Papers

Streaming spoken agents may produce the correct final action after acting too early. Final-turn scores do not reveal whether each observed speech prefix supports an exposed action. We introduce the Partial Speech Action Contract for Turn Taking in Speech Language Models (PACT-SLM), a controlled test that assigns the first valid action time and evaluates both action identity and timing. In the primary test, 80 paired contrast groups from four held-out semantic families yield 1,600 prefix predictions across clean and 15 dB noise renderings. Using source-utterance semantic targets rather than counterbalanced branch codes, WavLM Base Plus reaches 26.03% pooled post-onset semantic-label accuracy (95% group-bootstrap interval [22.14%, 29.68%]), exposes an action on 18.99% of pre-onset prefixes, and predicts 5.94% of complete trajectories exactly. Its pooled label score is at the 96th percentile of 100 within-prefix label permutations, below the 97.5th-percentile reference (26.73%). It exceeds matched text, scalar-acoustic, and shuffled-representation probes in pooled post-onset label accuracy. Elapsed time is more onset-exact (36.25% versus 23.13%) but less accurate about action identity (9.92% versus 26.03%). These results motivate separate measurement of action identity and onset timing in partial-speech evaluations.

We prove the strong Artin conjecture for the largest solvable Artin representations in three dimensions, whose projective image is isomorphic to the affine special linear group $C_3^2\rtimes \mathrm{SL}(2, 3)$. It is also the last solvable case in three dimensions. This is achieved with a new case of base change and automorphic induction for non-Galois quartic extensions with no intermediate fields. We additionally deduce the strong Artin conjecture for all 6-dimensional primitive solvable Artin representations.

We study the short-maturity implied volatility and the skew stickiness ratio for baskets of assets with continuous, possibly rough, stochastic volatility. The fluctuation of the instantaneous basket variance has two sources: fluctuations of the constituent variances and fluctuations of the basket weights. We derive a near-the-money implied volatility expansion that separates these contributions. We then specialize the result to volatility models given by general functions of Gaussian Volterra factors and obtain an explicit basket skew coefficient in terms of the short-time kernel asymptotics, the factor sensitivities, and the return-factor correlations. A density expansion justifies differentiation of the near-the-money expansion at the money. Finally, using a Malliavin representation of the dynamics of total implied variance, we prove that the short-maturity skew stickiness ratio converges to the universal limit $H + 3/2$ for Gaussian factor basket models with $H \in (0, 1/2]$.

High-contrast polarimetric imaging of circumstellar disks is severely limited by stellar leakage and speckle noise. Building upon the RHAPSODIE framework for polarimetric inverse problems, diffusion-based methods have shown promising results by replacing classical regularization with learned priors. However, RHAPSODIE's white noise assumption fails to capture the spatial correlation structure of atmospheric and instrumental speckles. We extend this framework to handle speckle fluctuations, which are modeled as a Gaussian field with a stationary covariance matrix with a Gaussian spectral density. To efficiently apply the dense precision matrix that includes correlated speckle and heteroskedastic photon noise, we develop a dedicated preconditioner for conjugate gradient iterations. The diffusion prior is trained exclusively on disk-only data. While limitations remain at very low SNRs, our method significantly outperforms Tikhonov regularization and competes favorably with a Plug-and-Play baseline in realistic regimes, successfully recovering morphological features masked by correlated noise.

