Recoverability Length Scales and Wilson Loops in Lattice Gauge Theories: Protocol, Definitions, and Conjectural Links to Confinement Diagnostics

We propose a numerical protocol and falsifiable conjectures relating quantum-information recoverability measures to confinement diagnostics in lattice gauge theories. For a tripartition A-B-C and collar width w, we define a Petz-type recovery error E_rec(w) and extract a recoverability length from threshold and fit criteria. Since gauge constraints obstruct naive factorization, the protocol is formulated in an extended-Hilbert-space (EHS) prescription by default, with an algebraic (gauge-invariant) variant outlined together with its subtleties (centers, sectors). We conjecture that E_rec(w) decays exponentially in gapped phases and that its scale tracks confinement scales set by Wilson loops. v2 executes the testbed that v1 only specified: on a Z2 ladder of four plaquettes (14 links, Gauss law enforced exactly, = 1 to 1e-6), the suite computes E_rec(w) and Wilson decay on the same ground states across five couplings. Findings: the pipeline runs end to end; xi_rec is identifiable at three of five couplings and nearly coupling-independent (0.21-0.31, spread x1.4), while the Wilson decay length varies strongly (0.38-6.9, spread x8.6): no tracking at ladder level. Because height-one ladders degenerate area and perimeter, the Wilson scale there is not a pure confinement scale, so this first dataset is inconclusive-but-cautionary for the tracking conjecture rather than a falsification -- and it sharpens the requirement: a genuine 2D lattice is needed. v2 further flags the TFIM control row shared with the companion framework note as unstable under regeneration, and adds series positioning. No v1 definition is changed.