M-Compatible Gauge Classification for Banach Presheaf Coboundaries: The ℓ¹ Maximal-Symmetry Endpoint

This preprint proves a conditional norm-selection result for finite Banach-presheaf coboundary systems. Given a finite poset P and a Banach presheaf F, coboundary defects live edgewise in the 1-cochain space C¹(P,F). The main theorem shows that if a diagnostic on these defects is faithful, additive across edges, and locally compatible with all bounded linear endomorphisms of each native stalk, then each local gauge is forced to be a positive scalar multiple of the native stalk norm. Consequently, the global diagnostic is a weighted ℓ¹ sum over edges. The unweighted global ℓ¹ form follows only after an additional edge-uniformity, single-orbit, or explicit normalization assumption. The result is not a universal claim about ℓ¹ geometry. It characterizes one specific observer regime: maximal bounded-linear local symmetry plus edge-additive aggregation. Weaker transformation monoids admit larger families of gauges, organized here through the M-compatible diagnostic taxonomy. In particular, CPTP monotonicity alone is treated as a compatibility condition, not as a theorem selecting the trace norm; trace-norm selection requires additional operational distinguishability assumptions. The paper includes a worked finite example, a falsifiability criterion, a claim-type ledger, a support ledger, and a Lean4-oriented mechanization status note. The central refutable claim is simple: a counterexample would be a faithful edge-additive diagnostic satisfying maximal bounded-linear local compatibility but not expressible as a weighted ℓ¹ sum of native stalk norms.