ARPI Core Framing — Zero as Boundary Condition

Within the Australian Resonant Physics Initiative (ARPI), Zero is treated not as absence, void, or a null state, but as a boundary condition that constrains and stabilises system behaviour.

The formulation:

Φ₀ = Σψᵢ

This is a conceptual representation, not a predictive equation. It expresses a coherent reference state (Φ₀) arising from the superposition of permissible modes (ψᵢ) under constraint.

This framing reflects established principles across physics and systems theory: boundary conditions determine admissible solutions; coherence arises through constraint; and stability precedes structure in physical, biological, and informational systems.

Under this view, Zero does not represent “nothing.” It defines the limit at which coherence is maintained, enabling organised form to emerge from constrained possibility rather than from emptiness.

Canonical Short Form

Zero defines the boundary condition that makes coherence possible.

Abstract Sentence (for papers and white papers)

This work treats Zero as a boundary condition rather than an absence, framing coherence and stability as emergent properties of constrained systems.

Methods / Conceptual Framework

Zero is introduced as a boundary condition defining the admissible state space of the system. The formulation Φ₀ = Σψᵢ is used as a conceptual representation of coherence emerging from constrained superposition, without implying predictive closure.

[ Zero (Boundary Condition) ]

              ↓

     [ Admissible Modes ψᵢ ]

              ↓

   [ Coherent Reference State Φ₀ ]

Figure description

Boundary conditions (Zero) constrain the admissible state space of the system.

Within this constrained space, permissible modes (ψᵢ) may coexist and superpose.

Coherence is expressed as a stable reference state (Φ₀) emerging from this constrained superposition.

This diagram is not intended as a physical model or causal mechanism. It serves as a conceptual scaffold illustrating how coherence arises from constraint rather than from unconstrained freedom.

Canonical Caption (use verbatim wherever this diagram appears)

Boundary conditions constrain admissible modes, from which coherence emerges.

Notes for Readers

• Zero is not interpreted as absence or emptiness

• ψᵢ denotes permissible modes within a constrained state space

• Φ₀ denotes a coherent reference state, not a measurable quantity

• The diagram is conceptual and non-predictive