The K41 Spectrum as the Unique Variational Minimiser of a Scale-Resolved Free Energy

DRAFT version. This advanced preprint remains subject to revision before journal submission. This preprint is Paper A in the turbulence split of the Functional Stability Theory programme. It isolates the unconditional variational result: the Kolmogorov K41 energy spectrum is the unique global minimiser of a scale-resolved free-energy functional under joint minimisation over energy profiles and admissible local flux closures subject to constant scale-to-scale flux. Version 1.2 is a maintenance and proof/paper-synchronisation release. It corrects the shell-Hessian scaling language, weakens the local UCU3 constant to a ratio-dependent positive constant, and states the bridge to companion Paper B as conditional on…