Search for a command to run...
Operational Semantics of Participant-Indexed Computation This paper derives the operational semantics of Contextual Compute from the K-Machine's foundational requirement that WHO is a fundamental dimension of computation. We formalise the Participant-Interaction-Context (PIC) model: the three irreducible semantic primitives whose presence, and whose categorical structure, force a machine in which consensus, ordering, and finality are participant-anchored and context-scoped — dissolving the need for anonymous global state, network-wide ordering, and external agreement. Six axioms — Conservation, Consent, Linearity, Witness Sufficiency, Composability, and Commutativity — are shown to be necessary consequences of the K-Machine's structure. Together they define the PIC value category VPIC: a symmetric monoidal category without a diagonal morphism. Participant-indexed contextual state strictly subsumes anonymous global state. Classical computation is the degenerate case at WHO = 0. The paper introduces Network Objects as the first primitive designed for linear types at the network level, and closes with a derivation chain tracing each formal result to its categorical source. Companion papers:Value, Information, and the Cartesian Degeneracy (CC2, Zenodo, https://doi.org/10.5281/zenodo.19148907)Contextual Compute: The General Theory of Computation (CC3, Zenodo, https://doi.org/10.5281/zenodo.19177337)