Beyond Proof of Possession: A Relational Theory of Authority

Proof-of-Possession (PoP) shows that an executor controls a key, token, or capability. It does not show which execution occurrence is being continued, nor in which causal history that authority remains valid. This paper separates PoP from Proof of Relationship (PoR) and from authorization itself, and moves the domain of authorization from holders and artifacts to execution occurrences situated in causal histories.

Building on Provenance Identity Continuity (PIC) and Proof-of-Continuity, it classifies executors by authorization-relevant equivalence relations, whose quotients form relational profile spaces. Positive predicates over profile transitions form a distributive lattice ordered by implication. This adds relational attenuation to authority attenuation: along one valid causal history, Cᵢ₊₁ ⊆ Cᵢ and ρᵢ₊₁ ⇒ ρᵢ. Causal history grows by prefix extension while authority and relational freedom shrink.

The paper proves dual monotonicity, combined closure, and origin relational closure; shows that the executor-dependent decision factors through the relational profile; and gives, conditional on explicit Witness Assumptions, a boundary-witnessed checkpoint construction that realizes the premises without successor-side PoP. Confused-deputy exclusion within a valid lineage follows from the continuity invariant; excluding request-caused effects presented outside it additionally requires complete mediation and causal attribution. An appendix maps a restricted subset of premises onto the open-source PIC-X implementation and states the gaps (https://github.com/ngallo/pic-model/tree/main/draft/0.1/pic-beyond-possession).