Ghost Collapse and Ledger Finality: Why Off-Ledger Being Is Either Illicit or Null Paper 61 of the NEMS Suite

The recursive-intelligence arc (Papers 56–60) establishes that what matters, what is known, and what affects structure must be semantically represented on-ledger. The remaining escape is: maybe there are real off-ledger entities—ghostly things not represented in the ledger. Paper 61 kills that move. We prove that any purported off-ledger entity is either determinacy-relevant (hence illicit under no-free-bits, Paper 27) or semantically inert (hence theory-null). No viable ontology of real-but-off-ledger ghost entities survives. Results are machine-checked in Lean 4 in the library of reflexive-closure-lean, with bridges to no-free-bits and. Trust boundary. The theorem targets ghost ontology (purported real-but-off-ledger entities), not every scientific use of "unobserved" structure. Hidden variables that affect adjudicatory structure must be ledger-relevant in the Paper 27 sense. See.