Strategies for Discharging the Log-Derivative Condition

Research Note 49 in the "Geometry of the Critical Line" programme. This note provides a systematic classification of the analytic obstructions to the log-derivative condition that arose during the Paper 48 phase, when the programme temporarily framed the endgame as a logarithmic-derivative condition for the completed SCT spectral zeta. That framing was later abandoned (Kill #79), but the route analysis remains useful as a retrospective map of the strategies explored and of the genuine analytic bottlenecks they exposed. Eight approaches are analysed with precise theorems needed, specific references, and honest viability assessments. Two approaches were identified as most immediately testable: the Mellin coefficient computation and the Evans trace-formula route. The Evans route was later ruled out (Kill #78). Three further approaches are viable with moderate additional work; three are obstructed. The synthesis identifies the true analytic bottleneck: the distributional quotient trace and the sub-leading Weyl correction.