Full Provenance on the COSS Causal Axis: An Event-Level Closure of Causal Attribution and Confused-Deputy Exclusion

This paper continues the Provenance Identity Continuity (PIC) sequence and makes the causal execution occurrence itself primitive. Where the earlier models wrote an authority event as (o, r, ℓ) ∈ O × R × L, here a modeled run is one Lamport-style causal partial order (E, ≺c). Each occurrence has a unique causal history, so the consistent event-lineage space is canonically isomorphic to the occurrence set, and PIC's O × R × L is recovered as its authority-behavior projection. COSS generalizes the same construction by replacing the authority behavior with an arbitrary behavior product while retaining one causal execution. On this semantics the paper proves an architecture-independent confused-deputy exclusion theorem. Ordinary PIC continuation on every ordinary causal edge gives C(e′) ⊆ C(e), hence ancestor-bounded authority along any ordinary segment, and at a multi-source ordinary join C(e) ⊆ ⋂ C(p) over the immediate predecessors. Authority carried on only one incoming branch therefore cannot be silently resurrected at a join, even when the branches share a common root: same root does not imply same continuation. With protected-effect mediation, an accepted effect caused by a request and connected to it by an ordinary authority segment can exercise only authority present in the request's origin context, so the lineage-form confused-deputy condition is contradictory. Temporal delay does not break causal ancestry, and temporal proximity does not create it. The paper then revisits Rajani, Garg, and Rezk (CSF 2016). Their capability semantics blocks explicit designation but not value, control-flow, or initial-heap attacks; their full provenance semantics proves CDA-freedom with endorsement for their whole region calculus. From the causal view these attack classes are different witnesses of the same request-to-effect ancestry, and full provenance is a concrete evidence mechanism for recovering data and control edges of the causal graph rather than a premise of the PIC theorem. The construction is finally lifted to the COSS product of heterogeneous security-state coordinates, with Product Continuity, projection and factorization results, heterogeneous translations, and explicit authorized relaxation events. "Total" is model-relative and ordinary-segment-relative: the result covers every represented PIC lineage-form instance whose request/effect pair satisfies the ordinary continuation premise, not physical or covert channels outside the event model, nor executions crossing an explicitly authorized non-conservative transition. Causal completeness, sound causal evidence, complete protected-effect mediation, and explicit non-conservative transitions remain realization obligations (https://github.com/ngallo/pic-model/tree/main/draft/0.1/full-provenance-coss-causal).