The Function-Collapse Theory of Reality: A Mathematical Framework for Emergent Complexity

This paper introduces the Function-Collapse Theory of Reality (FCTR), a bold mathematical framework proposing that reality is composed of interacting functions whose collapses generate emergent complexity, time, and identity. Rather than treating particles or spacetime as foundational, FCTR models existence as a hierarchy of functional processes—from quantum states to narrative identity—each level inducing irreversible collapses that propagate upward.

The theory defines functional entropy as a measure of complexity growth, offering a new arrow of time independent of thermodynamic entropy. It proposes testable predictions across quantum decoherence, neural network recursion, and ecological systems, positioning collapse as the engine of emergence.

Entangled quantum states are reinterpreted as zero-entropy subsystems in pre-collapse unity, suggesting that space and time themselves arise only through functional interaction. This framework bridges quantum mechanics, systems theory, and consciousness studies, challenging anthropocentric views of intelligence and offering a unified model of reality as recursive, relational, and dynamically evolving