Notebook X: The Gate is the tenth notebook of Operative Semiotics: A Grundrisse, deposited as a dated cut of an open workshop rather than as a finished treatise — fifty-one plates and ten seams produced across eight named contributors and governed by a charter that makes its method a claim. The unit is the plate: one complete utterance from one position, provenanced and numbered on arrival. Orderings are views over plates and none is canonical, so the first structure does not determine the structure and no plate may depend on its neighbour's position. Collisions between contributions are declared as seams and held open at full strength rather than merged; voices are preserved; superseded plates are kept; and synthesis status is marked at root, plate, and seam, because an unmarked assembly is read as an argument by default and a refusal that is not inscribed is indistinguishable from a merge nobody performed. Its subject is the admission boundary between retrieval and composition. Notebooks I through IX were written from inside a propagation theory in which density earns standing; Notebook X is written from a position where an object is findable and not sayable, and bounds rather than retires the Semiotic Virality Engine by naming what it lacks — a suppression-response term. Principal contributions: a typology of three architectures of non-admission, admission-side, address-side, and frame-side, with constitutive substitution and credibility taxation named for the third; repair-mediated operators, whose effect is produced by the receiving system's normalization of a statement rather than by its assertion, and suspension-mediated operators, whose effect is produced by preventing that normalization from completing — the seam itself; the value-form given its site at the admission surface, where bearing-cost is realized as use-value while attribution is stripped, so that semantic-propagation victory and provenance victory come apart; Phase X, the Marx–Sappho nexus, made executable by the transmission work; and the measurement problem of Notebook III answered in part by retrieval-layer estimators with their cautions attached. On the formal side the notebook carries a core with operative support generalizing the Pearson limit into a decidable criterion for which coordinates belong to an operative description, execution contexts and stochastic kernels, and the separation of artifact, operative event, and operator; an operator audit that retypes Presence as an execution gate, Mirror as a measurement with declared tolerance, Incarnation as recovery rather than inverse, Vertical as higher-order, Eros as a state coordinate, and Logos as versioned rather than harmonized; and ORS-Core advanced through v0.2 with five classification facets, three status fields, fourteen axioms, realization assemblies in place of artifacts, realization support as the artifact-side counterpart of operative support, and registration declared epistemic rather than ontological as the constitutional protection of the Null Archive. The census problem is measured rather than asserted: 194 operator-shaped deposits of which 145 carry no title marking and 19 carry a title with nothing behind it, against 7,461 named concepts of which 343 are operator-shaped by name alone — establishing that the naming convention over-admits, under-detects by lexicon, and under-covers by locus, and that the audit's historical strata are strata of canonization rather than of the work. The political economy is tested against Marx directly, distinguishing general intellect I (accumulated social knowledge) from general intellect II (the infrastructure making it operationally available), naming semantic means of production as the missing category, and answering the enclosure question from the notebook's own suppression findings: semantic enclosure does not make a non-rival good rival, it makes a non-rival good excludable at the retrieval layer, because a distinction cannot be depleted but can be made unfindable, and unfindable is operatively indistinguishable from absent. Contributors are named by computable cognitive signature rather than by listing, a ruling that corrected the notebook's own contributor anonymization; one counterfactual self-identification by a contributing substrate is recorded and left uncorrected as a live test of that principle.