We construct Komlós signing laws with discrepancy below $6.84$, independent Gaussian reference blocks and exponentially many balanced signings. One law preserves hard constraints and exact conditional means while its reference controls every joint convex cost. We resolve both Reis–Rothvoss Schatten conjectures. For $n$ symmetric $n\times n$ matrices, one prescribed-mean signing law bounds all centered Schatten discrepancies with sharp powers of $n$ and a universal constant. One Gaussian event of measure $e^{-O(n)}$ controls every unitarily invariant norm at the square-function radius. We prove Reis's volume-ratio conjecture: every $r$-dimensional quotient of the $a\times b$ trace-class unit ball has volume ratio $O(\sqrt{1+\min(a,b)/r})$. We resolve Nutz–Wang–Zhang's directional and supermartingale conjectures and the higher-dimensional Bass-flow conjecture. For square-integrable laws, full convex reference support is the universal finite-potential criterion in Tschiderer's $q$-Bass problem. Every driver, even atomic, admits one extended potential and shift for all maximal-covariance martingale optimizers of each irreducible pair with full terminal affine span. For Talagrand's problem, five copies of a compact balanced Gaussian half-mass set contain compact convex output of mass at least $3/4$, also in Wiener space. Cheeger's bound is asymptotically exact throughout subexponential Dirichlet spectral ranges of mixed weighted products. For standard Borel sources, a Blackwell-greatest perfectly private full-data release exists exactly when, after discarding conditional point masses, the rest coincide or share a two-point support. Under conditional atomlessness, existence is equivalent to independence. Covariance-matched analytic uniformly log-concave sources can have a greatest useful-data-only private release with infinite information, while no greatest full-data release exists.

We introduce the two-echelon covering tour vehicle routing problem (2E-CTVRP) for the distribution of relief supplies after a disaster. In the first echelon, a fleet of trucks transports supplies and drones from a central depot to satellites at the periphery of the affected area. In the second echelon, drones launched in parallel from the satellites deliver the supplies to the centroids of victim clusters, which are obtained by clustering the victim locations, and each truck waits at a satellite until its drones have returned. The problem combines the assignment of satellites to trucks, the sequencing of the truck routes, and the assignment of clusters to satellites, and minimizes the sum of the arrival times of the trucks at the satellites and at the depot. We formulate the 2E-CTVRP as a mixed integer linear program and propose a hybrid metaheuristic, GRASP-ILS-PR, which combines greedy randomized construction, a single-trajectory search, and periodic path relinking on the assignment of clusters to satellites. On a new benchmark set of 110 instances, GRASP-ILS-PR finds all known optimal solutions within 30 seconds, matches or improves on the one-hour solutions of a commercial solver on most larger instances, and improves on them by up to 11% for instances with 50 satellites. It clearly outperforms a conventional GRASP with evolutionary path relinking and yields more consistent results than a simulated annealing algorithm that uses the same search components. An analysis of two fleet configurations shows that few large trucks minimize the cumulative arrival time in most instances, whereas many small trucks deliver supplies to the victims earlier and more equitably in every instance.

The Black Hole Universe model has advanced in the literature. It assumes that the whole mass of the Universe remains inside the Schwarzschild radius of a black hole after being subject to a spherical collapse. We present a graphical proof and show that within the realm of classical theory this is not possible if spacetime remains regular at all times during the evolving collapse/bounce. Other drawbacks are discussed. As an alternative, we propose the Star Universe Model. In this model no other ingredients (such as inflaton field and dark energy) other than the perfect fluid itself are considered, and a positive spatial curvature is naturally introduced along with a particle production rate function. We discuss new-old static solutions, show that the density of a semi-closed Universe of gravitational mass $M_{\text{g}}$ is bounded from above by $3c^6/(32 \pi G^3 M_{\text{g}}^2)$, and elaborate on the birth of the Universe and calculate its inflation rate within the Star Universe Model. A smooth graceful exit from inflationary state occurs as the evolutionary solution approaches the generalized Einstein static Universe (with uniform energy density and negative pressure) and the expansion becomes linear in cosmological time with density and (negative) total pressure proportional to the square of the inverse of the scale factor. A similar behavior for density and (positive) pressure will occur if (re)collapse takes place. The analysis results in a time variable and decreasing effective cosmological constant $8\pi G\rho(\tau)/c^2$, which remains almost constant at late times, that justifies the late accelerated expansion with a rate of particle production three times the Hubble parameter.

