The ℤ₂ Topological Substrate in the GDUM Framework — A Non-Mediatic "New Aether" Ontology

This paper presents, within the framework of the Generative Digital Universe Model (GDUM), a purely topological ontological structure that substitutes for the classical mechanical aether — the ℤ₂ topological substrate. The substrate is defined solely by a two-sheeted covering generated by a binary conjugate Deck involution; it presupposes no discrete geometric atoms, carries no hydrodynamic degrees of freedom, possesses no material energy density, and supports no vibrational excitations. It is thereby strictly distinguished, at the ontological level, from the 19th-century mechanical aether, superfluid-vacuum models, quantum-medium substrates, and all varieties of "new aether" models. The topological flux conservation axiom (Axiom 0.4) and the five integrability conditions of the Conditional Structure Theorem (CST) act as Layer-1 constraints that filter admissible covering-sections; the reading functor acts on these constrained sections and, in the representational layer, gives rise to Lorentzian spacetime geometry, quantum phase structure, and the physical content of gauge channels such as gravity and electromagnetism. The paper further derives, for the electromagnetic channel, the first-principles reading relation of the fine-structure constant, α⁻¹ = π · W_K^{em,2π}, and unifies dark matter and dark energy as distinct projections, through local and global reading windows respectively, of the second-order homotopy residue K⁽²⁾ specific to the gravitational–cosmological channel. Finally, the substrate is systematically compared with contemporary spacetime-emergence programs — loop quantum gravity, causal dynamical triangulations, the pregeometry program, the amplituhedron, entanglement gravity, the holographic principle, superfluid-vacuum models, and string theory — clarifying its unique position as a purely topological algebraic relation.