Theory of Semantics: Mental Configuration

Volumes I–IV of the Spatial Configuration (Isong, 2026c, 2026d, 2026e, 2026f) established a universal, isomorphic grammar of co-presence, constraint, and spectral equilibrium for arbitrary relational systems. This volume executes the definitive mapping: the layers ℓL are specified as mental models, knowledge domains, symbol systems, and cognitive modalities of an observing subject. We formalize the Mental Configuration M as a weighted Multiplex graph whose nodes are mental representations and whose layers are distinct cognitive architectures (epistemic, linguistic, logical, affective, procedural). We derive the static geometric diagnostics of cognition — Fragility as cognitive dissonance, Collision as overdetermination, Elasticity as cognitive flexibility — and prove that the semantic residual tension rn from the formal Theory of Semantics (Isong, 2026a) is exactly the L2-norm of the static wave residual in the Mental Configuration. Crucially, we identify the coarse-graining topological invariant Tn as the Clarified Multiplex Spectral Gap (M). The unified update rule demonstrates that thinking is the spectral relaxation of a self-perturbing Multiplex graph under volitional topological surgery.