What does this research mean for the field?

Geometric structures such as space, distance, and manifolds are not fundamental primitives, but emerge dynamically as stabilized harmonic resonances from the relational dynamics of wave phases and transport processes. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

The aim is to establish a mathematical framework where geometry stems from wave phase dynamics.

May 19, 2026Open Access

wave geometry(updated version)

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The aim is to establish a mathematical framework where geometry stems from wave phase dynamics.
Develop a pregeometric framework based on discrete nodes and wave states.
Explore how distance and geometry arise from harmonic resonance and phase connections.
Demonstrate the relationship between classical Riemannian geometry and nonlinear wave equations in the continuous limit.
Geometry is derived as a stable organization of phase relations through resonant dynamics.
Synchronization phenomena and topological defects are incorporated into the framework.
A unified perspective is presented that may lead to new research pathways in quantum geometry and analogue gravity.

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Implication

Wave Geometry reveals how geometry emerges from wave dynamics, potentially transforming our understanding of physics.

Cite This Study

Ren Matsuoka (2026) studied this question.

synapsesocial.com/papers/6a0bfde8166b51b53d3793ad https://doi.org/10.5281/zenodo.20252140

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wave geometry(updated version)

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Discussion

Implication

Cite This Study

wave geometry(updated version)

Key Points

Discussion

Implication

Cite This Study

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