A Functional Boundary Argument for the Riemann Hypothesis via Omega-Coherence

We propose a coherence-based boundary functional Ω(C, s) that constrains the nontrivial zeros of theRiemann zeta function ζ(s) to the critical line Re(s) = 12 , supporting the Riemann Hypothesis. Rootedin the Unified Theory of Observation (UTO), this functional models ζ(s) as a coherence amplitude ina probabilistic Data Substrate, ψn(x), with zeros representing observer-driven collapses governed bythe unified equation Ω(C, ψ). The Coherence-Consciousness-Locality (CCL) principle, Energy CreationMatrix, and Logic Virus operator ensure maximal coherence on the critical line, while the GravityReturn stabilizes the collapse process. We extend the argument with variational eigenvalue framing,M¨obius invariance, and symmetry considerations, suggesting that the Riemann Hypothesis reflects afundamental coherence condition in substrate-observer dynamics.Keywords: Riemann Hypothesis, Omega-Coherence, Unified Theory of Observation, Law of Ob-servation, Zeta Function, Critical Line, Coherence Functions, M¨obius Invariance, Observer-SubstrateInteraction.