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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Spacetime as a Relational Manifold

Authors: Bailey, Denis;

Spacetime as a Relational Manifold

Abstract

Spacetime as a Relational Manifold develops a relation‑first account in which spacetime is not a four‑dimensional container but the joint expression of two fundamental relational operators: orientation (time) and separation (space). The paper argues that neither space nor time is primitive. Instead, both emerge from the dynamics of a generative relational field. Time arises from the coherence of orientation across updates; space arises from the stabilization of persistent non‑coincidence. When these operators cohere, they generate a unified manifold whose structure reflects the system’s available relational degrees of freedom.The paper introduces the Universal Triad—generation, boundary, and expression—as the minimal structure required for dimensionality to appear and for geometry to stabilize. Curvature is interpreted not as deformation of a background metric but as a pattern of constraints on allowable relational transformations. Expansion is explained as the increase of generative bandwidth, represented by the radius of the relational hypersphere, rather than as motion into a pre‑existing void. This framework dissolves the container model, resolves the problem of time, and grounds spacetime structure in the internal dynamics of relation itself.

Keywords

relational ontology; generativity; separation and orientation; emergent spacetime; dimensionality; relational manifold

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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