Goal-Relative Assurance of Dynamically Generated Execution Traces

Robert Betts, Martyn Riley, and Jamie Riley-Betts · Riley Betts Ltd

When an agent builds the path, assurance cannot mean “the approved process was followed.” The claim is that this trace meets this goal relative to this boundary, and that the boundary covers the floor the institution required.

This page is the abstract. The PDF is the paper. Terms are in the glossary.

Abstract

Traditional process assurance obtains much of its tractability from process invariance. A process is specified, approved and repeatedly executed against different cases. Individual cases may introduce different facts, evidence, exceptions and dependencies, but the process itself remains substantially stable. Assurance can therefore focus on whether an execution conformed to an approved process and whether the assumptions surrounding that execution were satisfied.

Agentic orchestration changes this structure. For consequential processes, such as regulated client onboarding, both the execution trace and the assumptions on which its acceptance depends may vary from instance to instance. An agent may select evidence, tools, branches, ordering, repetitions, escalations and external dependencies dynamically. The assurance problem can therefore no longer be expressed adequately as proof that a fixed process was followed.

This paper develops a goal-relative formulation. Let G_a denote the governing goal for cases of type a, x_i the actual execution trace for instance i, and A_i the assumptions and dependencies materially associated with that execution. The claim P(G_a, x_i | A_i) states that there is an acceptable proof or evidentiary object establishing that execution x_i satisfies G_a relative to the execution boundary A_i. That is not the proof inside discharge. This alone is insufficient. A proof can be valid relative to its declared boundary while that boundary omits assumptions that governance requires for the goal. We therefore distinguish a mandatory goal-assurance floor A_G, an instance-specific proof-support set A_g^i, and the actual execution boundary A_i. Write:

A_g^i ⊨ A_G

when the instance-specific proof-support set satisfies the mandatory assurance floor. Hygiene is separate:

A_g^i ⊆ A_i

Boundary Sufficiency requires both:

A_g^i ⊨ A_G ∧ P(G_a, x_i | A_g^i)

Discharge is stricter. It holds only if those hold, the remaining residue is acceptable under the governing policy, and:

A_g^i ⊆ A_i

Residual trust is consequently goal-relative. R(A_g^i) is the residue of the proof-support set. R(A_i) is the residue of the execution boundary. From A_g^i ⊆ A_i it does not follow that R(A_g^i) ⊆ R(A_i). A valid proof does not empty R(A_g^i). P(G_a, x_i | A_g^i) does not entail R(A_g^i) = ∅. The local-discharge conjunct of Betts (2026), ¬Need(T, x | A), is not restated here, because the execution is not a member of the support. In agentic systems the execution can itself introduce, replace or discharge assumptions, making the proof boundary partly endogenous to the execution. The governed object is therefore not a process definition but an instance-specific assurance model connecting goal, execution, proof support, execution boundary and residual trust. The paper does not claim runtime assurance, goal-oriented specification, dynamic assurance, proof-carrying artefacts, or residual trusted assumptions as new. The contribution is a formally checked goal-relative assurance model for dynamically generated consequential execution. Discharge holds only if proof validity, floor satisfaction, residual-trust acceptability, and boundary hygiene all hold. The first three are distinct. Hygiene is a further conjunct of that only-if. A run may partly construct the boundary against which it is later accepted. That situation is set out in §§12–15. The companion development does not define the boundary as a result of the execution. It machine-checks the model's central identities and supplies countermodels for the claimed non-entailments.

Keywords: goal-relative assurance; agentic orchestration; proof boundary; trust residue; process assurance; governance; formal verification; machine-checked metatheory