The term has different actual meanings, depending on the context (hierarchy level) being considered. Usually, it refers to the classical flat background space, but we believe that is not fundamental, but is instead derived from the unique phase-dependent solutions that fermions find.
Fundamentally, our waves are simple: they oscillate on one axis, with constant angular momentum when considered as a pair in a boson. In other words, the rate of phase change for all waves (bosons) is universal, and operate in one dimension.
In our physicality article, we describe how fermions form only at unique positional solutions, but in saying this we do not specify anything about the background space; we do not specify the number of dimensions, nor do we say whether it is flat nor curved.
What we do say is that many one-dimensional solutions (simply distance from a source point, and all unique conditions at that distance) in a complicated system will generalize to three-dimensional Euclidean flat space at larger scales. In very general terms, we can think of space as flat and Euclidean (or Minkowski with time), and therefore treat de-constituted matter as a propagating radial (spherical) shell, but fundamentally the shell is just the 'phase-localized' point on a one-dimensional line, and we project that into space.
This general picture would be inaccurate at the smallest scales where few waves interact, because simple unique phase solutions may exist for the network. This detail is only of interest in very specialized circumstances, leaving an option for exploration of the highest energies or abstract systems, but the generalization is sufficient for most purposes.
In this model, generalized space is flat. We appreciate that some readers might be here to understand how this relates to general relativity, but we can only offer analogues rather than plug-in equivalents to GR.
Every boson has a mass-energy attribute, which is transmitted with its propagation, and changes the positional solution of other overlapping bosons by phase modulation. This phase modulation either advances or retards the solution for the other waves, depending on the sign of the mass-energy, which looks like a positional change transmitted by a force, or space curvature with a time error.
We may construct statistics of vacuum, energy flux, classical momentum, and mass-energy, or other aether-like qualities, but none of these are fundamental in this model. However, we think that a bridge to GR is possible, using this model as a basis, on the understanding that it operates in a generalized flat space (like SR), not curved space (like GR).
Phase modulation do not result in Lorentz violations: all solutions are on the propagating shell, and the modulation results only in advancement or retardation of the condition that allows a fermion to form. [More...]
On a larger scale, fermions may have de-constituted and propagate for a long time without collapsing (due to its mass-energy, or the vacuum energy). Its availability for interaction will resemble an expanding spherical shell in 3D space. Constitutionally, fermions contain four waves, as two bosons, two of which will be available for interaction. This presents a system that approximates the EPR Paradox thought experiment, where action-at-a-distance is alleged for the collapse of entangled wavefunctions. Our interpretation of this scenario is as follows: the two wavefunctions may be collapsed independently, and the collapse of one wavefunction makes the remaining waves available for interaction. This does not transmit any useful information, but it does change the wavefunction, remotely enabling different opportunities for remaining wavefunctions from the same source event. Interestingly, this enables selection of spin states and geometric phase, without violating causality.