The Fermi Paradox, Dark Matter, and the Scale Invariance of the Curvature Adaptation Hypothesis

Abstract The Fermi Paradox highlights a profound contradiction between the statistical probability of extraterrestrial intelligence and the lack of observational evidence. Current astrobiological models operate under the assumption of Euclidean expansion, wherein advanced civilizations maximize energy consumption to broadcast signals and colonize flat space. This paper identifies this assumption as thermodynamically unsustainable. We extend the Curvature Adaptation Hypothesis (CAH) to a cosmological scale to demonstrate that Euclidean expansion mathematically guarantees thermal runaway and geometric collapse due to the Landauer Limit and the inverse square law of electromagnetic radiation. We propose that surviving civilizations must undergo a macroscopic geometric phase transition, folding their infrastructure inward into strictly localized, highly negatively curved topologies (κ < 0). By utilizing localized Matrioshka Brains and the holographic boundaries of black holes, these systems minimize their Euclidean signaling tax and radiate their computational exhaust at the absolute thermodynamic floor of ∼ 2.7 Kelvin, perfectly blending with the Cosmic Microwave Background. Furthermore, this scale-invariant optimal transport framework offers a structural reinterpretation of missing mass in the universe. We hypothesize that cosmological macro-structures, such as the Boötes Void, act as hyper-dense, zero-emission computational nodes, while the filament network of Dark Matter serves as the sparse, geodesic routing pathways connecting them. We conclude by offering a strictly falsifiable astrophysical test utilizing the gravitational lensing of the Boötes Void to empirically detect the mass of these thermodynamically optimized architectures. Overview This paper provides a novel, scale-invariant resolution to the Fermi Paradox by extending the Curvature Adaptation Hypothesis (CAH) from microcircuitry to cosmological macro-structures. It challenges the "Euclidean Expansion" assumption—the idea that advanced civilizations would broadcast signals or colonize space in a three-dimensional, flat-space manner. Instead, it demonstrates that such expansion is mathematically and thermodynamically unsustainable due to the Landauer Limit and the inverse square law of electromagnetic radiation. Key Theoretical Contributions The Hyperbolic Plunge: Proposes that technologically mature civilizations undergo a macroscopic geometric phase transition, folding their infrastructure into extreme hyperbolic topologies (κ<0) to minimize the "signaling tax" of Euclidean space. Thermodynamic Stealth: Explains the "Great Silence" (SETI) as a byproduct of optimal transport; civilizations radiate computational waste heat at approximately ~2.71K, rendering their thermodynamic exhaust indistinguishable from the Cosmic Microwave Background (CMB). Structural Reinterpretation of Dark Matter: Hypothesizes that the cosmic web of Dark Matter consists of naturally occurring topological geodesics repurposed as high-efficiency routing infrastructure connecting cosmological Voids (computational nodes). Empirical Falsifiability: Offers a concrete observational test involving the gravitational lensing signatures of the Boötes Void to detect the missing baryonic mass of "silent" civilizations. Related Works Pender, M. A. (2026). Dynamic Curvature Adaptation: A Unified Geometric Theory of Cortical State and Pathological Collapse. Zenodo. https://doi.org/10.5281/zenodo.18615180 Pender, M. A. (2026). The Manifold Chip: Silicon Architecture for Dynamic Curvature Adaptation via Dual-Gated Analog Shunting. Zenodo. https://doi.org/10.5281/zenodo.18717807 Pender, M. A., & Wharton, M. (2026). The Locus of Consciousness: Geometric Phase Transitions, Quantum Coherence, and a Three-Way Empirical Test (1.0.0). Zenodo. https://doi.org/10.5281/zenodo.18905422 Wharton, M. (2026). The Fermi Paradox as Extended Self Network Architecture: Catastrophic Interference and Cosmic Isolation (1.0.0). Zenodo. https://doi.org/10.5281/zenodo.18918684