The Mathematics of Consciousness: A Unified Formal Framework for Phenomenal Geometry, Information, Dynamics, Prediction, Hierarchy, Reflexivity, and Causal Structure v2

Matthew Arthur Carlo

doi:10.5281/zenodo.21912085

August 13, 2026Open Access

The Mathematics of Consciousness: A Unified Formal Framework for Phenomenal Geometry, Information, Dynamics, Prediction, Hierarchy, Reflexivity, and Causal Structure v2

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Key Points

To establish a comprehensive first-principles mathematical framework that unifies phenomenal geometry, cognitive dynamics, and existing neuroscientific theories of consciousness into a single formal system.
Constructed a 15-dimensional dynamical state vector governed by fifty-three foundational axioms and a differential evolution equation.
Derived category-theoretic projection theorems to evaluate mathematical reductions corresponding to major frameworks, including Integrated Information Theory, Global Neuronal Workspace Theory, and Active Inference.
Developed a computational simulation architecture incorporating stability analysis, bifurcation dynamics, and algorithmic approximations.
Proved the existence, uniqueness, minimality, consistency, independence, and completeness for all 16 interlocking structural components of the conscious object.
Demonstrated that prevailing consciousness models represent mathematically formal projections and reductions of the unified time-evolving vector field.
Generated testable empirical predictions linking mathematical anomalies, such as memory manifold instability and free-energy spikes, to observable neural signatures.

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Implication

Theoretical analysis formalizes consciousness as a 15-dimensional vector field, demonstrating that major consciousness theories represent mathematical reductions of a single unified framework.

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Matthew Arthur Carlo (2026) studied this question.

synapsesocial.com/papers/6a801a3a75c2e31742c86df4 https://doi.org/10.5281/zenodo.21912085

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The Mathematics of Consciousness: A Unified Formal Framework for Phenomenal Geometry, Information, Dynamics, Prediction, Hierarchy, Reflexivity, and Causal Structure v2

Key Points

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Implication

Discussion

Cite This Study

The Mathematics of Consciousness: A Unified Formal Framework for Phenomenal Geometry, Information, Dynamics, Prediction, Hierarchy, Reflexivity, and Causal Structure v2

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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