Recoverability Relations Without a Global Recoverer: A Strong-Field Decoding-Relation Specification and the Missing-Leg Finding

A classification of the (e5) recoverability question and its candidate class, not a certification of any recovery. Paper 61 typed a seat for "recoverability from horizon or static-patch degrees of freedom" and answered nothing — it kept the clause [record]-and-open, registering that the seat "would require a declared algebra of those degrees, a decoding relation, and a provenance/warrant condition; none is supplied here." Paper 71's Strong-Field Completion Charter locked the constructive successor — panel P-D, this paper — under its element-6 hard lock (owner-approved, verbatim): "P-D is locked unless a named decoding-relation candidate exists at its theme time; absent that, P-D publishes the missing-leg finding — an honest scoped/killed landing, never a silently solved gap." This paper consumes that charter unmodified and adjudicates the lock. The adjudication is against a content criterion. A DecRelCand — a named decoding-relation candidate — is any object declaring a map from an algebra of horizon or static-patch degrees of freedom that recovers held records from it (an admissible one, DecRelSpec, adds compatibility with Paper 61's ledger). An audit of the declared challenge set of recovery/decoding-map structures in the ALAC corpus and the cited strong-field literature — general and holographic quantum error correction, entanglement-wedge reconstruction, Hayden-Preskill decoding, islands / quantum extremal surfaces, the static-patch algebra, the corpus accounting-layer decoders, Paper 60's already-barred global-purification decoder, the general recovery formalism, and the Gate-VII rubric — refutes each by a named field: wrong domain, wrong codomain, barred evaporation/holographic physics, or an algebra supplied with no decoding map. The candidate set is therefore empty at this paper's theme time. The (e5) recoverability-relation declared class is uninhabited, and P-D publishes the missing-leg finding: CompletionStatus(recoverability relation) = killed via K0 — the decoding leg registered absent, never solved. Certified is structurally unreachable (the operative leg is absent); scoped is definitionally unreachable (no recoverability-relation instance is constructed). Forgetting the machinery returns Paper 61's registered ledger classification exactly. The leg reopens iff a decoding candidate arrives; the finding never enters P-C2. No endpoint physics; nothing adopted, calibrated, or scored. The pivotal near-miss is the static-patch / de Sitter observer algebra (Chandrasekaran-Longo-Penington-Witten 2023; Chandrasekaran-Penington-Witten 2023; Witten 2022): a genuine declared algebra of the very degrees of freedom the (e5) seat names — but it supplies no decoding map recovering Paper 61's held records, so a leg-1 algebra without a leg-2 map is not a decoding-relation candidate. Possessing an algebra of observables, or a state/evaluation functional on it, is not yet a decoding relation in the present sense. The foil retired is the Global Recoverer — the authority that would grant strong-field recoverability by default, the decoding step assumed rather than exhibited — retired preemptively as a guard against a future overread, since the corpus does not currently overclaim: Paper 05 marks recoverability conjectural, Paper 61 keeps the clause [record]-and-open, and Paper 60 already displayed and barred the one global decoder it named.