The N+1 Unknown Executor Problem
Distributed execution is not a sequence of positions. It is a sequence of causal steps across time.
A workload does not exist because it is next in a list. It exists because it was provisioned at a specific moment, in response to a specific event. It becomes an executor in an authority propagation only if it can securely carry that authority forward as a valid continuation of the execution chain.
When Workload n receives a message at time x, Workload n+1 is provisioned at time x + y, where y is a positive offset. The gap is real: the downstream executor does not exist yet when the upstream executor acts.
This is the N+1 unknown executor problem: authority must reach a successor that is not yet known, selected, or provisioned when the predecessor acts. Pre-binding authority to the holder, key, or channel of an unknown successor is therefore not always possible.
This has three consequences:
- Authority flows from origin — never re-created: within a chain, there is no moment where a new workload can bootstrap its own authority. Authority must arrive causally from what came before.
- Every hop must prove continuity, not possession: holding a token is not enough. The workload must demonstrate it is a valid continuation of the execution chain.
- Execution is temporal and causal, not positional: the chain is defined by what happened and when — not by topology or configuration.
This is why possession-based models are incomplete for distributed execution. They assume the chain is synchronous and positional. It is not.
The Canonical Execution Model
This problem is categorized by the Canonical Execution Model: execution as a causal chain in which each executor may come into existence only after its predecessor has acted. A system that claims to satisfy authority propagation MUST be designed and tested against the canonical execution model — if it works only when the whole chain is known in advance, it does not solve authority propagation.
Authority Continuity
PIC defines three invariants that must hold at every execution hop:
- Provenance: the causal chain is always traceable from origin to current state, unbroken.
- Identity: the origin principal
p₀is immutable throughout the chain. - Continuity: authority can only decrease at each hop. It never expands.
To uphold these invariants, every executor must prove — through a Proof of Relationship (PoR) — that its step is part of the temporal execution of that authority propagation: single-hop evidence binding it to its immediate predecessor. Composed transitively, these relationships form a Proof of Continuity (PoC), which preserves the formal model's monotonicity over both the operations and the execution characteristics. Relationship is local; continuity is global.
Under these invariants, authority cannot be re-created mid-chain, cannot escape its origin, and cannot expand across any dimension. The confused deputy problem becomes structurally inexpressible — not mitigated, but impossible by construction.