiency Potential: −c2 ln(ωCPA/ω∞)

ρE J m — 3 Local Energy Density

S — Specific physical system undergoing actualization

τCPA s CPA Timescale — (≡ 1/ωCPA)

ωCPA s —1 CPA Rate; local pace of actualization

ω∞ s —1 Asymptotic CPA Rate in vacuum