# Toward a Structural Mathematics of Consciousness: Heyting Algebras of Brain Dynamics Tested in Human Sleep EEG and a Whole-Brain Fly Model

Article · Rohit

- Archive id: doi:10.5281/zenodo.22995541
- Published: 2026-09-27
- Venue: Zenodo (CERN European Organization for Nuclear Research)
- DOI: https://doi.org/10.5281/zenodo.22995541
- Citations: 0
- Source URL: https://doi.org/10.5281/zenodo.22995541
- Provenance: openalex

## Abstract

This preprint develops a structural mathematics of consciousness in which the distinctions a brain can stably hold form a Heyting algebra built directly from its dynamics. From a discretised brain-state space, a transition graph at resolution ε gives a reachability preorder whose up-sets form the algebra. Three largely standard results follow: unity corresponds to indecomposability, classical logic corresponds to reversible dynamics, and contraction between two states corresponds to a Heyting subalgebra relation. Further propositions link the algebra to Shannon entropy, classical probability and limits on self-representation. The framework is tested on human sleep EEG (Sleep-EDF) and in a connectome-based model of the whole fruit-fly brain linked to a simulated body. In sleep EEG, the algebra separated wake, REM and deep sleep, mainly through which states are occupied, and a pre-registered temporal prediction failed on 21 held-out subjects. In the fly model, touch at two body sites ran as parallel pathways with specific cross-talk, and imposed sleep-like states raised the arousal threshold without changing the algebra beyond chance. The paper reports its failed predictions and controls in full. It addresses the structure of experience, not why experience exists. Analysis code and derived data are available from the author on request. AI assistance is disclosed in the paper. Keywords :- consciousness, Heyting algebra, intuitionistic logic, brain dynamics. sleep EEG, Conley theory, attractor lattices, Shannon entropy, Drosophila connectome, whole-brain model, FlyWire, mathematical consciousness science

_Abstract reproduced under CC-BY (publisher license, via OpenAlex)._

Topics: [Connectomics & Brain Mapping](https://space-kitty.com/topics/connectomics)

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