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Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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Mathematical Foundations of Radial Coherential Dynamics — Paper I: Coherent Fields, Adjacency Structure, and Pre-Metric Geometry

Authors: Cerezo, Arturo; AI Collaborative Panel;

Mathematical Foundations of Radial Coherential Dynamics — Paper I: Coherent Fields, Adjacency Structure, and Pre-Metric Geometry

Abstract

This work establishes the first mathematical foundations of Radial Coherential Dynamics (RCD) without presupposing spacetime geometry. Version 1.1 introduces the adjacency structure ∼, resolving the dimensional-collapse problem of v1.0 and allowing spatial structure to emerge independently of coherence. Starting from four primitives — a coherence field, a partial order, an adjacency relation, and a variational principle — we construct a fully pre-geometric framework where temporal and spatial structure arise from decoherence and adjacency, respectively. The paper defines the coherential graph, the proto-metric combining coherence and graph distance, the emergent topology, and the conditions under which Lorentzian geometry appears in the continuum limit. This is the first entry in the RCD Pregeometric Foundations series.

Keywords

causal structure, coherence field, emergent spacetime, adjacency graph, radial coherential dynamics, metric emergence, pregeometry, quantum gravity foundations

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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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