Zerofield Boundary The Absence Condition of Realised Structure - Paper 1a Abstract Primitive 0 of the Finite Realisation Closure (FRC) programme establishes that no physically realised configuration may contain an operational infinity. Primitive 1 establishes that realised systems must satisfy closure relations. Before closure relations can emerge, the framework must define the boundary separating realised relational structure from its absence. This paper introduces the Zerofield, representing the absence of realised relational structure. The Zerofield is not a physical field with degrees of freedom but a boundary condition describing the state in which no relational distinctions exist. This paper establishes the Zerofield as the structural boundary of the FRC framework and shows that any realised deviation from this boundary necessarily introduces relational distinction. Distinction therefore represents the first observable property of realised structure. The nature of this distinction and its structural implications are developed in the subsequent paper. Within the broader programme, the Zerofield defines the absence condition beneath the emergence of relational closure, lattice structure, gauge symmetry, matter excitations and gravitational geometry. Introduction Primitive 0 of the Finite Reversible Closure (FRC) programme establishes the principle of finite realisation: no physically realised structure may require an operational infinity for its specification, evolution or measurement. Primitive 1 introduces the concept of closure, requiring that realised systems satisfy relational closure relations under finite update. Before closure relations can appear, the framework must identify the condition in which no realised relational structure exists. Defining this condition establishes the boundary separating absence from the emergence of structure. This paper defines that boundary as the Zerofield. The Zerofield does not represent a background medium or a physical field. Instead, it represents the condition in which no relational distinctions exist. In this state there are no orientations, no locations, no scales and no geometric relations. Concepts such as distance, angle and direction arise only after relational structure appears. Under the constraint of Primitive 0, the Zerofield must not be interpreted as containing infinite energy, infinite density or any other infinite magnitude. It therefore represents a non-operational boundary condition rather than a measurable physical quantity. Defining this boundary allows the programme to identify the first structural property that appears when realised structure departs from absence.
Joe Bloggs (Mon,) studied this question.