Durée–Extension Projection Theory (N–Q–S): A Diagrammatic Unification with a Fixed-Point Axis

We study sequential quantum measurements within an operational N–Q–S architecture and prove three main results. (i) A tight order-effect bound with saturation conditions characterized by Halmos two-subspace blocks; the construction extends to POVMs via Naimark dilation. (ii) A Doeblin-type minorization for instruments, yielding a quantitative 1-norm contraction and an exponential mixing rate γ ≥ −ln(1 − δ)/Δt for the look–return loop. (iii) A monitored discrete-to-GKLS bridge: as Δt → 0 under standard stability assumptions, the certified rate transfers to a compatible GKLS semigroup. We define testable indices (ONS/PII/PAD) linking our bounds to behavioral order effects, and we supply complete proofs (main text/appendices) together with a reproducibility package (code, data, and figure scripts).