Complex Phase Cosmology 2nd Part 2: Collapse and Re-divergence — The Ontological Chain from the Event Horizon to the Big Bang

Part 1 of the Second Series proposed a measurement grammar for converting the phase angle θ from an input value arranged on the observational coordinate into an output value produced from local conditions. It did not, however, deal with what that grammar describes at the limit. The measurement equation produces a phase value under finite local conditions, but what that production means where matter can no longer maintain its own state requires a separate definition. This study deals with that limit. In standard gravitational theory, under very general conditions gravitational collapse leads to geodesic incompleteness, and the singular limit is treated as the point at which the theory can no longer give an answer. However, that a theory cannot give an answer and that there is nothing there are different statements. Starting from this distinction, collapse is redefined within a language in which the total amount is conserved. Five objects are treated, and they form one connected chain: event horizon → imaginarization → singularity → fractal re-divergence → Big Bang. Building on Part 1 (DOI: 10.5281/zenodo.19158235), Part 2 (DOI: 10.5281/zenodo.19332436), Part 3 (DOI: 10.5281/zenodo.19332612), Part 4 (DOI: 10.5281/zenodo.19412396), and Part 5 (DOI: 10.5281/zenodo.19445570) of the First Series, and on Part 1 of the Second Series (DOI: 10.5281/zenodo.22168235), this study moves from a grammar that produces phase to what that grammar describes at its limit. Core results established in this study: Event horizon = the boundary at which R's form as shown in the real world begins to collapse and passes into imaginarization. This is at a different level from Part 4 of the First Series classifying black holes as a local state of low θ, and the two are not identified Causal chain: increase of gravitational binding → exceeding of the stability limit of matter → chain collapse. The first two stages are standard physics; the stage added here is that this collapse is the loss of R's form as shown in the real world Singularity = a state that leaves R's form as shown in the real world and exists in the imaginary dimension. The definition of magnitude changes from volume or length to the norm of the phase expression, so this is not annihilation but the existing form no longer being maintained. The state cannot be designated by a single phase coordinate such as θ = 0 or θ = 0.5, which keeps it distinct in level from voids inside the R world Re-divergence = one more quarter phase rotation, not an event separate from the singularity but the next section of the same rotation. i · i = −1 is arithmetic; reading its arrival point as the position where a new form is shown in the real world is the extension added here Fractal recursion F_n = e^(iπ f(F_(n−1))) allows the transition to be repeated, so collapse and re-divergence are transitions permitted at every level where the transition holds, rather than exceptions at one Big Bang = the transition of becoming real again — not an event that happened once at the beginning but one repeated at every level where this transition holds. Under A5, this re-divergence is not a new total energy coming out of nothing but the conserved total energy passing through an additional rotation Throughout, A5 is applied rather than re-derived. The unit norm |e^(iπθ)|² = 1 remains a mathematical identity, and physical total energy conservation remains the separate bridge axiom established in Part 1. The unit norm equation is therefore not substituted directly into the singularity, while total energy conservation is held to be maintained even in this transition. Two things remain to be done. First, to establish the bridge axiom connecting the junction from collapse to the loss of R's form as shown in the real world. Second, to determine, together with the growth measure of the universe and the relations between phase domains, what the end means in a structure in which the rotation circulates. Whether the re-diverged form is a re-expansion of the same universe or a transition into another phase domain is left to Part 5. This research applies Juridical Structuring Methodology to cosmology, crossing traditional academic boundaries to propose a strictly falsifiable scientific framework.