This preprint presents a cosmological framework in which universes form a discrete genealogical sequence linked by nonsingular black-hole–to–white-hole transitions in a Loop Quantum Cosmology (LQC) context. Based on two externally anchored energy scales—the LQC critical density (ρcrit) and the CMB-calibrated inflationary density (ρinf)—we derive a single dimensionless inheritance factor K³= ρinf/ρcrit that governs the energy transfer across generations without additional adjustable parameters. By integrating thin-shell matching conditions, Raychaudhuri focusing, and the generalized second law of thermodynamics, we demonstrate that the cosmic lineage is strictly finite, yielding exactly eight viable generations. The paper identifies our universe's unique position within this sequence based on its mass-energy content and provides testable observational signatures, including a unique tensor-to-scalar ratio and an ultra-low-frequency stochastic gravitational-wave background (f₀ ≈ 2.4 × 10⁻¹⁴ Hz). This framework offers a deterministic alternative to infinite recurrence models, eternal inflation, and anthropic multiverses. The manuscript consists of a ~35-page main text aimed at readers familiar with General Relativity and LQC, supported by extensive technical appendices and a glossary for full verification of the derivations.
R. Steinmann (Mon,) studied this question.