Semantic Equilibrium: A Graph-Theoretic Framework for Constraint-Validated Medical Web Content

Abstract Consumer-facing medical web content remains predominantly prose-centric: clinically relevant assertions are embedded in narrative text with limited machine-verifiable structure. While biomedical ontologies (e.g., SNOMED CT) and web standards (e.g., JSON-LD) exist, most medical pages lack deterministic claim-level traceability, constraint validation, and computable coherence. Consequently, prevailing quality indicators—readability formulas, citation density heuristics, and probabilistic NLP scoring—provide weak guarantees for semantic integrity, defined here as the structural alignment of atomic claims, evidence references, and discourse roles required for safe clinical communication. This paper introduces Semantic Equilibrium, a formal graph-theoretic framework that models a clinical page as a constraint-validated Claim Graph and evaluates its integrity using a composite metric termed MizanScore. MizanScore quantifies three independent dimensions: (i) Balance Ratio, enforcing dialectical completeness between benefit and risk claims; (ii) Symmetry Integrity, measuring topological narrative closure via role-aware section mirroring; and (iii) Recurrence Integrity, detecting semantic drift of core claims across the narrative. The framework is implemented using a schema-native JSON-LD architecture with a SHACL-based publish gate that blocks deployment when structural constraints are violated. By treating clinical content as a glass-box engineering artifact rather than an opaque document, Semantic Equilibrium transforms content quality from a subjective editorial judgment into an auditable and computable property, enabling scalable governance of medical knowledge on the web.