Datasets:
Limits, counterexamples and non-claims
Structural restriction is real
Moment replay is exact for logits in a fixed vocabulary feature span, including an arbitrarily trainable backbone and trainable latent/span adapter. It is not exact for arbitrary future output heads. Affine transport handles checked changes in the same represented family; adding unrelated directions needs full historical q or new data. A frozen output basis tied to a trainable input embedding is not frozen in the required sense. The general full-q kernels support trainable/tied heads but do not obtain the moment-storage benefit. No nonlinear post-projection soft-cap or changing token identity is included in the moment theorem.
Capture must use the actual historical distribution, including any truncation/temperature used to sample, and retain correct contexts, rewards and complete-response masks. An action must have positive historical probability. Context IDs and version labels are caller contracts, not proof of correct collection. Marginal moment equality does not identify a causal environment or reconstruct a distribution.
Exact does not mean everything is free
The sequence objective head has O(NR) replay work after capture, but collection still generates tokens and traverses vocabulary probabilities, moment formation costs O(NVR), the feature bank uses O(VR) global storage, and the backbone/optimizer retain their own costs. Input-embedding gradients may themselves be vocabulary-sized. Record compression is favorable when V substantially exceeds R, and can be unfavorable for small vocabularies. Full-sequence algebraic cancellation does not remove the normalizer from the token objective.
The custom full-q kernels avoid retaining particular head activations. They still allocate working blocks and dense parameter gradients. They are first-order custom autograd paths, not general higher-order differentiation, distributed FSDP kernels or validated GPU kernels. The CPU recomputation fixture was slower, and the benchmark explicitly shows it. Chunk size, precision, architecture, bandwidth and hardware can change the tradeoff.
Conditional covariance is not task dominance
Independent equal-mass stratification improves the conditional auxiliary correction covariance at a fixed head and draw count. Safe head selection extends the chain to an equal-budget IID comparator. This does not order finite-run losses, rewards, exploration, total gradient covariance when coefficients are also random, sequence-residual products or wall-clock time. Sorting and CDF processing can cost more than the saved correction noise is worth. A single shared jitter across all strata does not have the independence proof and can be worse than IID; a counterexample is tested. Finite floating-point distributions approximate real-arithmetic identities, and extreme tails may trigger fallback.
Confidence gates can abstain and can be slow
Only registered bounded metrics are covered, conditional on fresh IID pairs, a fixed candidate and known valid bounds/error allowances. Unbounded real metrics require a different bound or an explicitly changed clipped objective. Repeated looks and attempts must use the persistent ledger; rolling it back or reusing the same holdout invalidates the guarantee. Zero tolerance on an exactly unchanged metric generally prevents finite-sample certification. Hybrid bounds can need more samples than Hoeffding. A non-acceptance is inconclusive evidence, not necessarily proof of harm. Single-process persistence is not a distributed transaction system.
Evidence and novelty boundaries
248 CPU tests and small synthetic experiments are not a formal proof assistant certification, independent peer review, production validation or general RL benchmark. Twenty bandit seeds favor the new sampled route on average, while full correction remains better on average. The Transformer demonstration uses four finite prompts and has no generalization claim. No native KLPO/Molt execution, pretrained-LLM experiment, GPU comparison, live HF upload, Windows execution, Docker build or GitHub Actions run occurred here.
KLPO already offers unbiased independent Monte Carlo and full estimators. This release does not "repair a biased default" or claim to surpass the upstream MC128 default with a B=8 benchmark. Standard stratification, Rao–Blackwellization, sufficient feature moments, custom recomputation, policy auditing and empirical-Bernstein bounds are prior art. The combination and explicit proofs/software may be useful, but exhaustive novelty priority and transformative system-wide performance are not established.
Security and social meaning
SHA-256 checks and numeric-only NPZ loading are integrity and serialization measures, not authentication, provenance certification, malware analysis of all dependencies, or scientific validation. Hostile code can bypass mutation counters. Public upload exposes every allowlisted release artifact; the user must confirm it contains no private data or credentials. This package contains synthetic demonstration data only. A project's requested author credit does not establish legal personhood, qualifications, publication acceptance or external endorsement.