Message Passing Without Temporal Direction: Constraint Semantics and the FITO Category Mistake
Paul Borrill
TL;DR
It is argued that conventional message systems embed a category mistake: they misinterpret logical dependency relations as temporal propagation processes and prove an equivalence theorem: under mild assumptions, a broad class of message-passing executions can be represented as constraint satisfaction problems, and conversely, constraint satisfaction instances can be realized as message-passing protocols.
Abstract
Message passing is widely assumed to be a fundamental primitive of distributed systems. This paper argues that conventional message systems embed a category mistake: they misinterpret logical dependency relations as temporal propagation processes. This error arises from an implicit Forward-In-Time-Only (FITO) assumption, which treats causality as intrinsically directed along a temporal axis. We formalize FITO as the imposition of a partial order over events and show that clocks, scheduling, and message propagation are representational artifacts rather than ontological primitives. We then reformulate interaction in terms of symmetric constraint relations, identify the minimal substrate of interaction independent of temporal direction, and prove an equivalence theorem: under mild assumptions, a broad class of message-passing executions can be represented as constraint satisfaction problems, and conversely, constraint satisfaction instances can be realized as message-passing protocols. We connect the result to Lamport clocks, Hewitt actors, Pratt pomsets, category theory, relativity, and indefinite causal order, and interpret engineering consequences for reflective and reversible link architectures such as Open Atomic Ethernet.