CSCT: Clock-Selected Compression Theory

CSCT offers an innovative axiomatic framework that elucidates the emergence of discrete symbolic representations from continuous neural dynamics. This theory integrates geometric constraints and phase-locked temporal selection to explain cognitive processes.

Core Axioms

The foundation of CSCT is built on five essential axioms:

Axiom	Name	Description
A1	Streams	Cognition operates on continuous, time-indexed streams.
A2	Constructive Compression	Representations are constrained to convex combinations within a simplex ($L^1$ geometry).
A3	Multi-Clock Factorization	Discrete events emerge via phase-locked clock selection (Na⁺/θ/NMDA gating).
A4	Irreversible Anchor	External anchors introduce thermodynamic directionality and stability.
A5	Barycentric Syntax	Complex operations arise from geometric interpolation, not mere symbol concatenation.

Key Findings

The theory presents several significant findings related to cognitive representation:

• Reliable Discretization: Emerges from continuous dynamics via clock-selected gating mechanisms.
• Long-term Stability: Irreversible anchors provide superior stability compared to self-referential systems.
• Implicit Binding: Feature binding emerges from a shared phase, independent of explicit concatenation.
• Semantic Grounding: Success is contingent on belonging to the convex hull, with a 96.7% success rate for in-hull versus 16.7% for out-of-hull in Experiment 8.
• Barycentric Syntax: Syntactic composition is achieved through interpolation within the simplex rather than algebraic rule manipulation.
• Ungrounded Symbol Acquisition: Mathematical instantiation of the "Chinese Room," where discrete codes are assigned without reconstructable meaning.

Experimentation

CSCT offers a range of experiments aimed at testing its axioms and findings:

• EX1-EX3: Single and multi-channel discretization and relational encoding.
• EX4-EX5: Stability with irreversible anchors and feature binding through shared clocks.
• EX6-EX7: Category recognition and relational internal timing.
• EX8-EX9: Semantic grounding and syntax inference using barycentric techniques.

##Further Reading For more comprehensive details about the theory and applications of CSCT, refer to the foundational paper:

Intelligence within Bounds: Why Cognition Requires a Closed Convex Hull https://zenodo.org/records/18408862

CSCT stands at the intersection of cognitive science and computational theory, providing a pathway to deeper understanding of how intelligences interpret and create meaning from the world.