Nous: Learning and Certifying Memory Decisions Before Source Calibration

Successful agent execution need not identify which future product improvement its user would value. We present a decision-specific audit that maps a declared observation channel and product-value contrast to compatible intervals and witness populations. Its foundations are established identification and decision theory; the contribution is an executable measurement workflow and a controlled study of its limits. A frozen experiment makes 4,800 requests to two pinned model snapshots on shared synthetic tasks. All 36 conservative primary intervals remain unresolved despite different execution accuracy. An exploratory 2,400-call follow-up records supplied preferences and resolves three of nine comparisons per model. A deterministic extractor resolves seven of nine without model calls or calibration observations, exposing unnecessary uncertainty introduced by model-generated reports. A further 14,400 controlled multinomial simulations distinguish structural ambiguity from weak identification and finite calibration precision. We propose a source-labeled decision receipt and provide an offline viewer for inspecting the audit. These results motivate preserving decision-relevant structured input and diagnosing why a decision is unresolved before collecting more telemetry. The study contains no human participants or real customer outcomes. Full proofs, raw model provenance, controlled experiments, and reproducible analyses accompany the report.

Agents that act on a compressed representation of their history face a structural risk: if the representation aliases histories with different optimal actions, no rule measurable with respect to the representation can avoid an irreducible per-round loss, and the agent may be unable to detect this from its own transcript. This paper develops a four-layer theory of self-certification of representation adequacy. The static layer defines decision-theoretic adequacy through a Bayes-risk grouping identity and prices a one-shot external verification by an exact total-variation threshold. The sequential layer poses certification as an optimal-stopping problem in the currency of task loss: we define an environment-wise certification complexity constant through a covering linear program, prove an information-task-loss lower bound for every delta-correct strategy, and give a Certification Track-and-Stop policy whose cost matches the bound asymptotically. A final boundary layer gives an explicit kernel-switching example and identifies the open theorem needed to cover policy switching or representation repair; it does not claim that the fixed-kernel guarantees extend to representation revision. The proofs of the two main theorems are given in full in the appendices.

When many reinforcement-learning policies achieve near-optimal return, a post-hoc auditor may have to distinguish among many behaviorally distinct but return-equivalent policies. We formalize this phenomenon through an occupancy-measure analogue of Rashomon capacity: the metric entropy of the near-optimal occupancy region, computed relative to an audited deployment class. Because occupancy measures identify behavior only up to occupancy equivalence, we formulate auditing at the occupancy-class level and distinguish exact local-query oracles from noisy sample-query oracles. Our main exact-query result is conditional: if the audited class contains a $2/H$-separated near-optimal packing whose local signatures are $b$-sparse, then exact local-query auditing requires $Ω(M/b)$ queries; when the packing realizes deployment-class capacity and $b=O(1)$, this becomes $Ω(2^{\Hopt^\cF(\eps)})$. We give a finite discounted hidden-branch MDP attaining this bound and show the exact Bayes success law. For noisy hidden-trigger testing, we prove a mixture lower bound of order $M/β$, where $β$ is the per-sample KL signal, yielding $Ω(2^{\Hopt^\cF(\eps)}/(ρ^2Δ^2))$ for capacity-order packings with $β=O(ρ^2Δ^2)$. We also provide a static target-recognition information lower bound, a transcript-compatible oracle-cover verification upper bound, and a canonical occupancy regularizer whose regularized audited capacity collapses when a trusted reference occupancy is available. Controlled benchmarks distinguish positive sparse-signature instances from high-capacity negative controls where exact auditing is easy, and map the noisy-trigger law to post-processed continuous-control and visual-RL auditing regimes.