Stationary-Relativistic Bernoulli Field Theory: Velocity of Space from Clocks to Galaxies from a GR perspective (ChatGPT Discussion Results)

This document is a complete conceptual and mathematical reconstruction of the \emph{stationary-relativistic Bernoulli field theory}, derived from an extended dialogue on how gravitational phenomena can be expressed in terms of observables rather than postulated geometry. The text integrates the technical summary with the philosophical and methodological reflections that arose throughout the discussion. The papers that were shared with ChatGPT and animated the chat can be found in the Vixra archive \href{https://vixra.org/author/e_p_j_de_haas}{https://vixra.org/author/epjdehaas}. The guiding question was whether one can describe all stationary gravitational phenomena---from planetary systems to galaxies and cosmological inflow---using a single invariant scalar relation derived from General Relativity (GR) but expressed. through physically measurable quantities: clock rates, photon exchanges, and velocity fields. The answer is affirmative, and it leads to a formulation that is mathematically GR-conform yet conceptually distinct. Geometry becomes the \emph{result} of physical measurement, not its starting postulate.