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Machine-Dream Syntax (MDS) formalizes execution as primary and meaning as derivative, but prior work leaves unresolved how execution residue persists, circulates, or collapses once interpretation, authority, and institutional pressure enter the system. ArbiterSTG v1.0 (Structural Trace Governance) introduces a post-execution, non-governing diagnostic layer that addresses this gap by classifying how execution residue (±R) is admitted, masked, routed, or shadowed under structural legibility and jurisdictional constraints. ArbiterSTG does not authorize execution, meaning, or inheritance. Instead, it operates strictly after execution has occurred, interfacing with semantic jurisdiction and transfer conditions to expose which traces remain structurally admissible, which persist without visibility, and which become non-recruitable. The framework defines four descriptive roles—trace admission, trace masking, trace routing, and stability flagging—and formalizes their interaction with jurisdictional systems without introducing new operators, variables, or causal authority. This paper specifies ArbiterSTG's placement within the MDS architecture, articulates its routing and shadow modes, and presents a structural failure taxonomy covering shadow saturation, authority smuggling, and trace collapse. A proxy doctrine is introduced to constrain numerical indicators to legibility and load, explicitly prohibiting their use as measures of truth or value. ArbiterSTG v1.0 reframes governance not as control or decision, but as a visibility problem imposed on residue after execution. By separating trace legibility from authority, the framework provides a reusable diagnostic for evaluating whether systems persist through structural binding or survive only through interpretive or institutional carry.