Priority Claim: Waveform as Fundamental Structure and Its Emergent Geometry

This project establishes a priority claim for a waveform‑first physical ontology. It asserts that waveform is the only fundamental, testable, and verifiable structure in physics, and that all observable physical phenomena arise from waveform behavior. In this framework, geometry is not a primitive feature of reality but an emergent consequence of waveform dynamics. The theory begins with the premise that all measurable interactions are waveform interactions, including those traditionally attributed to particles, fields, and spacetime. Spacetime itself is treated as a structured, dynamic waveform manifold, whose behavior can be described through a refined manifold equation. This manifold is not static; it relaxes over time, providing a natural explanation for cosmological expansion without invoking dark energy. Within this ontology, waveform dynamics can packetize discrete energy, producing behaviors currently interpreted as particle‑like. Stable geometric configurations — including toroidal forms — arise as emergent solutions of the underlying waveform equations rather than as assumed primitives. A tensor‑refined nested waveform construction, represented by Ψnst(𝑥,𝑦,𝑧,𝑡), serves as a concrete mathematical expression of this structure. This priority claim defines the foundational ontology (“waveform as fundamental structure”) and the hierarchy (“geometry as emergent”), establishing the conceptual and mathematical basis for subsequent work on specific geometric solutions, physical mappings, and domain‑level applications.