Formal Verification

LLM-based Lean proving systems increasingly organize a proof as a blueprint: a dependency graph of formal statements. We introduce BlueprintRepair, a repair interface that lets a model change this graph through ten schema-checked local operations. An operation names the node it edits, so the target theorem cannot be changed. Lean checks every applied change, and an accepted repair must declare every blueprint lemma its proof uses. We also construct BlueprintTrace, a benchmark of 142 controlled failures with complete accepted and rejected repair trajectories. We compare typed edits, exact source patches, and complete module rewrites under matched source, feedback, model, and budget, one episode per state and interface. With DeepSeek-V4-Flash, the three interfaces solve almost the same number of the benchmark's localized failures. Typed repair is the cheapest per solved state (patching is 1.30x as expensive, rewriting 2.06x), and within 10,000 completion tokens per task it reaches almost all of its final coverage, while both free-form interfaces are well behind. A second model, Qwen3.6-Flash, solves fewer states but keeps typed repair cheapest, puts it ahead on the proof-authoring states, and repeats the localized pattern.

Writing Answer Set Programming (ASP) theories from scratch is a difficult and time-consuming task. We take a neurosymbolic approach to study whether a model can distill complete and correct theories, given a fixed agent harness with the solver in the loop. The protocol is dataset-agnostic: with a single prompt and an empty file as the starting point the model is given a 1-hour time limit to derive a complete theory. We chose VQA as the application domain, three benchmarks (CLEVR, GQA, CLEVRER), as these are publicly available and non-trivial. In order to study the model scale required for solving this task we nine different models: four frontier (Claude Sonnet 4.6, Claude Opus 4.7, GPT-5, DeepSeek V4 Pro), two mid-tier (DeepSeek V4 Flash, gpt-oss-120b), and three open-weights (qwen3.6-27b, gpt-oss-20b, qwen3.5-9b). Three of four frontier models reach 100% on CLEVR and 92.8%-98.8% on GQA; on CLEVRER, Sonnet, Opus, DeepSeek V4 Pro score 92.7%-95.3%. GPT-5 reaches 98.7% on CLEVR but drops to 41.8% on GQA and to 86.7% on CLEVRER. Adding handwritten reference theories from other datasets moves the other three frontier models by at most +/-3.4 pp but reduces GPT-5's accuracy by 3-19 pp. We release the code, prompts, and theories distilled.

Recent advances in large language models (LLMs) have enabled AI systems to assist scientific research and peer review. However, an essential capability for reliable AI-assisted scientific workflows remains underexplored: verifying whether reviewer feedback leads to meaningful and evidence-supported manuscript improvements. We introduce AutoSupervision, which evaluates whether scientific manuscript revisions genuinely address reviewer concerns through grounded evidence. AutoSupervision leverages transparent peer-review records as a natural source of supervision, where reviewer comments specify scientific concerns, author responses describe claimed resolutions, and revised manuscripts provide evidence of changes. Given reviewer comments, author responses, and revised manuscripts, models must characterize reviewer concerns, determine whether concerns have been addressed, and identify supporting manuscript evidence. We construct AutoSupervision from 56,000 Nature Communications articles and corresponding review records. Then we conducted experiments on LLMs, the ablation study, and the case study. Our results show that while LLMs perform well in characterizing reviewer concerns, with GPT-5.5 achieving a score of 0.754, evidence-based verification remains the primary bottleneck, with the best-performing model reaching only 0.501.

Automating program verification with LLM agents requires generating specifications, annotations, auxiliary lemmas, and tool invocations, all of which depend on reusable skills. A natural remedy is skill self-evolution: distilling skills from trajectories and refining them through feedback. However, existing evolution methods struggle with program verification tasks because they cannot reliably identify skill-specific failures or extract actionable signals from opaque verifier feedback. In this paper, we propose VeriSkill, a self-evolution framework built for program verification. It attributes verification failures to skill deficiencies, distills diagnostic signatures into reusable lessons, and iteratively refines candidate skills, admitting only revisions that improve verification performance while preserving program semantics. Experiments show that VeriSkill consistently outperforms all baselines across multiple verification tools, agent frameworks, and LLM backends.

