The Atemporal AIEN Postulate
Causal semantics without clocks: an AIEN computation is defined by what causally depends on what, not by when those events occur.
Abstract
I propose that an AIEN computation is defined by what causally depends on what, not by when those events occur. Physical time characterizes a realization of the computation; it does not define the computation itself. The postulate has five parts: atemporal semantics, causal order as a strict partial order, immutable causal past, causal-cone admissibility, and schedule invariance.
The central correction: the Crumbline's "append-only" rule becomes causal immutability, not chronological order. The Crumbline is not a timeline; it is a causal record. The paper formalizes admissible extension of the causal graph, states the compiler theorem in both directions (every valid physical schedule preserving the graph realizes the same Omega computation), and specifies the schedule-invariance experiment that would test it. Postulate paper, v1.0; not peer reviewed; the experiment is specified, not run. Four independent reviews (three outside frontier models plus one programmatic check) were folded into v1.0; a fifth review (GPT-6 Astra) confirmed those repairs and found the remaining gaps, folded into this version: the Crumbline extension formalism now provably enforces causal-past immutability, schedule invariance is stated as a theorem with its hypotheses, semantic identity has a canonical definition, the experiment carries negative controls, and the novelty claim is argued against the concurrency literature.
Research artifacts
Cite
@misc{stapleton2026atemporal,
author = {M. Drake Stapleton},
title = {The Atemporal AIEN Postulate: Causal Semantics Without Clocks},
year = {2026},
month = {October},
version = {1.1},
note = {Postulate paper, not peer reviewed},
url = {https://aienos.com/research/atemporal-aien-postulate}
}