What question did this study set out to answer?

This work seeks to redefine the role of phase as the fourth generator in a closure framework, moving away from traditional spacetime interpretations.

June 3, 2026Open Access

PSOC4(3) and the De-Spatialization of Time: Phase as the Fourth Generator with the Phase-Spatial Replacement of Spacetime

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Authors

PLPhilip LilienUniversity Foundation

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Implication

This theoretical paper repositions phase as the fundamental generator, suggesting clearer ontological foundations over traditional spacetime concepts.

Key Points

This work seeks to redefine the role of phase as the fourth generator in a closure framework, moving away from traditional spacetime interpretations.
Introduced PSOC4(3) framework combining U(1) and SO(3) for phase and spatial orientation representation.
Developed a theoretical argument to reposition time as an outcome of phase relationships rather than a spatial coordinate.
Analyzed implications of phase-spatial closure for conceptualizing time and space.
Argued that treating time as a spatial axis leads to conceptual confusion.
Presented a clearer ontology by proposing phase as the fourth generator, decoupling it from spatial dimensions.
Demonstrated that time can emerge from ordered phase transitions rather than being a primitive aspect of spacetime.

Cite This Study

Philip Lilien (2026) studied this question.

synapsesocial.com/papers/6a1fc56bdee9eb8c0dce6d08 https://doi.org/10.5281/zenodo.20496605

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June 3, 2026Open Access

PSOC4(3) and the De-Spatialization of Time: Phase as the Fourth Generator with the Phase-Spatial Replacement of Spacetime

View Full Paper

Ask AI

Bookmark

Authors

PLPhilip LilienUniversity Foundation

Discussion

Member takes

Implication

This theoretical paper repositions phase as the fundamental generator, suggesting clearer ontological foundations over traditional spacetime concepts.

Key Points

This work seeks to redefine the role of phase as the fourth generator in a closure framework, moving away from traditional spacetime interpretations.
Introduced PSOC4(3) framework combining U(1) and SO(3) for phase and spatial orientation representation.
Developed a theoretical argument to reposition time as an outcome of phase relationships rather than a spatial coordinate.
Analyzed implications of phase-spatial closure for conceptualizing time and space.
Argued that treating time as a spatial axis leads to conceptual confusion.
Presented a clearer ontology by proposing phase as the fourth generator, decoupling it from spatial dimensions.
Demonstrated that time can emerge from ordered phase transitions rather than being a primitive aspect of spacetime.

Cite This Study

Philip Lilien (2026) studied this question.

synapsesocial.com/papers/6a1fc56bdee9eb8c0dce6d08 https://doi.org/10.5281/zenodo.20496605

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