Cosmological Boundaries Anchored in Tolman, Bekenstein, and Hawking Mechanics: First-Principles Derivation of Minimal, Intermediate, and Concurring Maximal Saturated Horizon Limits

Description Methodological Update Note (v1 to v2): The preliminary version of this work (v1) introduced the concept of Volumetric Tension in an exploratory manner, utilizing heuristic approximations and phenomenological toy models to map cosmological anomalies. We transparently acknowledge that those initial approximations lacked first-principles rigor. This updated and definitive version (v2) fully corrects these methodological limitations. All ad-hoc parameterizations (curve-fitting) have been eliminated. The framework is now derived strictly from classical thermodynamics, Landauer's Principle, and statistical mechanics fluctuation theorems, operating with zero free parameters. Abstract: This study establishes the absolute, parameter-free boundaries of the universe, treated strictly as a closed informational thermodynamic system (3D+t). By synthesizing Tolman's relativistic thermodynamics, the Bekenstein holographic limit, Hawking horizon mechanics, and Landauer's informational cost, we derive the primordial factory configuration of the cosmos at the Planck limit (t=tₚ) and its maximum saturation horizons. The model is anchored exclusively in the CODATA 2022 fundamental constants and observable baryonic mass, demonstrating that the anomalies attributed to the "dark sector" are direct, quantifiable consequences of the universe operating under informational saturation constraints and holographic elasticity. Key Findings: The mathematical integration of cosmological boundaries reveals a cascade of structural invariants (The Costa Constants: ₂₂, ₁₁₍, ₁, ₂) and provides the following resolutions: The Thermodynamic Partition (The End of Exotic Dark Energy): Vacuum energy density is not an arbitrary cosmological constant. Applying Landauer's Principle to the de Sitter horizon temperature dictates that exactly (2) 69. 31\% of the universe's energy budget must be consumed as a thermal-informational processing cost, matching the observed Dark Energy density perfectly. The Holographic Elastic Tension Effect (Dark Matter Resolution): In accordance with strict thermodynamic conservation, the partition mandates that the bulk matter occupies the remaining limit of 1 - (2) 30. 68\%. We demonstrate that the 5\% of primordial baryons do not require invisible particles (WIMPs) to bridge this gap; the supplementary gravitational attraction in galaxies and the clustering anomaly (S₈) emerge organically as the geometric response of the elastic spacetime grid (dictated by the Volumetric Tension ₁ 8. 8533) to baryonic matter distortion. Vacuum Decoherence and the 10^120 Catastrophe: The catastrophic divergence of Quantum Field Theory is resolved by imposing physical boundary cutoffs (R₌₈₍ to R₌₀ₗ). The transition of the initial density at the Planck threshold to macroscopic expansion is governed by classical statistical mechanics fluctuation theorems, diluting strictly by the square root of the volumetric decompression (₁₁₍) without fine-tuning. Cosmic Inflation and Cyclic Cosmology: Primordial expansion and Penrose's cyclic signatures are derived directly from quantum mechanical "limit overflows, " where the terminal photon's wavelength structurally breaks the dimensional boundaries of reality (/D₌₀ₗ 7. 95), precluding the need for hypothetical scalar inflaton fields. Conclusion: This framework does not claim an underlying microphysical "Theory of Everything, " but rather establishes a rigorous thermodynamic baseline. By replacing assumptions of exotic fluids (dark matter and dark energy) with immutable laws of statistical mechanics and information processing, the mathematics proves that the observable universe is self-sufficient and structurally elastic. We invite the community to evaluate these metrics as global constraints that any future quantum gravity theory must necessarily obey. Keywords: Thermodynamic Cosmology; Bekenstein-Hawking Entropy; Landauer's Principle; Holographic Elastic Tension; Emergent Dark Matter; Costa Volumetric Constant; Statistical Mechanics; Resolution of the Vacuum Catastrophe.