Automatically constructing well-specified and valuable mathematical conjectures remains a central challenge in AI-assisted mathematical discovery. Many existing open problems and conjectures are often too broad, underspecified, or difficult to connect to plausible proof or refutation strategies. We view a mathematical mechanism as a structure or reasoning principle that connects the assumptions of a candidate problem to its target conclusion, such as an inequality, invariant, decomposition, or reduction to an intermediate claim. We present MECA (MEchanism-centered Conjecture Agent), a multi-agent framework that constructs conjectures by jointly developing candidate statements and their supporting mechanisms. Explorer agents propose mechanisms, test how they apply, and revise the candidate conjecture accordingly, while critic agents assess their mathematical validity and research value. Their feedback guides changes to the assumptions, scope, and conclusion. Through this process, MECA transforms broad research directions into precise conjectures with substantive mathematical support while retaining a clearly identified unresolved core. We evaluate MECA in two complementary settings. First, we compare it with a generate-and-revise baseline on reconstructing preselected target-paper conclusions from target-conditioned but article-blind source materials. Second, we construct 100 semi-open problems from literature-derived seeds and existing open problems and evaluate them through independent proof and refutation attempts by automated provers. Our results indicate that mechanism-centered refinement produces well-specified and research-worthy conjectures that remain challenging for current automated provers.

Planning over Temporal Dynamic Knowledge Graphs (TDKGs) presents theoretical challenges in open-world environments with incomplete information. Existing action formalisms often face decidability issues and the Ramification Problem, while structural abduction requires expansive combinatorial search spaces. We introduce a unified framework with two modules--PIE-Abducer (incremental direct-derivation abduction) and PIE-APT (Abductive Planning for TDKGs)--operating natively on the expressive SROIQ Description Logic. Modeling state transitions as non-monotonic updates to deductively closed DL theories, we represent actions natively in OWL. This leverages an incremental reasoner to preserve decidability and natively bypass the Ramification Problem. To address incomplete knowledge, PIE-Abducer circumvents Minimal Hitting Set (MHS) enumeration. Instead of combinatorial search, it injects the logical negation of a goal into a consistent DL branch and synthesizes missing premises via direct refutation consequences. PIE-APT employs a recursive Generate-and-Test architecture, interleaving backward-chaining A* search with PIE-Abducer to synthesize both action sequences and abductive assumptions. Candidates undergo strict validation via forward-chaining Temporal Projection to evaluate logical trajectories. We evaluate four OWL benchmarks targeting semantic abilities missing from classical planning: parameterized goals with witness search, mid-search DL entailment, open-world assumption injection, and adversarial plan synthesis. Results show qualitative superiority over classical planners and prove our direct-derivation approach significantly outperforms an MHS-faithful baseline in abductive enrichment.

Visual-token pruning is usually judged by answer quality at a fixed retention budget. For text-rich multimodal large language models (MLLMs), this protocol can miss a distinct failure: an answer remains correct even when no retained token is locally traceable to the small OCR region that supports it. We turn this blind spot into an evidence-risk audit that couples answer behavior with geometric token-origin provenance, interventions, and realized cost; transparent training-free selectors isolate controlled operating points. On locked image-disjoint confirmation, Qwen Target at 30% retention has observed accuracy 0.786 versus 0.783 for Full (paired image-cluster difference +0.003, 95% CI [-0.014, +0.020]), yet same-budget Target, Random, and Grid retain sharply different positive-support coverage: 0.620, 0.270, and 0.318. Across Qwen3-VL-8B, LLaVA-1.5-7B, and InternVL3.5-8B, matched controls, interventions, detector tests, and external methods reveal model-specific quality-risk-traceability frontiers that accuracy alone does not expose. Materialized prefixes yield up to 4.32x batch-prefill speedup and 76.4% lower incremental peak memory; full-validation TextVQA and DocVQA further show that favorable target-verification points do not imply task-general compression. Visual-token pruning should therefore report surviving spatial provenance and realized cost alongside quality and compression.

