A tree interpretation of arc standard dependency derivation

We show that arc-standard derivations for projective dependency trees determine a unique ordered tree representation with surface-contiguous yields and stable lexical anchoring. Each \textsc{shift}, \textsc{leftarc}, and \textsc{rightarc} transition corresponds to a deterministic tree update, and the resulting hierarchical object uniquely determines the original dependency arcs. We further show that this representation characterizes projectivity: a single-headed dependency tree admits such a contiguous ordered representation if and only if it is projective. The proposal is derivational rather than convertive. It interprets arc-standard transition sequences directly as ordered tree construction, rather than transforming a completed dependency graph into a phrase-structure output. For non-projective inputs, the same interpretation can be used in practice via pseudo-projective lifting before derivation and inverse decoding after recovery. A proof-of-concept implementation in a standard neural transition-based parser shows that the mapped derivations are executable and support stable dependency recovery.