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 typed
operator defined only on closure outputs. Two closure targets are distinguished. (i)
Clausal NOT applies after predicational closure, selecting CLAUSE[t] (propositional
content) and yielding clausal negation in the auxiliary/do-support system. (ii) Constituent
NOT is a determiner-like operator Det_syn whose selectional domain is NP_syn, the
class of role-licensed nominal candidates (subject/object/topic), independent of lexical
headedness. The central claim is a closure gate: nominal potential is a necessary
prerequisite for syntactic role-closure, and NP_syn is the closure output. Therefore, if an
expression cannot be admitted as NP_syn in object-language (OBJ) conditions, NOT_syn
lacks a well-typed input and is undefined; any apparent 'not X' acceptability requires
metalinguistic (META) head insertion that shifts the target. We then integrate this gate
into a morphodynamic program: closed syntax is modeled as a potential well whose
boundary conditions predict where NOT is stable, where it drifts between clausal and
constituent sites, and where judgments become gradient. We provide (a) a fixed
environment inventory for NP_syn admission, (b) a boxed undefinedness theorem with
worked OBJ failure vs META repair derivations, (c) an external corpus slice with
heuristic complement-typing, and (d) morphodynamic proxies β (boundary strength)