From Relation to Phase and Relational Closure: Direction, Path Multiplicity, and Cycle Consistency in the Ω₀/A2 Programme
- 1Independent Researcher, Melbourne, Australia
Abstract
We organize two related reconstruction modules into a single conditional chain: persistent oriented relational dynamics can support a phase-like coordinate, and phase-bearing histories can support relative-phase-sensitive composition and cycle-closure tests. The first module derives S¹ and real rotational structure only under declared compactness, dimensionality, continuity, nonstalling, and persistence assumptions. The second establishes exact consequences of real vector combination and finite-graph cycle consistency while keeping the combination rule and physical observation map explicit assumptions. These mathematical results do not derive quantum amplitudes, the Born rule, or a physical gauge symmetry. They define a staged set of falsifiable bridges from relation to phase and from phase to candidate relational closure; physical identification remains open.
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BibTeX
@misc{wang2026from,
title = {{From Relation to Phase and Relational Closure: Direction, Path Multiplicity, and Cycle Consistency in the Ω₀/A2 Programme}},
author = {Yanghua Wang},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23472242},
url = {https://zenodo.org/records/23472242},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From Relation to Phase and Relational Closure: Direction, Path Multiplicity, and Cycle Consistency in the Ω₀/A2 Programme
AU - Yanghua Wang
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23472242
UR - https://zenodo.org/records/23472242
AB - We organize two related reconstruction modules into a single conditional chain: persistent oriented relational dynamics can support a phase-like coordinate, and phase-bearing histories can support relative-phase-sensitive composition and cycle-closure tests. The first module derives S¹ and real rotational structure only under declared compactness, dimensionality, continuity, nonstalling, and persistence assumptions. The second establishes exact consequences of real vector combination and finite-graph cycle consistency while keeping the combination rule and physical observation map explicit assumptions. These mathematical results do not derive quantum amplitudes, the Born rule, or a physical gauge symmetry. They define a staged set of falsifiable bridges from relation to phase and from phase to candidate relational closure; physical identification remains open.
ER -