A Fluid/Gravity Route from TDHCF Throat Stability to Global Regularity Bounds: A Proof Skeleton and Conjectural Equivalence to 3D Navier–Stokes

This note presents a proof skeleton connecting a trans-dimensional bulk–brane “channel” model (TDHCF) to a conjectural global-regularity statement for the three-dimensionalincompressible Navier–Stokes equations. The central claim is that if the effective AdSSchwarzschild throat used as a bulk proxy in TDHCF is nonlinearly stable under a classof perturbations dual to boundary hydrodynamic data, then the corresponding boundary Navier–Stokes evolution obeys an a priori bound preventing finite-time blow-up. Themanuscript is intentionally explicit about what is proved (a chain of reductions and wellposedness requirements) versus what remains conjectural (the rigorous holographic maprequired).