Woodins Ultimate L Conjecture for Supercompact Cardinals

Assuming delta is an extendible cardinal, prove that there is an inner model N contained in HOD such that N is a weak extender model for the supercompactness of delta and N satisfies V=Ultimate-L.

Source: Bagaria and Ternullo, Steel's Programme: Evidential Framework, the Core and Ultimate-L, Review of Symbolic Logic (2021), Conjecture 5.2..

Status Open Ultimate-L remains provisionally open with a formulation/consistency warning. The exacting-cardinal obstruction is conditional, not an unconditional disproof. Woodin's August 26, 2026 formulation remains conjectural but differs from the stated weak-extender-inside-HOD wording; equivalence requires specialist adjudication. The unrefereed broad proof essay was not accepted. Status reviewed Sep 14, 2026

Listed by ProofAtlas. Status qualification is attributed to ProofAtlas; no full resolution is certified here.