Core Definitions

This framework describes physical systems as dynamic flux processes rather than collections of static objects. The following definitions establish the minimal set of variables used throughout the model.

Flux Field (Φ)

Φ(x, t) is a continuous scalar or complex field representing the local state of the system. It encodes both activity (amplitude) and, when extended, orientation (phase).

Φ does not represent a substance. It represents a dynamic state.

Variation (ΔΦ)

ΔΦ corresponds to the local change of the field:

ΔΦ ≈ ∂tΦ  or  ∇Φ

Variation is the primary observable quantity. All measurable structure arises from differences in Φ.

Magnitude of Variation (E)

E is defined as the magnitude of variation:

E = |ΔΦ|

E characterizes the intensity of local change. It can be interpreted as an effective measure of spatial or energetic variation.

Coherence (Φc)

Φc measures the temporal persistence of the field:

Φc ≈ correlation(Φ(t), Φ(t + Δt))

High coherence indicates that a pattern reproduces over time. Low coherence indicates rapid decorrelation and instability.

Coupling (K)

K describes the interaction between two regions or systems:

K(A, B) ∝ Φc(A) · Φc(B) · C(A, B)

where C(A, B) represents structural alignment between the two systems.

Coupling is therefore not purely distance-based. It depends on coherence and compatibility.

Constraint

Constraint limits the evolution of the system by preventing:

• unbounded dispersion
• complete stabilization

It defines the regime in which structure can emerge. Without constraint, the system either homogenizes or collapses.

Existence (Operational Definition)

A system is said to exist if it maintains a stable dynamic pattern over time:

Existence ⇔ stable attractor under dynamic evolution

This definition does not rely on static properties, but on persistence through time.