NOT as a Closure-Gate Operator over Nominal Potential (NP_syn): A Two-Level Grammar with Morphodynamic Field Parameterization

This article argues that English NOT has a constituent use that is best analyzed as a typedoperator defined only on closure outputs. Two closure targets are distinguished. (i)Clausal NOT applies after predicational closure, selecting CLAUSE[t] (propositionalcontent) and yielding clausal negation in the auxiliary/do-support system. (ii) ConstituentNOT is a determiner-like operator Det_syn whose selectional domain is NP_syn, theclass of role-licensed nominal candidates (subject/object/topic), independent of lexicalheadedness. The central claim is a closure gate: nominal potential is a necessaryprerequisite for syntactic role-closure, and NP_syn is the closure output. Therefore, if anexpression cannot be admitted as NP_syn in object-language (OBJ) conditions, NOT_synlacks a well-typed input and is undefined; any apparent 'not X' acceptability requiresmetalinguistic (META) head insertion that shifts the target. We then integrate this gateinto a morphodynamic program: closed syntax is modeled as a potential well whoseboundary conditions predict where NOT is stable, where it drifts between clausal andconstituent sites, and where judgments become gradient. We provide (a) a fixedenvironment inventory for NP_syn admission, (b) a boxed undefinedness theorem withworked OBJ failure vs META repair derivations, (c) an external corpus slice withheuristic complement-typing, and (d) morphodynamic proxies β (boundary strength)