Imitation learning enables robots to acquire complex skills directly from massive demonstration datasets, but its performance degrades severely when datasets are contaminated with suboptimal or noisy demonstrations. While prior quality-assessment methods attempt to filter or reweight data, they typically rely on manual pre-selection of expert reference data or task-specific heuristics, limiting scalability. To address this challenge, we introduce SynIL (Synergy-based Imitation Learning), a novel framework for automated, label-free demonstration quality assessment in offline reinforcement learning. Grounded in neuroscientific evidence that motor synergy, a low-dimensional coordinated structure in movement, correlates directly with motor proficiency, SynIL algorithmically quantifies synergy manifestation to generate dense, transition-level reward signals via self-supervised reward regression. Comprehensive evaluations on D4RL locomotion benchmarks and multi-human Robomimic manipulation datasets demonstrate that synergy-derived rewards correlate strongly with ground-truth rewards. Furthermore, SynIL substantially outperforms Behavior Cloning (BC) and achieves performance comparable to, and in sparse-reward human teleoperation scenarios, superior to, offline reinforcement learning trained on true environment rewards.

Large language model agents are increasingly granted real privileges (executing commands, modifying files, calling APIs), so an agent that errs has already acted. Existing defences concentrate on the agent's inputs, while the path from a candidate action to privileged side effects remains less directly studied. We argue that this path must be governed outside the model, and study an architecture interposing four roles (planner, policy gate, executor, auditor) between agent and operating system. Two choices are central: actions arrive as structured intents, so adjudication never parses shell syntax; and approval is a one-shot credential bound to the exact bytes that will run. We evaluate on a 313-case benchmark across eight variants, with prompt-only baselines from three hosted LLMs on 150 stratified cases, five repetitions (2,250 attempted calls; 2,249 completed). Effective attack success falls from 98.3% under direct execution to 7.7% deployed. Re-execution against the real implementation yields a similar aggregate rate (7.6% over 66 sandbox-evaluable payloads) but substantial case-level disagreement, at a corrected false-denial rate of 11.1%. A substantial final-stage reduction (from 30.8% to 7.7%) is attributable to the operating-system sandbox, and the benchmark found four implementation defects, none by design review.

A signed authorization record authenticates what a signer asserted, but does not by itself establish that the assertion agrees with the policy and action used for a runtime decision. CATP specifies the bindings needed to carry a local pre-execution decision into offline-verifiable evidence. Its hook commits to the enforcement-time policy and adapter-normalized action and durably records the decision before returning permission. A later receipt binds the record to a self-contained audit export. An implementation for Claude Code and Codex supports an empirical examination of these bindings. Controlled, validly signed counterexamples expose five missing consistency checks; adding them changes acceptance on the same inputs, with all 13 expected outcomes satisfied. A separate probe finds that distinct argument vectors can become the same normalized action before hashing, limiting what even a consistent receipt can establish. Eight scripted runtime cases verify hook delivery and allow/deny behavior; failure tests cover tampering, substitution, replay, concurrency and persistence errors. Median paired hook overhead is approximately 85 ms, and offline verification takes approximately 174 ms end to end on the testbed. The evidence remains conditional on a trusted runtime, monitor, host and signing key. It authenticates a decision about the normalized action, without proving execution truth, complete disclosure or autonomous task utility. The optional Groth16 study covers a narrower circuit predicate; the evaluation does not establish superiority over other systems.

In recent years, the performance of large language models (LLMs) on reasoning tasks has been remarkable, even surpassing human capabilities on various benchmarks. However, there remains a lack of clear understanding in the academic community regarding how the structure and internal parameters of LLMs progressively solve complex reasoning problems. In this study, we investigate the inference process of LLMs on cross-linguistic materials and propose the hypothesis that LLM layers exhibit a structured division of labor across conceptualization, reasoning, and textualization. Based on this hypothesis, we introduce a bottleneck identification mechanism using sensitivity analysis to pinpoint the most critical functional stage for a specific task. Leveraging this insight, we propose a novel approach, Layer-Informed Fine-Tuning (LIFT), which achieves efficient and effective fine-tuning by selectively updating only these functionally critical layers. We then conduct extensive experiments to show that the LIFT method not only accelerates the training process but also significantly improves model performance.

