Recursive Gauge Collapse: A Law-Level Derivation of Dimensionality and Spacetime Structure

This paper presents a law-level framework showing that dimensionality, spacetime structure, and temporal direction are not primitive assumptions, but instead arise as the closure-stable fixed points of a recursive admissibility process.

Starting from a pre-dimensional, non-geometric gauge carrier, the paper formalizes three universal operators:

• Admissible re-presentation (∂): removal of inessential encoding and gauge scaffolding,

• Coercive persistence filtering (Δ): enforcement of stability via contraction of non-commuting structure,

• Reflective completion (Ω): closure under limits and lawful completion.

Dimensionality is shown to emerge as the minimal parameter for which a uniform coercive closure is possible, rather than being assumed a priori. Time appears as the asymmetric residue of completion, and structural hierarchies arise from the depth of recursive collapse required for stabilization.

The framework is domain-agnostic: it does not propose a new physical model, but instead supplies a universal admissibility filter that constrains which mathematical, physical, or informational structures can support stable, persistent observables. Any theory that fails to admit such closure cannot generate stable geometry, dimension, or causal structure.

This result provides a foundational constraint applicable across physics, mathematics, inference, and learning systems, and can be used as a pre-filter for narrowing the space of viable approaches to open problems before domain-specific analysis begins.