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This repository contains the materials associated with “Higher-Gauge, Dynamical Symmetry Geometry of Savant-Phase Cognition: A Biochemistry-to-Geometry Theory with Dimensionless and Dimensionful Predictions and an Empirical Test Protocol.” The work develops a mathematically structured theory of reversible savant-like cognitive phases by linking mesoscopic neurochemistry, cortical network organization, higher-gauge geometry, and experimentally measurable brain dynamics. The central idea of the project is that savant-phase cognition can be modeled as a specific dynamical configuration of the brain in which local detail-preserving precision becomes unusually strong inside selected cortical modules, while large-scale contextual integration becomes comparatively weaker or differently balanced. Rather than treating such states as isolated clinical curiosities or purely descriptive psychological phenomena, the framework aims to explain them as lawful, parameter-dependent cognitive phases that arise from the interaction of biochemical modulation and geometric constraints on information flow. At the biochemical level, the theory introduces effective extracellular fields for major transmitter systems, including glutamate, GABA, acetylcholine, dopamine, noradrenaline, and serotonin. These fields are treated as mesoscopic control variables that evolve in space and time and influence cognitive organization through well-defined coupling maps. From these biochemical variables the framework derives a set of interpretable control knobs, including excitatory-inhibitory balance, sensory precision, prior or policy precision, integration gain, and flexibility. These controls are then used to modulate a geometric action describing local representational rigidity, inter-module coherence, predictive weighting, and state-switching dynamics. At the geometric level, cognition is modeled on a cortical manifold covered by overlapping functional charts, with local feature representations organized by bundle-like structures and their interactions encoded through higher-gauge connections. In this picture, local cortical modules can become geometrically “stiff,” meaning that internal feature transport becomes increasingly path-dependent and detail preserving, while global inter-module transport can become more or less coherent depending on the state of large-scale integration. This leads to a precise distinction between local precision and global glue, which is one of the main conceptual contributions of the work. To make the theory empirically meaningful, the manuscript introduces operational order parameters and practical proxies. In particular, it defines module stiffness as a measure of local curvature energy and holonomy dispersion as a measure of the variance of large-scale loop transport across brain networks. These quantities are paired with discrete graph-based estimators such as Ricci-type curvature, loop-transport statistics, connection-Laplacian summaries, and a Variable Symmetry Index that quantifies effective invariances of local cortical representations. The result is a framework designed not only to be mathematically coherent, but also to connect directly to data. The repository also reflects the fact that the project is not purely formal. It includes a simulation-ready dimensionless model and a dimensionful model with physically interpretable concentration, time, and length scales. These models are used to generate explicit predictions for entry into and exit from savant-like phases. In the proposed scenario, locally increased excitatory dominance and cholinergic precision, together with relaxed dopaminergic prior control, can drive a target module into a high-rigidity, detail-dominant state. Conversely, increased large-scale noradrenergic and dopaminergic integration is predicted to restore broader contextual coherence and reduce holonomy dispersion. In this way, the theory proposes not only a mechanism for heightened local precision, but also a mechanism for reintegration. A major strength of the project is its effort to define a concrete experimental pathway. The manuscript outlines an agent-agnostic protocol combining proton magnetic resonance spectroscopy, functional MRI, optional MEG, pupil-based arousal measures, and locus-coeruleus-sensitive imaging proxies. These tools are mapped to the model’s control variables and order parameters in a way intended to make the theory falsifiable. The paper also includes a detailed data-processing pipeline, robustness analyses across graph constructions and parcellations, statistical modeling plans, and explicit falsification criteria. This makes the work suitable not only for theoretical discussion, but also for structured reuse by researchers interested in computational neuroscience, network geometry, neuroimaging analysis, and consciousness-related brain dynamics. Beyond savant-phase cognition narrowly understood, the repository may also be of interest to readers working on predictive coding, neuromodulation, cognitive phase transitions, higher-order geometry in neuroscience, and the problem of how local and global aspects of cognition are coordinated. One of the broader implications of the work is that unusual cognitive profiles may be understood as excursions within a controlled, low-dimensional regulatory landscape, rather than as disconnected anomalies. In that sense, the project proposes a reusable framework for studying how biochemical modulation can reshape the geometry of cognition and alter the relation between precision, abstraction, integration, and conscious access. This repository is therefore best understood as a cross-scale theoretical and methodological package. It brings together formal geometric structure, biologically motivated control variables, numerical modeling, experimental observables, and reproducible analysis pathways. Whether every element of the framework is ultimately confirmed remains an empirical question, but the project is designed so that its claims can be tested, refined, or falsified with current computational and neuroimaging tools. That combination of mathematical ambition, biological grounding, and experimental openness is the defining contribution of the work.