PNR Equation Model V2.1: A Topological-Dynamic Framework for Systemic Non-Return

PNR Model V2.1 estimates dynamic proximity to a structural condition of systemic non-return using network topology alone — a graph's structure, per-node state, and the trajectory of topological energy over time. This is an independent architecture from PNR Model v1.1 (Zenodo DOI 10.5281/zenodo.18900828). It does not replace or correct v1.1; it makes a different structural choice, replacing v1.1's explicit Intervention Capacity term with purely topological measures, and should be cited separately. The core normalization was corrected after a documented failed attempt: an initial version was not scale-invariant across network sizes (verified: Psi drifted from 0.80 to 0.97 for the same relative topology as network size grew from 10 to 200 nodes). The corrected normalization is verified constant across the same range. This paper's central result is a proven negative one: an Adversarial Identifiability Test constructs two systems with identical topology, identical energy trajectory, and therefore identical Psi(t) throughout, but radically different real recovery capacity (final states of 0.68 versus 0.18). This demonstrates that topology is not, in general, a sufficient proxy for recovery capacity — disclosed here as the model's defining boundary, not as an informal caveat. PNR V2.1 is presented as a structural-dynamic model of proximity to non-return, evaluated strictly within its observed state space — not as a universal predictor of recoverability. It is a falsifiable hypothesis, not a validated instrument. A tested, executable Python reference implementation is included. Related work: see also "The Correspondence Equation" (Zenodo DOI 10.5281/zenodo.22543572), an independent framework addressing representation-reality drift.