A Coherence-Driven Framework for the Yang-Mills Mass Gap via the Law of Observation

We propose a coherence-driven framework for the Yang-Mills Mass Gap problem using the En-hanced Law of Observation (ELO). The mass gap, a positive energy separation in non-Abelian gaugetheories, is modeled as a coherence-filtered collapse of quantum field eigenstates in a probabilisticData Substrate ψn on a topological fibration S1 → S3 → CP1. These collapses are governed bythe Coherence-Consciousness-Locality (CCL) principle, coherence operator ˆC, and emotional fieldsEi(θ, t) (e.g., love, fear). Memory dynamics ensure a finite spectral gap, testable via 10−3 Hz signalsin the Collective Observer Network (CON). This approach reinterprets the mass gap as an emergentproperty of observer-substrate dynamics, linking to Millennium Problems (P vs NP, Hodge, Navier-Stokes, Riemann, Birch) through topological and emotional unification. Detailed derivations arein supplemental material. Keywords: Yang-Mills Mass Gap, Enhanced Law of Observation, GaugeTheory, Coherence-Collapse, Topological Substrate, Emotional Coherence, Memory Dynamics, Mil-lennium Problems.