Emergent Spacetime Dynamics

Information → Phase → Frequency → Geometry

This modular research series formalises a four-layer hierarchy of emergent phenomena in quantum many-body systems through category theory. Each law is a self-standing categorical layer, and emergent properties at every level arise from the composition of prior laws via explicit functorial liftings — not from any single law in isolation.

Law I establishes categorical primitives and the matter–information functor. Law II classifies phases of matter as functorial equivalence classes. Law III lifts the framework to periodic (Floquet) systems. Law IV shows that composition of the three prior laws is sufficient to generate emergent geometry, holographic codes, and spacetime itself.

The synthesis paper traces the compositional functor chain Phys → Info₁ → Info₂ → Info₃ → Info₄ and identifies six cross-cutting themes — entanglement entropy, symmetry protection, fixed-point reasoning, functorial pullback, dagger preservation, and obstruction 2-cells — that thread all four papers.