Articles and Infinitival to as Typed Closure Gates: A Two‑Level Grammar with OBJ/META Regimes, HTSA/HTCA Wells, and Testable Falsifiers

This paper extends the English ghost-system program from phonology (Y-trajectory nuclei;CH-trajectory consonants, etc.) into morphosyntax by treating the articles the/a/an and theinfinitival marker to (verbal article) as typed closure gates – partial , well-defined operators thatapply only to independently admitted bases and return closed, hostable objects (NP_syn andPred_INF). The central claim is domain-restriction: D_art and TO_inf are not free-combiningfunction words but edge-licensed constructors whose definedness is strictly limited toclosure-ready inputs. This yields a two-level grammar with a regime discipline: in OBJ,mention-heads and quotation are prohibited, forcing undefinedness for hard classes (the frankly,to frankly); in META, mention-constructors create admissible targets, producing systematictarget-shift repairs.We formalize the architecture with (i) a typed operator inventory, (ii) a Head–Tail ContainerArchitecture (HTCA) that locates closure sites on well-licensed edges, and (iii) aRED/DED-based diagnostic battery that separates independent admission (HOST + RED/DED)from the behavior of the closure gates themselves, eliminating definitional circularity. A workedderivation panel demonstrates OBJ failure vs META repair, and a falsifier list makes theproposal empirically vulnerable rather than metaphorical.Finally, we provide a preregisterable gate-signature experiment (48 critical / 48 filler items,full analysis scripts) and an external UD-EWT corpus slice with uncertainty-boundedclosure-rate estimates. The result is a unified, testable account in which articles, infinitival to(verbal article), and phonological ghost connectors (Y, CH) fall under a single typedclosure-gate ontology, predicting where unithood, undefinedness, and META-licensed rescuemust cluster