The Continuum — Part I: Logical Genesis of a Postulate and a Reading of E=mc² as a Pressure Depression

We present the logical foundation of a physical model based on a single postulate: the existence of a primordial physical medium (the Continuum) with properties determined by the fundamental constants G,ħ,c; for matter, a mass scale is needed in addition, the proton mass, which is a starting datum and not a result. Through a chain of arguments — each step motivates the next choice — we propose that such a medium is a quantum superfluid at Planck density, in which motion at v=c closes into toroidal vortices: material particles (whether a stationary, localized vortex really exists in this fluid remains to be shown).
 
From this structure we propose the hypothesis that rest mass is a pressure depression ΔP distributed over the topological volume V_p of the vortex. The relation E=ΔP·V_p=mc² is an identity: ΔP, written as P₀ (3/(256π))α_g², coincides with m_p c²/V_p, so that E=mc² and the cancellation of G follow by construction; E=mc² remains an input, it is neither derived nor verified. The factor 256π/3 is the volume of the sphere of radius 4r_b in units of r_b³. It follows that ΔP=6.028×10³⁴ Pa; a von Laue balance could halve this value (possible factor of 2, open problem). The resulting central pressure is of the same order of magnitude as the first direct measurement (Jefferson Lab, Burkert et al. 2018), but any model that concentrates m_p c² within ∼1 fm gives the same order: it is not a discriminating test. The location of the sign change of the pressure remains an open problem.
 
This work constitutes Part I of a series. Subsequent parts develop, on the same foundations, a proposal for the structure of elementary particles (masses, mixing angles as comparisons with data) and for emergent gravity, with the hypotheses declared in each part.