Dimension-W and Archetypal Constraint Eigenmodes: An Axiomatic, Fractal Framework for Physical Law, Cognition, and Meaning

Abstract This paper presents a unified theoretical framework integrating physics, cognition, and meaning through Dimension-W, a pre-differentiated constraint layer within the Unified Consciousness Substrate Theory (UCST). We formalize archetypal constraint patterns as irreducible, scale-invariant eigenmodes of constraint space that govern coherence, persistence, and intelligibility across physical and cognitive domains. A minimal canonical set of archetypal constraint eigenmodes is defined, along with axioms of minimality, inversion, and recursion. We introduce a transformation algebra describing lawful transitions, collapse, and reintegration among archetypes. Crucially, we show that meaning and consciousness arise via recursive constraint mirroring, wherein an observing system models both external constraints and itself as a constraint-bearing entity. This framework reframes physical law as coherence selection, cognition as constraint integration, and symbolism as executable compression. Applications are discussed for physics, psychology, artificial intelligence, and systems design.