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Learning--Reasoning Correspondence (LRC) proposes that augmenting training examples with symbolic-style inference tuples can improve small-agent learning. We test this claim in a controlled finite replication that fixes rule-chain and symbolic gridworld task families, ten paired seeds, size-matched neural and neuro-symbolic conditions, and oracle trace-bearing tuple diagnostics. Relevant regularized LRC improves final out-of-distribution accuracy in both executed local benchmarks: 0.945 versus 0.496 for the neural baseline on rule chains and 0.905 versus 0.405 on symbolic gridworld planning. Mechanism-isolation margins remain positive against noisy-tuple and no-regularizer ablations, with bootstrap intervals [0.207, 0.219] and [0.236, 0.253]. Tuple confidence is also better calibrated and more faithful than noisy augmentation under the available oracle traces. The stronger sample-efficiency claim is not established: all predeclared samples-to-threshold comparisons at 0.80 and 0.90 validation accuracy are censored on the executed grid. The evidence therefore supports LRC as a local mechanism for final OOD generalization in controlled finite tasks, but weakens claims about threshold sample complexity and leaves public bAbI/MiniGrid replication as future work.

Small language models are increasingly used as lightweight reasoners over structured records, but their behavior under tabular distribution shift is poorly characterized. This paper evaluates whether counterfactual feature interventions improve robustness when rows are verbalized as reasoning examples. We construct an oracle synthetic benchmark of mixed-type tabular rules with threshold, conjunction, disjunction, exception, and interaction families; generate matched no-augmentation, random-row augmentation, nuisance-counterfactual, label-preserving perturbation, and decisive counterfactual-intervention regimes; and evaluate 625 method, shift, rule, and seed cells. Decisive counterfactual intervention augmentation improves mean out-of-distribution accuracy by 21.3 percentage points over no augmentation and 17.0 points over random-row augmentation, with bootstrap intervals above zero. It also improves paired counterfactual consistency by 35.5 and 29.4 points over the same baselines. The original success criterion is only partly met because in-distribution accuracy retention is -2.3 points relative to the no-augmentation baseline, exceeding the pre-specified tolerance. The evidence supports counterfactual interventions as a useful robustness stressor and training signal in oracle tabular rule tasks, while limiting claims about real data until intervention-feasibility and shift manifests are available.

Learning-Reasoning Correspondence (LRC) proposes that neural agents become more sample efficient, robust, and interpretable when explicit inference tuples are generated, serialized into the input, and regularized for consistency. We test that claim in a finite, matched-capacity replication across three task families: Boolean structural-causal intervention prediction, SCAN-compatible command recombination, and gridworld planning imitation. The executed model class is a fixed hashed linear neural proxy with identical feature dimension across learned conditions, ten paired seeds, five data fractions, thirteen conditions, tuple-validity checks, ablations, oracle-symbolic upper bounds, confidence calibration, paired tests, Holm correction, and wall-clock runtime gates. The headline LRC claim is not supported in this regime: no primary endpoint passes the full conjunction of effect threshold, Holm rejection, runtime ratio at or below two, valid baseline floor, and architecture-fit gate. Raw gains are visible but conditional: causal OOD improves by 14.5 percentage points with Holm rejection but exceeds the runtime gate and remains outside the requested architecture class; command sample efficiency passes raw and statistical thresholds but is diagnostic because the full-data baseline floor fails; gridworld sample efficiency is large but not Holm-supported, and gridworld OOD remains below the 10 percentage-point target. Tuple evidence is mixed: full LRC produces high parse and semantic-validity rates, corrupted or feedback-removed tuples degrade behavior, and oracle tuples outperform learned tuples, so tuple quality appears relevant but insufficient to rescue the headline performance claim.

We test whether a next-nearest-neighbor coupling supplies one finite-size control scale for both the spectral crossover from integrability and the onset of eigenstate thermalization in an open spin-$1/2$ XXZ chain at $\Delta=1$. Dense exact diagonalization was executed for $L=8,10,12$ in total-$S^z=0$ sectors resolved by reflection parity, with $\lambda\in\{0,0.05,0.1,0.2,0.3,0.5,0.7,1.0\}$. The computed diagnostics do not support a clean Poisson-to-Gaussian-orthogonal-ensemble rise in the mean spacing ratio: the reflection-even high-$\lambda$ values remain near $0.35$--$0.40$ rather than approaching $0.5307$. Off-diagonal matrix elements of a parity-preserving central-spin observable show partial $1/D$ consistency, but the adjacent-size ETH exponents drift from near one at small $\lambda$ to about $0.78$ and $0.72$ at $\lambda=1$. Half-chain entanglement increases toward a Page-like comparator, reaching about $0.86$--$0.92$ of the full-space Page value at $\lambda=1$. Independently extracted crossover scales do not coincide: spectral midpoint crossings are absent for $L=10,12$, whereas ETH midpoint estimates occur near $\lambda\simeq0.31$--$0.36$. At the executed sizes, the evidence is a finite-size failure atlas for the proposed single-scale collapse rather than confirmation of a universal crossover law.