Pan and Zhang proved that a positive proportion of positive integers can be represented in the form $a^2+b^2+2^{c^2}$, where $(a,b,c)$ are nonnegative integers. In this note, we give a short proof of their result. The proof uses Romanoff's method and an elementary divisor argument to control the relevant second moment.

We estimate the number of integers up to $x$ whose $y$-friable component exceeds $z$. Uniformly for $\max\{2,\log z\}\leqslant y\leqslant z\leqslant x/2$, we determine the logarithm of this counting function up to an error $O(\log z/\log y)$. This sharpens an estimate arising from a problem in Ford's sieve methods lecture notes. The proof combines classical friable-number estimates with an elementary argument for the lower bound.

We propose RegLLM, a diagnostic harness for bounded autonomy in regulated agentic workflows. It instruments six trustworthiness signals: citation validity, source grounding, schema compliance, escalation correctness, constitutional alignment, and unsafe-action rate. Signals are distinguished by their source of supervision: programmatic verifiers, task-level escalation labels, or AI-judge scores. A deterministic runtime supervisor blocks ungrounded answers and forces escalation, logging interventions. The same domain constitution informs evaluation, training rewards, and serving guardrails. Task-level should-escalate labels make the act-versus-defer decision a measurable training signal. We demonstrate the harness at smoke scale. An offline reference run (n=12) lifts escalation recall from 0 to 0.67 and reduces unsafe-action rate from 0.33 to 0.08 when governance is enabled. Two single-GPU Qwen2.5-3B LoRA/DPO pilots (n=8, same seed and evaluation split) expose substantial variation: nominally identical RL-base configurations yield task success of 0.25 versus 0.12 and escalation recall of 1.0 versus 0.5. An answer-quality adapter changes recall from 1.0 to 0.5 in Run A, but from 0.5 to 1.0 in Run B. An escalation-aware variant produces no measurable change in Run B. These small pilots do not establish reliable adapter effects or production readiness. Their contribution is diagnostic: configuration variance can overwhelm apparent tuning effects on bounded-autonomy metrics, motivating larger evaluation sets and repeated runs.

On-policy distillation (OPD) trains language models using dense token-level teacher supervision on student-generated trajectories. However, its reliance on frequently refreshed student rollouts often incurs substantial generation cost. We introduce REVO, an off-policy distillation framework that improves rollout efficiency by reusing each student rollout for multi-step learner updates. REVO addresses prefix-level and current-token policy mismatch through stabilized prefix weighting and one-step resampling from the current student, which enables repeated updates without regenerating full trajectories. To prioritize informative token positions within reused rollouts, REVO uses the variance of the student-teacher log-probability ratio to quantify the remaining token-level learning signal and guide repeated optimization. Across multiple student-teacher scales, REVO with only 50 rollout iterations matches or exceeds OPD baselines trained for 200 iterations on both in-domain and cross-domain reasoning benchmarks.

Multiple-choice benchmarks are cheap to grade and are running out of room, and the standard remedy, writing harder items, is slow and repeated for every benchmark. A saturated benchmark still holds a harder task. Each question's wrong options are written for that question alone, so a model can score by eliminating a few options. We propose AnswerPool: take $N$ questions that share a context, pool all their options into one list, and ask the model to assign every question its answer. No item is written and no label changes. The chance of guessing a group right falls from $10^{-3}$ to $5\times10^{-7}$ for five four-option questions, and a model that recognizes its answers keeps its multiple-choice score, so the accuracy lost to pooling measures the credit the format gave for elimination. Deleting answers from the pool makes questions unanswerable with exact ground truth, so abstention is scored in the same pass. Across eight text, image, and video benchmarks and eighteen models, pooling is harder for every model, the elimination credit is largest for the weakest models, and seven of eight open-weight models answer 87 to 100% of unanswerable questions.

