RFP-12: Dangerous-Core Realizability, Coercive-Intersection Analysis, and Standard PDE Recompilation

Dangerous-Core Realizability, Coercive-Intersection Analysis, and Standard PDE Recompilation

RFP-11 reduces any assumed finite-time singularity, under the shared theorem assumptions, to a path lying within the triple-action core 𝔯_danger=𝔇_RFP∩D_mid∩D_SV∩D_freq. This round asks: can this dangerous core be proven empty? Cycle I's answer: not with the inequalities established so far. Adds an approximate-Laplacian-eigenfunction coercive action, proves its exact L² spectral-variance formula; proves mid-strain critical intermittency forces UV strain intermittency beyond every fixed Fourier cutoff; proves two synchronization NO-GO results, showing action divergence alone does not force simultaneous dangerous geometry. Recompiles the rigorous Cycle I results into standard PDE language. The residual dangerous core is not proven empty; full chain necessity, finite obstruction, and Navier–Stokes regularity remain OPEN.