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

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. The companion Paper B, Anomalous Dissipation and the Turbulent Cascade: A Variational Free-Energy Derivation of Kolmogorov Scaling, is published under the existing Turbulence/Skeleton concept DOI 10.5281/zenodo.19056813. Paper B treats the conditional Downhill Flux / NLw / ND route to anomalous dissipation. The two papers share the same turbulence programme but have separate DOI lines: Paper A is the unconditional K41 theorem; Paper B is the conditional cascade/anomalous-dissipation route. The FST Hub / master overview is maintained under concept DOI 10.5281/zenodo.20130499. Public sources and computational artefacts are mirrored in the GitHub repository research-line/functional-stability-theory/fst-physics/k41-variational-minimiser. Files K41_Variational_Minimiser_v1_en.pdf -- English version. K41_Variational_Minimiser_v1_de.pdf -- German version. K41_Variational_Minimiser_v1_kombi.pdf -- combined English/German PDF. Status Advanced preprint. Subject to revision before journal submission.