Non-Markovianity Certification under No-Meta Obligations for Agents

Non-Markovianity certification for agents under no-meta obligations: audit-ready, fail-closed, ledger-only evidence.Anytime-valid e-process / e-value tests safe under optional stopping, built from committed telemetry contracts.Operational Markov order is defined relative to logged interfaces (pre/post fields), not hidden internal state. This work specifies a protocol-level standard for certifying (or rejecting) non-Markovianity claims in open, partially observed, and adversarially operated systems. The verifier is constrained to commit-before-observe telemetry and declared, replayable artifacts (no privileged sensors, no hidden reward channels, no meta-observer). Evidence is produced via anytime-valid e-processes (test martingales / e-values), enabling continuous monitoring without invalidating error control under optional stopping. Four certificate families are defined: (A) prequential declared-model compliance via sequential likelihood ratios; (AU) constructive memory witnesses via forecast competition between an order-L baseline and a declared memory-augmented predictor under explicit memory/compute budgets; (B) matched-context dual-run witnesses with verifiable sign/label randomization; and (BU) randomize-after-start segments that separate start acquisition from randomized evaluation to avoid selection bias. Auditability is enforced by deterministic canonical serialization, hash-chained ledgers, explicit matching requirements including probe-time pre-fields, tombstone accounting for missingness/censoring, and optional transparency-log publication for third-party verification.