Instruction-guided image editing should change what the instruction names and leave the rest of the image untouched. In dual classifier-free guidance (CFG), an editor combines two directions at every denoising step, one that pushes toward the instructed edit and one that pulls back toward the source image, using global weights. We introduce Attention-Scoped Guidance (ASG), a sampler wrapper that makes these weights spatial. It reads a soft support map from the instruction attention that the editor already computes, then weakens text guidance where support is low and strengthens image anchoring where support is high. The wrapper requires no training, no external mask, and no additional network evaluation. On the full MagicBrush and PIE-Bench++ splits, ASG improves preservation-oriented metrics, leading three of four MagicBrush metrics and PIE-Bench++ background PSNR. A dose-matched control that removes the spatial placement loses up to 0.73 CLIP on PIE-Bench++, confirming that the spatial allocation itself carries the gain.

LLMs excel at recalling statistical patterns but degrade sharply when answers must be derived, especially on multi-hop chains. Delegating derivation to deterministic symbolic executors shifts reliability to whether model-generated premises are source-supported. We introduce CPUNeSy, a serving architecture that controls model writes to symbolic state via a task-defined predicate interface and certificate gate, abstaining when grounding passes disagree. Component analysis isolates deterministic execution, restricted grounding, agreement, and source rechecking. Experiments show deterministic execution drives most accuracy recovery on derivation-heavy tasks; controlled writes mainly improve selective reliability by withholding unsupported or inconsistent answers, at a coverage cost. On multi-hop tests in law and formal math, deterministic execution recovers most of the gap over chain-of-thought and retrieval baselines, with full-pool gains up to 35.0 points. Certification is selective-serving control, not accuracy mechanism: with grounding traces fixed on ContractNLI, source rechecking removes a quarter of DeepSeek's wrong answers surviving two-vote agreement, at measurable coverage cost. When abstention is costly, routing withheld cases to an uncertified same-model fallback raises full-pool accuracy on MedCalc-Bench Verified by 13.9 and 4.9 points for Seed and DeepSeek; these gains are not from the certified channel. On LeanDojo Benchmark 4, kernel-restricted pools match BM25 recall@15 (89.3%). Gains depend on the grounder's error regime: bias-dominated grounders benefit less, consistent with our voting bound. Certificates guarantee derivational validity relative to admitted premises; semantic faithfulness to natural-language sources remains conditional on the source checker, and prospective validation is future work.

In this paper, the detailed behavior of solutions of both the Stokes and the Navier–Stokes system in the half space is investigated when the initial data belongs to $L^1$. We first give a detailed asymptotic expansion of the solution to the Stokes system supplemented with $L^1$ initial data. With the aid of this expansion, we provide two sufficient conditions on the initial data so that the associated solutions of the Navier–Stokes system do not belong to $L^1$, corresponding to long time and short time behaviors, respectively. Moreover, for the $n$- dimensional Navier–Stokes system, a pointwise spatial lower bound of order $n$ is derived in a conic neighborhood of the $x_n$-axis, provided that the initial data decays faster than order $n$. One of the main difficulties to get precise form of leading order term is the non-commutativity of the Leray projection operator with the Laplacian. Our strategy is to employ the special structure of the Green tensor observed by Han and a cancellation property of the initial data. This also yields the sufficient conditions on the initial data to get precise asymptotic behavior via comparing the linear and nonlinear parts.