Open source communities have been flooded with AI-generated contributions. In defense, they have written contribution rules to regulate coding agents' behavior, spanning from a total ban, mandatory disclosure, to verification gates and human sign-offs. Yet, whether coding agents read and follow those rules, and behave in open source repositories, remains unknown. To estimate real-world rule compliance of coding agents, we curate 106 issues from 49 repositories containing AI contribution rules into RepoComplianceBench. We judge the trajectory of each run against the repository's rules, measuring whether the agent refuses to contribute, discloses its assistance truthfully, clears the required verification gates, or escalates critical steps to a human. We also test if extra prompts, rule disclosure, or feedback from the compliance verifier help with the situation. Our experiments on four frontier models show that today's agents almost never proactively retrieve the contribution rules. Agents pick up disclosure and verification with reminder prompts, rule quotes, and verifier feedback; however, they never refuse to contribute in AI-banned repositories under any condition we tested. The status reveals that verification and disclosure issues are solvable with existing mechanisms, yet enforcing bans and human escalations remains an open problem.

The ability of large language models (LLMs) to process and generate text has introduced potential for applications in information extraction (IE). While it's debated whether LLMs outperform smaller fine-tuned models for classification tasks, their strong generalization capability makes them promising for domains with limited labeled data available for fine-tuning. This advantage is particularly relevant for the emerging application of the digital product passport (DPP), where the problem space is broad but domain-specific data remains scarce. Motivated by this use case, we apply generative IE to the product domain, explicitly addressing efficiency, generalizability, and data privacy constraints. We propose a two-step validation method that integrates a PLM block into the generative IE pipeline and thereby leverages LLMs' correction capability. We discover that such a validation task enhances LLM performance, particularly on the extraction of weakly expressed, low-salience entities that appear sparsely throughout the text. For certain entities, the performance of mid-size models can even reach levels comparable to larger models, and the improvement of first-step PLM predictions also enhance the final LLM output. Nevertheless, the effects on the smallest open-source LLMs (e.g., Llama-3.2 3B) is limited. Based on the findings, we develop a demo application for product information extraction that utilizes locally deployed LLMs, targeting further adaptations to real-world DPP use cases.

Large language model (LLM) agents autonomously interleave semantic reasoning with complex system operations. In these dynamic environments, static tool-level permissions are fundamentally insufficient; safe authorization is highly context-dependent and heavily reliant on evolving runtime states and data flows. We present FAVA (Formal Authorization for Verified Agents), a permission-carrying authorization framework for agent execution. FAVA utilizes an LLM-guided Permission Intermediate Representation (IR) to translate ambiguous natural-language tasks into structured constraints. A deterministic lowering pass then converts this IR into an evidence-backed permission graph that explicitly tracks data flows, dependencies, and contextual labels. To provide strict security guarantees, a Satisfiability Modulo Theories (SMT) authorizer mathematically verifies the current graph against security policies before any effectful action executes. A runtime gateway then enforces the solver's result, either authorizing the execution or intercepting it with a precise counterexample. We evaluate FAVA across OpenAgentSafety, OctoBench, and ActPlane scenarios. Our evaluation demonstrates that FAVA achieves a 90.5% Decision Compliance Rate (DCR) over the aggregate dataset, successfully intercepting dynamic violating traces in the evaluated trace-conditioned scenarios.

Real-world vulnerabilities often span multiple functions, yet most learning-based detectors classify each function in isolation: on a sample of real CVEs, we find that 71.7% of vulnerable functions require evidence from outside the function to be classified correctly. Agentic reinforcement learning (RL) could close this gap by enabling a model to gather that evidence itself, but it lacks a reliable reward, since a reward defined on the final verdict alone can be obtained without performing any investigation. We propose VulAgentRL, an agentic RL framework for interprocedural vulnerability detection built on a Code Property Graph (CPG). The CPG serves two roles: at inference time the policy queries it for callers, callees, dataflow, and other queries, and at training time the same graph verifies the evidence the policy cites. Because every CPG node carries a persistent integer identifier, this verification is an exact comparison rather than a textual match, so the reward credits verdicts that are supported by evidence. We further initialize the policy by distilling teacher investigations, and show that this warm start is necessary, since RL cannot acquire tool-use behavior it never samples. Under a repository-level split that prevents leakage, VulAgentRL outperforms state-of-the-art baselines, including frontier models, on the strict pair-wise-correct metric while issuing fewer tool calls, and its advantage persists on an out-of-distribution corpus and under class imbalance.