Asynchronous research services often expose a deceptively small integration boundary: submit a job, poll until a terminal status appears, and read an artifact manifest. A wiring problem at that boundary can turn a missing artifact, stale run identifier, malformed manifest, or trace gap into a false success. This paper defines an artifact-bearing smoke profile for that boundary and evaluates it against a local fixture-harness evidence package assembled for this study. The executed evidence contains a 480-row prediction table over 45 finite fixture cases, nine regimes, and five seeds, plus a finite symbolic audit over 64 Boolean assignments. The contract profile produced no false passes on non-pass fixture rows, detected status, manifest, and trace boundary violations in the local matrix, and preserved the distinction between fixture evidence and production reachability. The result supports a scoped claim: a compact smoke profile can make the dispatch, terminal-status, manifest-integrity, byte-integrity, and trace-continuity obligations explicit enough to reject targeted local failures before a generated artifact is treated as a valid research output.

Randomized SVD is often run with a fixed oversampling parameter, even though approximation quality is driven by the spectrum and by the power-iteration count. We test whether the stable rank of a matrix can govern the oversampling needed to reach a target relative error, and whether this yields an a-priori rule that is independent of ambient size and target rank. The answer is conditional. In finite Gaussian range finding, global stable rank alone does not remove target-local tail dependence: for power-law spectra with exponent greater than one half, stable rank can remain bounded while a normalized tail quantity grows with the target rank. We define a power-filtered rank that contracts under subspace iteration, derive a conditional oversampling threshold under an explicit intrinsic-tail premise, and validate the algebra with seven symbolic checks. Executed experiments on 1,728 synthetic randomized SVD runs and 648 real-matrix runs show mixed empirical support. Normalizing by filtered rank improves collapse only slightly on average, with mean relative spread improvement 0.019 over global stable rank. Conditional tail fits are mostly decreasing in oversampling per filtered rank, but a finite two-parameter rule has only 80\% training and held-out coverage and no feasible cell in the tested calibration grid. On SuiteSparse SNAP/ca-GrQc, MovieLens 100K, and a Fashion-MNIST train slice, matched-accuracy transfer rows show zero positive sketch-column savings. The supported conclusion is therefore not a universal stable-rank-only law. Effective rank is useful when paired with power filtering and tail-local diagnostics, and the resulting rule should be treated as a scoped calibration rather than a general replacement for existing oversampling heuristics.

Parameter averaging is often used as a cheap way to smooth stochastic optimization trajectories, and a natural hypothesis is that the averaging horizon should grow as a cosine learning-rate schedule decays. We evaluate this hypothesis for small supervised classifiers under symmetric training-label noise. The proposed readout is a deterministic cosine-scheduled exponential moving average of parameters, compared under matched seeds with the final iterate, fixed-coefficient EMAs, and uniform tail Polyak averages. The executed study covers Gaussian blobs, two moons, handwritten digits, and breast-cancer classification, with 20 deterministic seeds per dataset and noise level, clean validation and test labels, and raw plus temperature-scaled probability metrics. The main result is negative: in the preregistered two-hidden-layer MLP condition, cosine-scheduled EMA achieved 0 of 4 dataset-level primary successes against the strongest non-scheduled averaging baseline on raw top-label ECE. Raw ECE was worse for cosine-scheduled EMA on all four datasets, even though test NLL and accuracy often improved. The algebraic filter properties of the schedule were verified, and the readout reduced late validation-NLL variance relative to a fixed EMA with coefficient 0.999, but sharpness and path-movement diagnostics did not support a broad smoothing explanation. These findings reject the headline calibration-stability claim for the tested small-classifier regime while preserving a narrower conclusion: schedule-coupled averaging is a valid convex readout with useful loss-stability behavior, but raw calibration gains are metric-dependent and cannot be inferred from smoothing alone.