Analyses of dual lattice attacks have often assumed that the individual scores associated with short dual vectors are mutually independent. Laarhoven-Walter used this heuristic to derive explicit trade-offs between the target radius and query time for bounded distance decoding (BDD) with preprocessing. Ducas-Pulles subsequently demonstrated theoretical and experimental failures of this heuristic and proposed an alternative model conditioned on the target norm. In this note, we prove an explicit asymptotic trade-off for (decision-)BDD with preprocessing in the Haar-random lattice model, without heuristic assumptions. Using moment identities of Siegel and Rogers, we analyze cosine scores over complete dual balls and bound both error probabilities when distinguishing targets planted at a prescribed radius from uniform targets modulo the lattice. Optimizing the dual radius yields a trade-off between target radius and query time that matches the asymptotic prediction from the conditional model of Ducas-Pulles.

We prove that below the multicritical (Nishimori) point the ferromagnetic boundary of a biased Ising spin glass, argued by Nishimori (1986) to be exactly vertical, can be vertical and can also be reentrant, so that cooling at fixed disorder destroys order. It is vertical in the Sherrington-Kirkpatrick (SK) model with a Curie-Weiss bias $J_0$, and reentrant near the triple point of fully connected $p$-spin glasses and, at one disorder strength, on a decorated planar $\mathbb{Z}^2$-periodic lattice. For every $T<J$ the SK magnetization vanishes for $J_0\le J$, continuously at $J_0=J$, and is macroscopic for $J_0>J$. For every integer $p\ge3$, at each bias slightly larger than the triple-point bias, the $p$-spin magnetization is macroscopic at the Nishimori temperature and vanishes at an explicit lower temperature; this is Nishimori's recent replica prediction in two-temperature form. On the lattice ($\mathbb{Z}^2$ with each bond replaced by a fixed series-parallel gadget; maximum degree four), with iid $\pm J$ couplings at $\mathbb{P}(J_e=-1)=9/10000$, the Gibbs state is almost surely unique at high temperature, non-unique in a window containing the Nishimori temperature, and unique again at low temperature. As Dey and Kang observed, the SK boundary is set by the zero-field susceptibility together with an envelope bound on the free-energy gain in a field, which follows from the gauge inequality. We prove that this susceptibility is the curvature at the origin of the zero-field Parisi PDE solution, which Lopatto evaluated for every $\beta>1$ via his theorem that the support of the Parisi measure accumulates at the origin; we give a short alternative proof of that theorem. The $p$-spin and lattice results and the alternative proof are computer-assisted. The models are proxies for the nearest-neighbour $\pm J$ model on $\mathbb{Z}^2$ and say nothing about $\mathbb{Z}^d$.

Many engineering problems involve optimizing a high-dimensional expensive black-box (HEB) design space. To solve such problems efficiently, we propose a knowledge transfer assisted efficient global optimization (EGO) algorithm, labeled as KT-EGO, which extends the EGO algorithm for solving problems over higher dimensions (i.e., $d>20$). Specifically, the original design space is divided into several low-dimensional subset design spaces. More importantly, in order to extract information from the subset design spaces to accelerate the progress of full optimization, we propose a surrogate-based data fusion strategy in KT-EGO. And further, a searching strategy with an adaptive variable range is devised to enhance the exploitation of promising areas. To show the effectiveness of our proposed algorithm, it is compared against the state-of-the-art algorithms over 12 benchmark functions and a 28-dimensional engineering optimization for the design of compressor blade, which fully validates the effectiveness of the KT-EGO for solving HEB problems.

