Definition. Session lineage tree [ftip-00CG]
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    A session lineage tree is a finite rooted directed tree \(\mathcal T=(V,E,r)\) whose edges point from a parent session to a directly spawned descendant. Each node \(v\in V\) carries an immutable session identifier, its resolved harness and inference stamps, a local event stream, and a local realized cost \(c_v\in \mathbb R_+^m\).

    For a node \(v\), let \(\mathcal T_v\) be the induced subtree containing \(v\) and all its descendants. Distinct children of one node have disjoint node sets. Messages between branches are events in their local streams and do not merge their identities or costs.