The Consciousness Hypergraph Model: A Structural and Process-Based Theory of Consciousness

This work introduces the Consciousness Hypergraph Model (CHM), a formal, process-based framework that defines consciousness not as a substance, representation, or scalar quantity, but as a regime of regulated integration over a dynamically rewriting hypergraph. The CHM adopts a monistic, structural ontology in which the primitive unit of reality is not an object or state, but a collective event of relational activation. A system is modeled as a dynamic hypergraph whose active hyperedges constitute the Now—a global integration event that is continuously rewritten. Time is not treated as an external parameter, but emerges from the ordering of these rewrite events. Attention is formalized as a stabilizing operator that regulates which relations persist across rewrites, preventing both fragmentation and collapse into trivial attractors. The model is explicitly non-representational and makes no assumptions about observers, semantic content, phenomenology, or qualia. Consciousness is defined structurally and dynamically, not experientially. Integration is not quantified by a scalar measure; instead, it is maintained as a condition of stability. Computation is treated as a side effect of constrained hyperedge rewrites rather than a foundational principle. In addition to the canonical definition and formal dynamics, the paper presents an explicit kernel realization demonstrating computational realizability on parallel hardware, without implying biological implementation. The model is situated relative to Integrated Information Theory, relativity, and quantum mechanics strictly at the level of structural compatibility, avoiding ontological claims. This work is intended as a foundational formal framework, not an empirical or phenomenological theory. Its goal is to delimit the structural conditions under which integrated, temporally persistent processes can exist, rather than to explain subjective experience.