The Curvature Adaptation Hypothesis: Dynamic Information Geometry as a Regulated Resource in Neural Computation

Abstract Neural systems do not merely compute over fixed architectures. They regulate the effective geometry through which information and influence are routed across a physically bounded, metabolically constrained substrate. The Curvature Adaptation Hypothesis (CAH) proposes that this regulation is central to neural function: effective information geometry is a dynamically managed physical resource whose state-dependent modulation helps determine whether processing remains locally specialized, achieves transient large-scale integration, stabilizes across time, or collapses into dysfunctional regimes. This paper presents CAH in its current form, distinguishing it from earlier formulations that emphasized broad whole-network transitions toward globally integrative routing states. The current framework instead places explanatory weight on the selective recruitment of a load-bearing routing scaffold, particularly within the lower-curvature tail of the network’s transport structure. This scaffold is proposed to bear disproportionate importance for integrative success, making it a more precise and empirically tractable target than whole-network geometric summary measures alone. Formally, the framework employs Ollivier–Ricci curvature, optimal transport cost, and inhibitory control parameters as observables linking biological regulation to network-level transport organization. Biologically, SST-mediated dendritic gating and VIP-mediated disinhibition are proposed as plausible actuators of geometry modulation. On this view, neural competence is not a drive toward maximal integration, but the regulated management of disciplined access: the capacity to recruit sufficient transport support for coordination and maintenance without forfeiting selectivity, stability, or recoverability. Summary This paper presents the Curvature Adaptation Hypothesis (CAH) in its current form as an entry-point position paper for the broader framework. CAH proposes that neural systems do not merely compute over fixed architectures, but dynamically regulate the effective geometry through which information and influence are routed across a physically bounded, metabolically constrained substrate. Effective information geometry is therefore treated not as a passive anatomical backdrop, but as a regulated physical resource with consequences for local specialization, transient integration, temporal stability, and pathological failure. The paper distinguishes the current framework from earlier CAH formulations that emphasized broader whole-network transitions toward globally integrative routing states. The present account instead places explanatory weight on the selective recruitment of a load-bearing routing scaffold, particularly within the lower-curvature tail of the network’s transport structure. In this way, integration is reframed as a structured achievement supported by asymmetrically important transport relations rather than as a uniform global state. The manuscript clarifies the biological and formal core of the framework, outlines its control-theoretic implications, identifies what the hypothesis currently helps explain, and specifies what kinds of findings would support, constrain, or falsify it. Broader implications for emotion, identity, and conscious organization are discussed as downstream extensions of the same transport logic. The paper is intended to serve as a conceptual front door to the CAH research program and a launch point for its companion technical and philosophical developments. Related Works CAH Foundations: Dynamic Curvature Adaptation: A Unified Geometric Theory of Cortical State and Pathological Collapse. https://doi.org/10.5281/zenodo.19424978 A Control-Law Extension of the Curvature Adaptation Hypothesis in Hierarchical Transport Networks. https://doi.org/10.5281/zenodo.19270109 Beyond Mean Curvature: Lower-Tail Routing Structure in Controlled Hierarchical Networks. https://doi.org/10.5281/zenodo.19324674 CAH Perspectives, Interpretations, and Bridge Notes: The Biological q10 Tail as a Layered System: Rich-Club Scaffold, SST Actuation, and Thalamocortical Thickening. https://doi.org/10.5281/zenodo.19477954 Computation as Constrained Transport: A Geometric Perspective on Information Processing. https://doi.org/10.5281/zenodo.19410259 Emotions as Computation Under Constrained Transport. https://doi.org/10.5281/zenodo.19600710 Emotion Vectors and Constrained Transport: A Possible Bridge from Claude's Interpretability to Bounded Interiority. https://doi.org/10.5281/zenodo.19622120 CAH Philosophy of Mind Extensions: Organized Physical Interiority: A Philosophical Perspective on the Curvature Adaptation Hypothesis. https://doi.org/10.5281/zenodo.19488348 The Governed Inside: Emotion and Agency as Nested Interiority. https://doi.org/10.5281/zenodo.19498895 Sub-Governance in a Bounded Interior: Imposition, Evocation, and the Geometry of Inner Guidance. https://doi.org/10.5281/zenodo.19536825 Compressed Geometric Seeds: Reconstructive Access and Model Fit in a Bounded Interior. https://doi.org/10.5281/zenodo.19547996 Identity and the Bounded Interior. https://doi.org/10.5281/zenodo.19578281