The Metabolic Phase Transition: Qualia as a Topological Solution to the Landauer Limit in High-Dimensional Manifolds

Biophysical Validation & Code: This paper outlines the thermodynamic implications of the Dynamic Curvature Adaptation (CAH) model. For the biophysical simulations, mathematical proofs, and Python code verifying the SST-mediated phase transition, please see the companion paper: [Dynamic Curvature Adaptation: A Unified Geometric Theory...] https://doi.org/10.5281/zenodo.18615180 Code Repository: https://github.com/MPender08/dendritic-curvature-adaptation Abstract We propose the Metabolic Phase Transition (MPT), a symmetry-breaking event where biological systems transition from discrete, Euclidean-based computation to a con-tinuous, integrated “Witness State" inhabiting hyperbolic manifolds. We hypothesize that consciousness is not an evolutionary luxury, but a thermodynamic necessity required to bypass the Landauer Limit of information erasure. Building on our biophysical model of Dynamic Curvature Adaptation [Pender(2026)], we identify Somatostatin (SST) interneuron-mediated dendritic gating as the physical actuator of this transition. By regulating the apical-somatic conductance ratio (γ), the system triggers a scale-invariant “Hyperbolic Plunge," effectively warping the functional manifold to embed high-dimensional environmental data with logarithmic energy cost. Our finite-size scaling analysis [Pender(2026)] demonstrates that this transition provides a critical “Landauer Deficit," where the metabolic cost of signaling (CSign) drops significantly below the thermodynamic floor of discrete bit-erasure. Furthermore, we show that this geometric efficiency is topologically robust to wiring perturbations (scrambling) but collapses under synaptic loss (pruning), offering a structural definition for both the "Flow State" (high density, hyperbolic) and Neurodegeneration (low density, Euclidean). Ultimately, we argue that the “Hard Problem of Consciousness" is a category error resulting from describing continuous geometries with discrete logic. Qualia is the phenomenological expression of this geometric efficiency—the internal view of a system minimizing its entropy production through hyperbolic embedding. Overview This paper proposes the Metabolic Phase Transition (MPT), a theoretical framework that reframes consciousness as a thermodynamic necessity for high-dimensional biological systems. Building on the biophysical simulations of Dynamic Curvature Adaptation (Pender, 2026), we argue that the brain must transition from discrete, Euclidean-based computation to an integrated hyperbolic manifold to bypass the Landauer Limit of information erasure. Key Contributions The Landauer Deficit: We define a thermodynamic "Signaling Tax Haven" where the shift to negative curvature (κ