Papers 61–62 exclude all same-level and ghostly grounding candidates: ghosts (Paper 61), syntax, object-level semantics, equal-status externality, and self-actualizing ledger (Paper 62). Paper 63 proves that actuality requires ground (Theorem 63. 0) from the no-free-bits machinery (Papers 27, 61): ungrounded actuality would be a determinacy-relevant free bit at the ontological level. From this we derive the Alpha theorem: if nontrivial reflexive reality exists, then there must exist a necessary pre-categorial ontological ground of its actuality. We call this ground Alpha. The library in reflexive-closure-lean is 0 sorry, 0 custom axioms at the suite norm for that library. Trust boundary. "Alpha" here is the formal role from the squeeze—not an imported religious or contemplative label in theorem statements. See.
Nova Spivack (2026) studied this question.