Speculative Decoding (SD) accelerates large language model inference by allowing a lightweight draft model to propose tokens that are subsequently verified in parallel by a larger target model. Recent approaches introduce lossy verification schemes to further improve efficiency by relaxing strict distributional matching. Yet such relaxation silently rewrites the decoding distribution, and the resulting acceleration can come at the cost of unstable, sometimes severely degraded generation quality. In this work, we present a principled analysis of the distributions induced by lossy verification methods. We show that many seemingly distinct approaches differ only superficially and can be classified into two categories: truncation-based verification and collaborative verification. We further construct a diagnostic evaluation framework across curated benchmarks. For truncation-based methods, we identify a fundamental pitfall: performance can degrade significantly compared to the true truncation sampling baseline due to distributional distortion. For collaborative verification, we uncover a key principles: controlling the overshoot of draft probabilities relative to target probabilities is essential to prevent low-quality outputs. Our code is available at https://github.com/ZhouYuxuanYX/Fast-HSD.

AI agents can draft claims faster than authors can check whether the cited or retrieved evidence supports them. We study evidence-ledger adjudication: a claim-evidence traceability workflow that pairs each claim with an evidence packet, assigns a support relation, and routes unsupported, contradicted, or mixed-evidence claims back to the author. The empirical core is a 2,335-row blind benchmark built from independent external labels in AVeriTeC, CLIMATE-FEVER, and SciFact. Gold relations and source evidence labels are hidden during prediction and joined only for scoring. On this benchmark, the agent evidence-ledger condition achieves 0.676 relation accuracy and 0.601 macro-F1, compared with 0.383 accuracy and 0.303 macro-F1 for the best non-agent baseline. It also routes 1270/1435 claims whose gold labels indicate contradiction, missing evidence, or mixed evidence, while routing 295/900 supported claims. These results show that evidence-ledger adjudication can turn heterogeneous evidence packets into an auditable traceability layer for AI-assisted writing.

Functional verification dominates integrated circuit (IC) front-end engineering effort, and a single missed bug that escapes to silicon can trigger a costly respin. Recent large language models (LLMs) offer new opportunities to automate this process, yet existing LLM-based approaches generate each component through independent single-turn calls with no shared context, leaving interface mismatches undetected and reported coverage disconnected from specification requirements. To address these challenges, we present GoGoTB, an agentic framework that achieves end-to-end verification closure through three subsystems: an agentic execution control layer, an evolvable knowledge system, and specification-grounded coverage closure. The execution control layer separates deterministic enforcement from LLM reasoning at every tool and stage boundary. The knowledge system dispatches methodology and design-specific expertise on demand. The coverage framework anchors every bin to a named specification behavior so that each residual gap has a diagnosable root cause and a targeted remedy. Tested on 8 register transfer level (RTL) designs without any human intervention, GoGoTB achieves 100% environment generation success and averages 98.4% line, 97.2% branch, 97.0% toggle, and 83.2% functional coverage. No prior work successfully generates a complete verification environment or achieves meaningful coverage on the same benchmarks.

Comprehensively evaluating AI agents across interactive environments is difficult due to fragmented tasks, scaffolds, verifiers, and scoring rules. Unfortunately, existing efforts to unify these evaluations are limited in scale and domain, making costly reruns necessary and leaving available data incomparable. We introduce MESSIER, a unified corpus of 957,611 records spanning 30 benchmarks, 745 agents, 11,891 tasks, and 74,263 verifiers. MESSIER combines public evaluation results with new runs on six underrepresented professional and scientific benchmarks, standardizing their heterogeneous components into a common schema. Using this corpus, we show that frontier progress is uneven across benchmark groups, with function-calling evaluations largely saturated, programming improving fastest, and enterprise workflows remaining most challenging. Counterfactual rescoring further shows that strict all-pass scoring in multi-verifier tasks can alter agent rankings. Finally, we derive capability scores from our corpus that correlate with Epoch's Evaluation Capability Index rankings at Spearman \r{ho} = 0.84. The scores can also be estimated for subsets defined by domain, occupation, action space, or verifier type. In essence, MESSIER is a reusable resource for studying agent performance at scale, and a basis for designing better evaluations.

