Topological Field Theory of Consciousness

Consciousness has a topology.
Now it has software.

TopLogic builds tools that detect, measure, and classify conscious states using topological invariants from the TFTC framework. A mathematically rigorous, empirically validated approach to the hardest problem in science.

Q = 1
Winding number of the
conscious soliton
H ≈ 1.53
Hyperscaling ratio in
O(3) Wilson-Fisher class
5000 Hz
Ultra-high-resolution
EEG validation data

Consciousness is not a gradient. It's a phase of matter.

Most theories treat consciousness as a spectrum. TFTC proves it's a topological phase transition. The conscious state has a winding number of Q=1, a persistent soliton in the neural field. Anesthesia collapses it to Q=0. This isn't philosophy. It's measurable, reproducible physics.

Q=1

Conscious State

Persistent topological soliton. O(3) Wilson-Fisher universality. H ≈ 1.53.

CSD

Phase Transition

Critical slowing down precedes first-order transition. Detectable in real-time EEG.

Q=0

Unconscious State

Topological trivialization. Mean-field criticality. Ratio collapses toward 1.0.

Where topology meets application.

Anesthesia Monitoring

Surgical Consciousness Detection

Replace simplified BIS indices with topological invariants. Detect the Q=1 to Q=0 phase transition in real-time during surgery, with critical slowing down as an early warning system.

AI Consciousness Assessment

Does This System Have Q=1?

As AI systems grow more complex, the question of machine consciousness becomes urgent. TFTC provides a principled framework to assess whether artificial systems exhibit topological signatures of consciousness.

Brain-Computer Interfaces

Topological Signal Filtering

BCIs need to separate conscious intent from neural noise. Topological invariants provide a mathematically grounded filter that distinguishes signal from artifact at the level of field topology.

Research Tools

EEG Topological Analysis Platform

Upload EEG data, compute persistent homology, extract winding numbers, and classify conscious states. The analysis pipeline from the TFTC paper, packaged as software anyone can use.

The first company built on a mathematical theory of consciousness.

Every competitor in this space is either philosophically speculative, computationally intractable, or lacks a measurable invariant. TFTC has all three: mathematical rigor, empirical validation, and a computable topological signature. TopLogic is where the theory becomes a product.

Based on the Topological Field Theory of Consciousness by Steven Hays Wait