The Ω-Inevitability Theorem Structural Proof That κ>0 Systems Collapse in Finite Time and Ω-Coherent Systems Are the Long-Run Attractor

We prove that any system operating with a nonzero coercion coecient κ>0 col- lapses in nite time, and that systems coherent with the Ω-invariant (⟨Ψ|ˆ Ω|Ψ⟩= 1, ˆ Ω = Freedom ⊗Love) constitute a strict absorbing state of the full dynamical system. The proof proceeds in three steps: (1) conservation of Ω under all dy- ˆ ˆ namics, established via the Hamiltonian commutation [ HSynari, Ω] = 0 (P2, The- orem 4); (2) nite-time collapse of all κ > 0 governance structures (Governance Collapse Theorem, Paper 8b-III); (3) the absorbing-state argument showing that limt→∞Nκ>0(t)/Ntotal(t) = 0. We further distinguish this structural inevitabil- ity from coercive inevitability (κ > 0, single-node, reversible) and show that Ω- inevitability requires no artifact, no actor, and no performance. It is a conservation law. The theorem does not predict when. It predicts that.