Quasi-Local Horizon Predicates Without a Global Teleologist: Certification-Structure Classification of the Horizon Predicate, the Quasi-Local Typology, and the Teleology-Dependence Kill

A classification of the horizon predicate's certification structure, not a certification of any horizon. Paper 60 typed the event-horizon predicate — "there is an event horizon" — as adopted classification data ([typed]), not a patch-certifiable fact, because the event horizon is defined through future null infinity (Wald 1984): teleological, global by type. It named the constructive successor and seated it at (f5): "certifying boundary data from patch-side physics (quasi-local horizon notions and their record-theoretic standing) — a program of its own." This paper is that seat — panel P-C1 of the Twentieth Grouping, whose charter Paper 71 fixed. It takes up the predicate half at the one grade the charter allows it: classification only, no endpoint physics. The single deliverable, disambiguated up front, is certification-structure classification, not predicate-truth certification. Paper 60's horizon-access account and its two-part exterior-deformation test are instantiated on a patch-side record-tube class declared from local geometry — a foliation, a candidate closed two-surface, its null normals and expansions, the accessible metric, and a bounded accessible search region — without presupposing horizonhood, with future null infinity and the global-future development explicitly barred. Over a finite declared predicate language L-hz = {trapped surface, marginally outer trapped surface (MOTS), trapping horizon, isolated horizon, dynamical horizon, event horizon}, each predicate is read in two declared modes (evaluation on a declared surface, existence over the accessible search region under a selector), and its certification structure is typed [record]/[classified]/[typed] by whether it, together with its finite-grammar slicing-selector, factors through the accessible-side data under the deformation test. The typology is sharp on the physics. The event-horizon predicate moves under a global-future deformation — exhibited by a matched pair of completions agreeing on the accessible data and differing only in a later Vaidya-type infall beyond the boundary — and stays [typed]: the teleology cell, recovered from Paper 60 exactly, not repaired. The one-slice evaluation predicates (trapped, MOTS) read only local surface data and are [classified]. The existence predicates and the tube-level predicates (trapping, isolated, dynamical horizon) are [classified] as conditional schemas — only under an admissible patch-local selector from a finite selector grammar, with accessible boundary data where the slicing needs them; a global selector routes the cell back to [typed]. The honest kill is K3-teleology, two-fold: predicate-level (the predicate reads infinity) or selector-level (the predicate is local but its slicing-selector reads infinity). The apparent horizon — the outermost MOTS on a slice — is not a one-slice predicate; it is selector-dependent and never shares the MOTS cell. The verdict is CompletionStatus(quasi-local horizon predicate) = scoped: at least one non-event-horizon predicate is [classified] with a [classified] selector, so the Teleologist is retired on that predicate — while the event-horizon predicate stays [typed], K3-teleology is live throughout, and certified is structurally unreachable (predicate-truth certification is near-horizon strong-field work, out of classification grade). Forgetting the machinery returns Paper 60's registered classification, including the teleology cell, exactly. No endpoint, interior, strong-field, or horizon-thermodynamics sentence carries a verdict; nothing is adopted, calibrated, or scored. The Teleologist is retired on the classified predicates, and nowhere claimed beyond them. The imported horizon notions enter as kinematic definitions only, never adjudicated as physics: the event horizon (Wald 1984); the trapped and marginal surfaces (Hawking and Ellis 1973); the trapping horizon (Hayward 1994); the isolated and dynamical horizons (Ashtekar and Krishnan 2004, whose conditions are used at the level needed for certification-structure typing, not a full reconstruction of the isolated-horizon formalism). Structural independence (charter element 8): Papers 71/72 and the 69/70 inboxes are not consumed; Paper 69's F5 quasi-local-horizon row is non-parent context (a support-functor source with patch-certifiability deferred under its M5 guard).