Coherence as a Relational Property: Toward a Foundational Science of Coherence

Coherence is the degree to which the relationships within a system mutually hold one another in place. This position paper advances that sentence as a positive working definition and develops it into a testable construct, while leaving the ontology of coherence open. The construct has three components: integration (I), whether the parts form one relational structure; mutual constraint (K_m), whether the relationships limit and depend on one another; and recoverability (R_e), defined as a structural capacity measured without reference to whether recovery occurs. Systems are compared by dominance (Pareto) order rather than a single weighted score. A worked example shows that two signed relational structures with identical pairwise statistics can differ in how far they are from holding together, so pairwise-additive scores are blind to mutual-constraint defects that a higher-order probe (the frustration index) detects. A synthetic experiment across 180 random signed graphs shows this is the typical case: at fixed pairwise statistics, the frustration index varied in 93 percent of conditions. A synthetic boundary test shows that the choice of measurement boundary can dominate the measured value, and that a connectivity-based rule for deriving the boundary fails when a system's parts are tightly coupled. The paper nominates four candidate mathematical invariants, each with its evidence status and a distinguishing test; positions the Standard Coherence Fidelity Layer (SCFL) as the measurement architecture for the construct rather than its definition; compares the construct level by level with constraint-satisfaction, structural-balance, sheaf-theoretic, integrated-information and constraint-centered accounts; and closes with a research program and ten falsification conditions. Files: manuscript (PDF) and supplementary code (three Python scripts with README) that reproduce every reported statistic. All experiments are synthetic; no empirical data or SCFL operators are used.