Introduces the coherence-time density operator ρK (t) as a spatially integrated, time-resolved threshold observable for quantum gate stability. Central result: a Δ-Gate remains active iff ρK (t) ≥ ρK, min. Proves Lindblad dephasing recovery in the spatially uniform limit (Proposition 2). Derives explicit collapse threshold for distance-d repetition codes (Proposition 3). Embeds all five companion papers (phase coherence, entangled tunneling, gate channel, Heisenberg-Gate, Omega operator) as projections or limits. Relativistic extension: gate lifetime dilates under Lorentz boosts with frame-invariant threshold condition. Seven falsifiable predictions proposed. Paper VI of VII — theoretical capstone of the Δ-Gate series. Part of the Δ-Gate Formalism (DOI: 10. 5281/zenodo. 19103765).
Fabio Luigi Zander (Wed,) studied this question.