AIM Framework glossary
Non-Commutativity Propagation (N3)
Canonical definition
Canonical-definition layer: The network-layer axiom restatement establishing that the order-dependence of Belief updating within a single Individual entails path-dependence of collective Belief trajectories at the population scale. When the coupling strength between Individuals () is sufficiently large, the order in which an Individual receives Evidence from different network neighbours affects the Belief Register non-trivially, because the updating contexts associated with different neighbours do not combine in a sequence-neutral way. Two Individuals receiving identical sets of Evidence propositions in different orders arrive at different Belief Registers. Across a network, this means that the collective Belief state of a population reflects the sequence and coupling structure of Evidence flows, not only their content. Path-dependence of population Belief trajectories is the expected regime of the coupled network system rather than a pathological special case. See Appendix A.5.7.2 for the full restatement and derivation.
Explanation
The order in which Evidence reaches an Individual changes the Beliefs the Individual arrives at, not merely the speed of arrival. When this effect propagates across a network of Individuals, each updating on conclusions expressed by neighbours whose own conclusions were shaped by sequence, the population's collective Beliefs become a record of how information flowed as much as what information was available. Institutional arrangements that govern the sequence and coupling structure of Evidence flows are therefore architecturally consequential, not merely procedurally important.
Epistemic status
Framework-Specific Construct.
Derivation
Appendix A, Section A.5.7.2; Chapter 13, Section 13.4.7; Chapter 14, Section 14.6.2.
Also in the entry
Source: Appendix A.5.7.2.