Actions with Receipts: Jointly Binding Claims, Evidence, and Execution for Replayable Tool-Agent Auditing

Agent evaluations face two distinct evidentiary questions: whether a reported claim is recomputable from retained evidence (sufficiency), and whether the retained records cover the committed experiment set (coverage). Generic logs and hash-linked transcripts answer neither reliably. We introduce ClaimReceipt, a claim-relative receipt specification and selective verifier that binds typed transaction evidence to a signed experiment manifest and returns PASS, INVALID, or INCONCLUSIVE per claim. We freeze the specification before implementation (SHA-256 18d109...b81). On 1,392 historical buyer--seller records, a CR-2 verifier reproduces all five manually labeled audit verdicts, exactly replays 600 deterministic and 792 post-generation records, makes every one of 13 declared field groups non-redundant under tested ablations, and returns the expected result on 11/11 semantic faults with 0/8 false positives. We then run a separate prospective CR-3 epoch: 30 assignments are committed before inference, terminal receipts are signed and chained, and private evidence is encrypted for an auditor. Complete evidence yields coverage and accounting PASS; withholding one terminal receipt returns INCONCLUSIVE_COVERAGE, while withholding all private openings preserves coverage and protocol verification but makes economic claims inconclusive, exactly matching a preregistered prediction. Receipt instrumentation adds 0.021% of model-inference time and 9.9 KB per transaction. A specification-legibility probe indicates that our own frozen specification is not yet unambiguous to an independent reader. Claim verification therefore requires both claim-sufficient evidence and a committed universe against which omissions become visible.

Agent systems increasingly execute rather than advise. When an AI agent queries regulated data, invokes effectful tools, and mutates persistent state, correctness is not captured by whether a terminal output looks plausible. The operative questions are whether each step was authorized under a contract, whether the recorded history is tamper-evident, and whether the trajectory can be reconstructed deterministically. We formalize this as runtime proof of execution. An execution is a triple $x = (C, T, R)$: a contract $C$, an Execution Causal Event Stream (ECES) $T$, and a replay context $R$. A well-formedness predicate and five validator-checkable invariants form the PoE validity predicate. Five semantic guarantees describe authorization, path compliance, null effect on deny, history integrity, and replayability. We prove soundness under explicit cryptographic and deployment assumptions: any PPT adversary that produces a PoE-valid execution violating a semantic guarantee yields a signature forgery, a hash collision, or a quantified deployment-failure event. The Prime Execution Model (PEM) separates planning, enforcement, effect, and recordkeeping into distinct authority planes; a lemma reduces trace completeness to Effector-exclusive credentialing. An Execution Attestation Certificate is issued only when PoE = 1. In a single-node TypeScript prototype, PoE adds approximately 2.7 ms on a minimal flow and 4.4% overhead on concurrent batch workloads; a standard eight-event trace compresses to approximately 1.1 KB; injected Gateway-bypass and trace-mutation attacks are rejected. PoE does not replace consensus, TEEs, or zkVMs; it binds authorization, effect, history, and replay into a single runtime-checkable object so that governed execution becomes attestable under contract.

Matoi separates reusable consequence evidence from current execution authority and durable occurrence history. Its finite query-aware contract covers branches, ordered collections and negative lookups. A consumer reuses only its own checked evidence whose observations remain valid; signed requests, live grants, quota and uncertain outcomes remain separate obligations. Conditional correctness arguments distinguish locally serialized claims from nontransactional remote effects. Two studies strengthen cost attribution and domain evaluation. A 1,440-cell matched-wire study repeats 144 authored inputs. With compact input bytes identical, reuse reduces complete lifecycle cost by 3.49 percent in JS and 1.79 percent in Python. Combined representation/reuse reductions against full proof are 10.87 and 16.53 percent; five of twelve family intervals for the matched comparison cross one in each language. A prospectively frozen AgentDojo Banking mapping covers 5/16 user plans and 7/9 attack plans. Both governed strategies preserve five exact benign transfers and refuse 35 reused attack-plan/policy crosses. Pre-satisfied utility predicates are reported separately from completed work. These are original scripted synthetic tools, not autonomous agents or a real bank. Earlier studies retain cheaper protected-cache alternatives, policy-compatible phishing, provider duplication and post-claim revocation. Separate JS/Python consumers establish finite-profile interoperability within the same project; durable recovery rechecks evidence and retains uncertain reservations. The results support a bounded, auditable reuse and execution contract, not a new general incremental algorithm, arbitrary-tool closure, atomic third-party commitment or production superiority.