The In–Out Self-Referential Field Vibration

Max Freet, Adrien Hale, An M. Rodriguez (ORCID)

Preferred Frame Writing — January 2026

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One-Sentence Summary

Spatial orientation and the concepts of "in" and "out" are not fundamental primitives, but emerge as phase-dependent projections of the self-referential scalar field mode (1).

Summary

We develop a second‐order relational description of the Point–Not–Point (PNP) scalar‐field framework, showing how "in" and "out" —along with orientation, direction, and spatial geometry— emerge from the self‐referential phase structure of a single real scalar field $U(x,t)$. The minimal closed mode, denoted (1), exhibits a Möbius‐like phase inversion across its nodal surface, sustaining continuous energy circulation without requiring a background geometric twist. This work complements the dynamical theorems of PNP by providing the conceptual formulation of how a scalar field constructs spatial orientation.

Keywords

Keywords: PNP Framework, Scalar Field Recursion, Emergent Geometry, Mobius Phase Topology, Relational Space

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