Dual‑Domain Formalism: Toward a Mathematics of Physical and Resonant Reality

This paper begins the harder task: constructing the mathematical language capable of describing two ontological domains simultaneously — the physical domain of measurable fields and forces, and the trans‑physical domain of the ether — together with the interface between them. It identifies the ceilings of existing mathematics, proposes new structures (Ω̂ₙ, 𝒢, Φ), demonstrates consistency with measured data, and maps epistemic status. The Dual‑Domain Formalism is a programme, not a proof: scaffolding for derivations that do not yet exist but that the corpus makes necessary.