X72-64: Validated Viscosity Half-Line Positive Adjoint Theorem

Continuing from Round 63's convergence of the small-viscosity gap to a selection problem for a single slow Jost scattering line (STOP-C67), this round changes strategy: rather than attacking the singular ν→0⁺ matching head-on, it closes the compact viscosity segment piece by piece using "finite-kernel + infinite-tail" a posteriori validated interval certificates, and proves the large-viscosity end directly by a global Banach contraction, with the two segments joining exactly at ν=0.7. This yields the "Validated Viscosity Half-Line Positivity Theorem": a₃,±(ν)>0 for all ν≥10⁻⁴ — the first time an entire segment of the positive-viscosity parameter line, rather than scattered sample points, has been elevated to a theorem, ruling out the full second-order analytic hidden remedy of the two √17 hidden source circles within this range. The gap narrows to the sole remaining singular thin band 0<ν<10⁻⁴ (STOP-C68), left for the next round to bridge the endpoint to 10⁻⁴; this round includes numerical verification scripts and CSV data.