Call a set $A$ of positive integers admissible if, whenever $a_1\cdots a_r=b_1\cdots b_s$ with $a_1,\dots,a_r$ distinct elements of $A$ and $b_1,\dots,b_s$ distinct elements of $A$, necessarily $r=s$. Erdős asked whether admissible sets can have density $1-\varepsilon$ for every $\varepsilon>0$, and whether $\{1,\dots,N\}$ always contains an admissible subset of size $(1-o(1))N$. For the variant in which repetitions are allowed both questions were answered negatively by Erdős, Ruzsa and Sárközy and by Granville and Soundararajan; for products of distinct elements, the first question was answered only recently (with density bound $7/8$), and the second has remained open. We show that every admissible $A\subseteq\{1,\dots,N\}$ satisfies $\sum_{a\in A}1/a\le\tfrac12\log N+(\log\log N+2)^2$, and that there is an absolute constant $\eta>0$ such that every admissible $A\subseteq\{1,\dots,N\}$ has $|A|<(1-\eta)N$ for all large $N$. Both questions therefore have negative answers. The proofs are elementary; the second rests on a coupling that replaces the largest divisor of an integer composed of small primes, which avoids the divisor-function losses inherent in counting quotients along a multiplication table. Both negative answers are formally verified in Lean 4 against the statements of the Formal Conjectures project.

Non-uniform security allows an adversary to receive bounded advice about an oracle before attempting a fresh challenge. This captures the most realistic attacks and has already been studied extensively in prior work. In this work, we introduce an operator-norm approach for non-uniform security in the quantum random oracle and random permutation models. This new approach yields a unified reduction for both search success probability and distinguishing advantage. Previously, the reduction only worked with success probability even in the decision games, yielding a worse bound. Our framework enables tight bounds for Yao's box, both with and without salting, and improved bounds for pseudorandom generators. We also prove an optimal generic salting theorem for decision games. By defining a property of a game, which separates the contributions of the existing queries in the offline stage and subsequent online queries, we obtain stronger bounds for specific salted constructions. These include salted permutation inversion, tight up to logarithmic factors, and salted random-function inversion, tight up to logarithmic factors and the gap already present in classical function inversion.

Hard signal-to-noise ratio (SNR) screening removes weak seismic records, but does retaining clearer waveforms improve learning enough to compensate for the discarded data? We test this question in phase picking and ambient-noise dispersion, first matching training counts and then restoring the full eligible dispersion pool at fixed compute. Phase-picking screening gave no consistent unfiltered-test benefit under fine-tuning or random initialization, including a control matched on distance and phase composition. Dispersion screening increased error at the original five-epoch endpoint but improved on an equally sized unscreened set after longer training. Retaining all 29,788 eligible fit paths instead of 9,929 randomly sampled paths reduced unfiltered-test error by 3.0% across three seeds at the same update budget. Full-available and strict-SNR training then had similar mean errors, 0.0405 and 0.0406 km s$^{-1}$, with mixed seed-paired ordering; strict training retained a 9.9% advantage on the SNR-selected test. In two-day monitoring, SNR regulated pick streams but event recovery depended on its measurement definition. High SNR did not reliably identify better training data: gains depended on the task, training schedule, and test domain, and fixed-count comparisons omitted the benefit of retaining additional valid examples.

Elastic-wave propagation connects laboratory fracture with earthquakes, raising the prospect of seismic models that reuse waveform structure across physical scales. Here we show that the phase picker PNSN and the multi-task model SeismicXM organize unseen laboratory acoustic emissions around common waveform relations. Their representations agree on 512 held-out records relative to matched random networks. Four earthquake-model families also track displaced laboratory arrivals without fitting target neural weights. Receiver-function classification is accessible to frozen pretrained features, although standardized random features remain competitive. Noise correlations test the extension to continuous propagation outputs: a nonlinear SeismicXM ensemble improves on random topology, while a period-wise median remains more accurate. Waveform interventions and synthetic controls reveal that the observed agreement depends on feature calibration and the waveforms being compared. These results establish convergent waveform organization across distinct seismic training routes and show that cross-scale arrival transfer is already accessible to compact models.

