HDOV Bridge: Correspondence between Functional Accessibility ηₚ and the Dynamical Scalar Field nₚ(x)

The unified HDOV formulation introduces a master propagation equation for physical modes Ψ in real media, in which a scalar quantity of functional accessibility ηₚ appears. This equation describes, with predictive power, phenomena as diverse as ultrafast coherent attenuation in X-ray scattering (TRXS) at femtosecond scales, the emergence of functional precursors at the heliopause (Voyager missions), the damping of gravitational ringdown after compact mergers, and cosmological attenuation usually attributed to effective dark energy.
Generalized HDOV promotes this functional accessibility to a dynamical scalar field nₚ(x) with an explicit Lagrangian, a symmetry-breaking potential, vacuum expectation value ⟨nₚ⟩, Yukawa-type couplings to fermions, and non-minimal coupling to curvature. This theory predicts a light, neutral scalar excitation with mass mₙₚ ≈ 20.5 MeV, testable in intensity-frontier experiments and potentially contributing to (g−2)ₘᵤ.
This paper builds the formal bridge between both descriptions: (i) it identifies ηₚ as the effective/macroscopic limit of the same field nₚ(x); (ii) it shows that the unified HDOV master equation arises as the effective propagation equation for a mode Ψ immersed in an nₚ background; (iii) it interprets the multiscale observational signatures attributed to ηₚ as indirect measurements of nₚ; and (iv) it highlights that direct searches for the light scalar particle around ~20.5 MeV provide an independent and complementary falsification channel. In addition, it incorporates the holographic vacuum HDOV module, in which the same functional accessibility regulates the effective vacuum energy and cosmic acceleration without introducing a fundamental cosmological constant.