The Hydrodynamic Universe Superfluid Information, Metric Emergence, and the HQC Research Programme

This monograph presents Hydrodynamic Quantum Cosmology (HQC) as a mathematically

organised research programme, not as a completed theory. Its central hypothesis is that the

vacuum may be modelled as a microscopic information substrate whose long-wavelength regimes

appear as quantum phase dynamics, phase-locked tetrad geometry, crystallised matter sectors,

and residual wake stress.

Version 0.2 reorganises HQC around an explicit evidential hierarchy. The proposed proof

chain begins with a microscopic phase-network action, passes through a superfluid continuum

limit, uses Hopf spinor phase transport and Plebanski simplicity to select tetrad geometry,

and then splits the infrared stress tensor into crystallised sectors Γb and residual sectors Γd.

Observable particles, constants, and charged-lepton hierarchies are therefore not independent

geometric numerology; they are downstream spectral and overlap targets of the routed Γb soliton

problem. Dark-sector modelling is likewise not inserted as a density ratio, but is assigned to

T

wake

µν , the residual phase/wake stress produced by the same substrate action.

The strongest current route is the Hopf/Plebanski boundary-crystallisation programme. The

spin-2 character of the Plebanski metricity obstruction motivates a primitive Z5 monodromy

condition and a candidate boundary determinant, but the decisive microscopic closure remains

open. HQC becomes a first-principles theory only if the Einstein coefficient, baryonic/dark

routing, wake coefficients, determinant ratios, and Γb-sector spectral data are derived from the

action and boundary conditions without observational fitting.

The purpose of this draft is therefore twofold: to preserve the unifying HQC ontology in a

precise mathematical form, and to expose the exact points at which the programme can succeed

or fail. Every major claim is labelled as theorem, derivation sketch, ansatz, phenomenological

fit, falsifiable prediction, speculative extension, or open problem.