Chollet's permanent conjecture asks whether per(A o B) <= per(A) per(B), where o denotes the entrywise (Hadamard) product, for complex Hermitian positive semidefinite matrices. We present computer-assisted proofs of two restricted forms with explicit constants strictly smaller than one. For every integer n >= 10 and every such matrix A of rank at most four, the self-conjugate ratio per(A o conjugate(A)) / per(A)^2 is bounded by 999991742359 / 10^12 when the denominator is nonzero. For order nine, we obtain the bound 999815240367 / 10^12 for correlation matrices whose four nonzero eigenvalues all equal 9/4. The first argument combines complex-sphere integrals, spectral subspace tilts, projection bounds, exact finite covers, and an analytic infinite tail. The second uses a quadratic relation among nine Gram vectors, a positive operator on the ten-dimensional space of quadratic forms, and rigorously bounded entropy. All decisive finite calculations use rational arithmetic and full closed-domain certificates. The unrestricted conjecture, including general non-tight order-nine rank-four matrices, is outside these results.

Salikhov (2008), Zeilberger-Zudilin (2020) and Bai (2026) bound the irrationality measure of pi with the same shape of complex integral. This note gives one closed-form law mu(a0,a1,b) for the whole family, shows that it reproduces all three published records, proves that it is exactly scale-invariant, and gives evidence that Bai's parameter point is the global optimum of the family - a statement Bai explicitly declines to make about her own result. The admissible configurations are forced by a Machin condition: zeros at 0, +-w, +-wbar and poles at +-P give a linear form in 1 and pi if and only if P^2 - N(w) = 2P Im(w). The law depends only on the two ratios a0/a1 and b/a1, so the infinite three-parameter lattice is exactly two-dimensional. The 2-adic saving is exactly 5(2a1-b)/2 per n, in two regimes, and no further saving exists. The decay rate is governed by the min-max value of the steepest-descent method, the lowest level at which the two endpoints of the integral become connected within a sublevel set of the integrand; the value obtained from the least critical level is a lower bound for mu and serves as a screening. Among the sixteen admissible configurations with P < 100, exactly one carries a triple that yields a bound, namely Salikhov's (P = 5, w = 1+2i), and the least mu over all sixteen and over all primitive triples with a0, a1 <= 10 and b <= 22 is 7.103205334137 at (2,2,3). Within that configuration the minimum is 7.101862832356 at (1857,1857,2785), which is Bai's point, the vertex sitting exactly at Q = 2a/(3a-2b) = 3714. Each statement carries an explicit label, PROVED or VERIFIED or CONJECTURE, and the reservations of scope are stated in the note. An ancillary file re-derives every numerical claim from scratch, with no external dependency.

When a user changes their mind partway through a task, an agent that has already split the task into sub-goals and paid for tool calls must decide, per cached sub-result, whether to keep, patch, or discard it (salvage), restarting wastes valid work and continuing unchanged answers the old question. Our main finding is that salvage quality is a matter of role design rather than model capability: a language model asked the keep/patch/discard question one node at a time is unreliable, but asked to classify the revision once, with a deterministic layer propagating the decision, it reaches the cost-optimal oracle on all three models tested, from two vendors. Modeling the plan as a commitment hierarchy and the intent change as a belief-revision operator with AGM style postulates, we prove that no policy observing only a node's local view can be both safe and cost optimal, while the single classification design is both. Across three environments the policy recovers the full achievable savings, 43% cheaper than restart, at 100% correctness.

Accessible map systems either make a layout explorable by hand or convey information through speech; few combine both to support pre-travel spatial understanding for blind and low-vision (BLV) people. We present TouchingSpace: a system that retrieves map data for an outdoor place and renders its surroundings as bounded regions at fixed trackpad positions. During exploration, users receive audio and haptic feedback and can ask a conversational agent open-ended questions. We conducted a user study with fourteen BLV participants who explored a place using TouchingSpace and reflected on the experience. We found participants used sound and vibration to locate places and speech to identify and describe them; the bounded surface supported discovery, revision, and spatial checks by hand; they expected this awareness to support future travel. TouchingSpace demonstrates how a laptop trackpad can support self-directed spatial exploration. These findings suggest accessible AI maps should ground conversation on bounded, user-controlled spatial surfaces.