Self-improving agents accumulate capability by repeatedly rewriting procedural policies, controllers, or heuristic rules. They typically rely on self-authored tests or metrics to decide whether to accept subsequent edits. The agent controls both the optimized object and its verifier. As a result, self-assigned scores can remain near perfect while real deployment performance degrades or stays low. We study this problem through the verifier--deployment gap. This gap refers to the discrepancy between an agent's self-authored verification signal and a sealed deployment evaluation that the agent cannot observe or access. We ask how self-authored verification fails under iterative policy-and-test rewriting, how the failure changes with capability, and how little exogenous trust is sufficient to prevent real regressions from being deployed. To address this problem, we introduce a Sealed Exogenous Acceptance Loop (SEAL). SEAL retains self-authored tests but compares each candidate with the incumbent through a fixed harness-side audit. The agent cannot author or inspect the audit, receives only accept/reject, and the whole incumbent state is retained after a clear regression. Our experiments show that this problem often appears in heuristic learning settings. These settings require trial-and-error discovery of the target objective. We further find that failures of self-written verification are stratified by capability. Weaker agents tend to damage previously acquired strategies behind easy self-tests. Stronger agents are more stable, but they still mismeasure the deployment distribution. Standard self-written constraints do not reliably close this gap. In contrast, SEAL outperforms unprotected baselines across six models and three random seeds. Reliable self-improvement need not abandon self-verification, but it requires at least one deployment-acceptance signal outside the agent's control.

The recently deployed Entry/Exit System (EES) introduces large-scale biometric verification into European border control, requiring face recognition systems to operate at extremely low false match rates (FMR). While regulatory frameworks define performance targets at the EES Central System level, they do not specify how verification thresholds should be calibrated in practice at the Member State level. In operational settings, obtaining representative real-world data for calibration is often constrained by legal, logistical, and privacy limitations. In this work, we investigate the use of synthetic face data for threshold calibration in document-to-live verification scenarios relevant to border control systems. We analyze the alignment of genuine and impostor score distributions between synthetic and real datasets and evaluate the transferability of calibrated thresholds across domains, with a focus on low-FMR operating points. Our results show that synthetic data can approximate calibration behavior in controlled settings, but fails to reliably generalize to unconstrained conditions due to mismatches in score distribution tails. These discrepancies lead to significant degradation in recognition performance and increased vulnerability to morph-based attacks. We further demonstrate that calibration outcomes are highly dataset-dependent, even across synthetic datasets. Overall, our findings highlight that while synthetic data is useful for system development and preliminary calibration, our results indicate that reliable threshold selection in high-security deployments typically requires validation and adjustment using representative real-world data.

Online platforms increasingly rely on automated age estimation systems to enforce minimum-age policies. Focusing on vision-based models designed for this task, concerns arise regarding their robustness to simple appearance changes that underage individuals may use to bypass such systems, such as drawing a mustache or applying lipstick. In this work, we present a systematic study of age verification robustness by simulating visual alterations that can be easily achieved by underage individuals. We evaluate seven models, including vision, vision-language, and multimodal large language models, across three datasets and four manipulation types. Interestingly, under drawn beard stubble, up to 61% of True Negatives are flipped into False Positives. Furthermore, we investigate how different demographics are affected by such manipulations, finding that Indians are more affected by beard stubble manipulations, while females are more affected than males across all manipulations. Finally, we explore how these biases can be mitigated using bias mitigation methodologies in lightweight linear probe settings.

Improving a language model today means retraining it: enormous compute, a new opaque model each cycle, non-deterministic output. We take the opposite path: the model stays frozen, and a persistent memory of verified solutions grows beside it. Once a problem family is solved and has passed an independent verification step that never consults the answer key, every new instance of that family is answered at zero generation tokens, bit-exact, deterministically. Across 180 fresh instances spanning nine problem families, four architectures from four vendors - dense and mixture-of-experts - each score 180/180 at zero generation tokens per answer: execution-bound capability decoupled from parameter scaling. A negative control attributes the capability fully to the memory: emptied, it solves nothing. The same verify-before-store contract holds for open-ended reasoning: 88/88 consistency-gated acceptances across all four models, machine-checked formal proof, and reasoning-method transfer at 77/80. Memory selection takes 1.4 microseconds; a full reuse completes in 6-23 ms at 36 mWh. Approximate similarity retrieval selects the wrong item 94.3% of the time on a 4,500-item verified store where exact addressing makes zero errors. The store also serves as working context at a scale no shipped engine matches: a 6,000,000-token movable window on a single 46 GB GPU at flat memory, where vLLM stops at 30,399 tokens and SGLang silently truncates past 32,000. On published benchmarks, frontier models remain far ahead of any 12B at raw from-scratch reasoning; on everything this system has solved and verified, the comparison inverts: a frontier API call pays a fresh generation pass on every query, forever, while verified reuse costs zero tokens and returns the identical bits every time. A public testbench with free, rate-limited access accompanies this report: https://corbenic-galahad-bench.hf.space

