Coherence Web: A Network Model for Knowledge Validation

We formalize a network-theoretic model for measuring how well knowledge elements "fit together" — the coherence web. Each element \(c\) in the web is a node in a weighted hypergraph whose value derives not from intrinsic properties but from its position in the network. The coherence number \(\kappa(c)\) quantifies how strongly \(c\) is supported by verified neighbors. We prove ten theorems characterizing the monotonicity properties of coherence under connection and verification operations. Key results include: (1) connecting nodes strictly increases degree, (2) verification strictly increases the verified count, (3) connecting clusters yields superadditive growth, and (4) isolated nodes have zero coherence. The framework provides a foundation for research prioritization, theory unification, and knowledge validation. All results are formally verified in Platonic with 13 hypotheses and 10 theorems.