The Infolding Universe Cosmic Expansion and Black Holes as Calabi-Yau Geometry

Correction Note — February 25, 2026 The projection identity in §2.2 and Appendix A.1 assumes a ten-dimensional spacetime with six compactified internal dimensions. This assumption is inconsistent with the three-phase framework developed in the companion paper (Reynolds 2026, "One Crossing, Three Phases"), which derives exactly three spatial dimensions from algebraic necessity and prohibits a fourth. The Kaluza-Klein reduction yielding a(t) ∝ Vₓ⁻¹″³ therefore operates within a framework the author's own program excludes. Independent verification (Kasner analysis of vacuum 10D Einstein equations) confirms that the 1/3 exponent does not emerge from 10D dynamics in any case; the vacuum solution yields 5/6. The core conjecture—that cosmic expansion may be a geometric projection rather than metric stretching—is not withdrawn. The mathematical implementation presented here is incorrect and requires replacement. If the Calabi-Yau structure represents the algebraic geometry of the three-phase structure rather than literal extra spatial dimensions, the projection identity must be rederived from the phase structure, not from dimensional reduction. The volume conservation postulate (a³Vₓ = const) is also withdrawn as stated. It is incompatible with the Kasner constraints of the framework it invokes. The conjectures, falsifiability conditions, and open questions in the remainder of the paper are unaffected. Abstract. We propose a geometric reinterpretation of cosmic expansion in which the observable universe occupies the interior of a dynamically evolving Calabi-Yau manifold. In this framework, what observers perceive as the expansion of four-dimensional spacetime is a projection effect of higher-dimensional geometric evolution—the manifold curving inward in its extra dimensions, a process we term infolding. We further propose that black holes correspond to topological gaps in the Calabi-Yau structure—places where the manifold’s topology opens into higher-dimensional cycles. This identification reframes the black hole singularity as a topological feature rather than a point of infinite density, offers a geometric basis for the information paradox, and suggests a natural relationship between cosmic expansion and black hole formation through topological transitions. We identify existing mathematical structures in string theory—conifold transitions, moduli evolution, and Hodge number classification—that could formalize these conjectures, derive the Kaluza-Klein projection identity linking internal volume contraction to external scale factor growth, show that the same identity applied locally near a conifold point yields an effective metric with event-horizon behavior, and specify observational signatures—including topological anisotropy of the Hubble parameter and cycle-constrained black hole mass spectra—that would distinguish this framework from standard ΛCDM cosmology.