Grounding and Obstruction: Explanatory Edge in Higher-Order Metaphysics

Grounding in higher-order metaphysics raises a transcendental question: what must be in place for complete explanation to be possible at all? Our central claim is that polynomial-functor reconstruction gives the right native language for that question. Grounding doctrines can be presented so that candidate dependence architectures become concrete local shapes, unresolved demands become positions, and success or failure is read off from whether local data collapse to a least admissible completion class or stabilize at an explanatory boundary. Working in a finitary typed fragment, this paper proves four bridge results. First, finitary grounding doctrines admit a burden-normal polynomial presentation. Second, strict grounding is characterized classwise by globally unique refinement-stable completion, stable discharge of all burden-families, and vanishing explanatory residue; in class-realizing doctrines this yields a presentation-initial core. Third, unrestricted operator-return principles force non-liftability and therefore block strict collapse. Fourth, when collapse fails but visible burdens stabilize, the surviving edge factors canonically through, and under eventual realization is identified with, the explanatory one-hole boundary rather than treated as a metaphorical shadow. The final payoff is positive as well as negative. In the upwards-essence case, a recurrent unresolved direction burden can re-enter as a higher-order explanandum and generate a stable, character-detectable invariant on the explanatory boundary. The result is not just a failure theory for grounding, but an account of how transcendental argument operates inside higher-order metaphysics.