Complex Matching Distance and Stability for Minimal Projective Resolutions, with Applications to Persistence

We develop a stability theory for minimal projective resolutions of $\mathbf{P}$-modules, where $\mathbf{P}$ is a finite metric poset. We use the Gülen--McCleary distance on $\mathbf{P}$-modules together with a new complex matching distance on bounded complexes of finitely generated projective $\mat