The Essence of the Cosmic Big Bang and the Primordial Existence of Dark Components in the GDUM Framework (Integrated Final Version)

Within the GDUM hierarchical architecture, the Big Bang is not a creation-like explosion emerging from nothing in the conventional physical picture, nor an ontological singularity of the spacetime manifold at t = 0, nor a quantum bounce event in the framework of loop quantum gravity. Its essence is the past-horizon interface corresponding to the integrability boundary of the readout functor, which rests on the same ℤ₂ Deck orientation-involution structure as black-hole horizons, forming a strict topological conjugate-duality relation. At the programmatic layer, there exist no geometric-physical concepts whatsoever—no time, temperature, density, or spacetime—only the static and eternal ℤ₂ double-leaf conjugate structure, the second-order homotopy residue, and the core axiom of topological flux conservation; there is no evolution, no birth or death, and no spacetime boundary. Upon entering the computational layer, this underlying topological structure is processed structurally via covering lifts and Pinᶜ classification, and is then uniformly translated and mapped—only within representation windows satisfying the integrability criterion of the readout functor—into a pseudo-Riemannian spacetime picture accessible to human observers. The "Big Bang" defined by the community through cosmic evolutionary backtracking is, in essence, merely the causal boundary of the representational geometric system: when observation and extrapolation cross this interface, the geometric reconstruction rules of the readout functor fail completely, no longer yielding well-defined local metrics, causal fields, or particle states; it is a boundary cut-off of the geometric description only, not a birth node or a rupture locus of the underlying topological structure. Meanwhile, this framework remains fully compatible with the empirically established conclusions of the hot Big Bang: within a stable representational readout window, it can completely reproduce the full evolutionary sequence of Big Bang nucleosynthesis, primordial CMB fluctuations, and cosmic structure formation, remaining self-consistent with all existing astronomical observations. It also thoroughly abandons the inflaton pre-hypothesis of the standard cosmological model: primordial nearly scale-invariant perturbations require no artificially introduced inflaton field to smooth out the horizon and flatness problems, but arise directly from the global second-order homotopy topological residue, thereby circumventing the ad-hoc assumption of an inflaton field from the very bottom layer. This model is essentially differentiated from Penrose's CCC conformal cyclic cosmology and from loop quantum gravity quantum-bounce models: Penrose's CCC constructs a temporally cyclic cosmic picture based on conformal matching of spacetime, while loop quantum gravity replaces the Planck-scale singularity through quantum-geometric reconstruction and realizes a bouncing cosmic evolution. In the GDUM system, by contrast, there exists neither a temporally preceding universe nor a dynamical bouncing process: black holes and the Big Bang are merely dual representations, along two opposite readout directions, of one and the same constant topological substrate. The Planck scale, as the lower resolution bound of geometric readout, and the Big Bang, as the boundary of the cosmic causal horizon, belong to two independent readout-constraint systems, and no coupling or coincidence relation exists between them.