Measurement Dynamics: Coherence, Bifurcation, and Human Flourishing Measurement in Self-Referential Systems

This manuscript introduces Measurement Dynamics, a coherence-based measurement framework for tracking stability, drift, collapse risk, and restoration in self-referential systems — with primary application to human flourishing measurement. The framework identifies coherence C (t) as the central invariant and derives a closed family of observables: drift velocity (v), epistemic acceleration (a), deviation from maximal coherence (D), stability margin (m), and restoration dynamics (ρ). System behavior is classified into four dynamical regimes — λ (stable), γ (drift), κ (collapse-approaching), and ρ (restoration) — determined by coherence derivatives rather than domain-specific ontologies. The γ→κ regime transition is formalized as a saddle-node bifurcation, yielding three directly testable consequences: critical slowing down as drift velocity approaches vcrit, irreversibility of the fold transition, and substrate-scaled threshold variation. The coupling term Γ (t) is shown to produce measurement-system invisibility in self-referential contexts — a formal explanation for why coherence degradation is not detectable from within the framework until after the bifurcation has occurred. Operationalization is grounded in measurement quanta — atomic structural observations (timestamp, expressive magnitude, inter-entry interval) — which establish a substrate-agnostic, dimensionless resolution for coherence reconstruction. Attentional stability is developed as the primary coherence proxy for human systems, with systematic justification against five competing candidates. A Monte-Carlo synthetic cohort (N=20, T=200) validates the internal measurement architecture across all four scenario classes, with six embedded figures. A Minimum Viable Pilot protocol (N=40, 26 weeks) is specified with preregistered success criteria for the bridge claim temporal precedence hypothesis. The framework descends from the Upstream Coherence Measurement Stratum (UCMS) and the parent SCFL architecture (Brogdon 2026, DOI: 10. 5281/zenodo. 19057170). Synthetic cohort data (CSV, seed 2026) and simulation code are provided as open companion artifacts.