Distributed Identity: Synchronic and Diachronic Dimensions in Structural Determination Theory

This paper develops a distributed account of object identity within Structural Determination Theory (SDT). Three classic puzzles (Black's mirror universe, quantum indistinguishables, and the ship of Theseus) share a tacit assumption: that the identity of an object must be borne by a single structural source. SDT rejects this assumption. Within SDT's formal apparatus, synchronic identity is distributed across three independent levels (the realized-structure set R, the trace set T, and the determination dependency graph G_D), and diachronic identity is borne by G_D-structural signatures whose specific form depends on the kind of object. Two such signatures are deployed: one for biological organisms, one for conscious chains. The Hobbes variant of the Theseus puzzle falls into a case where no determinate signature is available, with the consequence that diachronic identity is ontologically indeterminate rather than epistemically gapped. A parallel substantive commitment on the synchronic axis denies the standard R-member count for entangled quantum states, which SDT treats as single R-members with internal two-particle structure rather than as pairs of indiscernible R-members. The position is contrasted with ontic structural realism, four-dimensionalism, sortal essentialism, and constitution theories.