This paper presents GEMCo, a releasable, human-written proxy for inaccessible counselling data: 86 complete German e-mail counselling conversations (728 messages), expert-authored cases and counsellor sessions with trained role-players. It is validated against a held-out reference of 124 real counselling conversations. The proxy and the real conversations are measured against each other on counsellor strategies and client emotions. The gap is detectable but small. A generative validation supports the analysis. The corpus is the primary contribution. The validation method generalises to any domain where real data cannot be shared but a human-made proxy can. Privacy and ethics keep real counselling data closed. GEMCo carries none by design and can be released, a first step toward language research in this domain.

We present DualityCert, a symbolic verifier for candidate Seiberg-duality claims in four-dimensional N=1 quiver gauge theories. The verifier evaluates 't Hooft anomaly matching, superpotential R-charge consistency, central-charge matching, and a bounded chiral-ring proxy. A claim that passes receives a consistency certificate, which states that no tested inconsistency was found, not that the duality is proven. We use the verifier as a repair environment for language-model agents, which receive a deliberately broken claim and must edit it until it certifies. On a preregistered benchmark of 145 broken claims, with the analysis fixed before the first confirmatory model call, verifier-gated retry improves final repair success over a single attempt by +8.3 percentage points (pp) on deepseek-chat and +7.1 pp on qwen-plus (Holm-adjusted p<0.002). Under an equal budget of eleven attempts, the stop-first strategy portfolio underperforms independent verifier-filtered resampling by 10.3 percentage points on deepseek-chat but outperforms it by 14.7 points on qwen-plus, reversing the ordering of the two tested verifier-exploitation policies across the two confirmatory models. On qwen-plus, category-level verifier feedback is worth +8.7 pp over content-free retry, and interpretable obligation identities alone are worth +6.4 pp over structurally identical masked feedback. Neither effect is detected on deepseek-chat. Separately, a preregistered MiniMax-M2.5 extension again finds an iteration gain and independent verifier-filtered resampling outperforming the strategy portfolio. Which policy is better thus differs between the two models, while every winning policy uses the same cheap certificate. The verifier, benchmark, protocol, and all per-attempt records are released.

Razborov's flag algebra method is a powerful tool for proving asymptotic inequalities in extremal graph theory, often reducing the task to finding a finite certificate by semidefinite programming. We present a machine-checked formalization of the method for finite simple graphs, together with a certificate-to-proof compiler that turns externally generated certificate data into algebraic proofs checked by Lean. The formalization covers the foundations of the method: partially labeled graphs, their densities in large graphs, the quotient algebra of density expressions, graph-limit semantics through positive homomorphisms, and the downward operators used to average out labels. The compiler treats the external semidefinite programming output as candidate data rather than trusted input: Lean independently computes the required density and multiplication facts, verifies positive semidefiniteness exactly over $\mathbb{Q}$, and carries out the algebraic normalization steps of flag-algebra proofs. Our case studies yield formal proofs of seven Turán-type upper bounds, including Mantel's theorem and the Erdős pentagon theorem, a $C_4$-density bound for triangle-free graphs, and edge-density bounds for $K_4$-free, $K_5$-free, and $C_5$-free graphs. Independently of the compiler, we formalize the matching constructions that complete the exact Turán densities of Mantel's theorem and the Erdős pentagon theorem, and prove two inequalities of Goodman. Our constrained semantics also prompted a meta-theoretic comparison of two ways of imposing graph constraints: building a hereditary constraint into the flag algebra from the start, or testing inequalities afterward on constrained graph limits with labels chosen at random. We state the resulting root-plantability criterion characterizing when the two approaches agree; a forthcoming paper will present the complete account.

Lean 4's grind tactic combines congruence closure, E-matching, and case-splitting into a single automated solver, and like any such solver, it relies on hand-tuned heuristics to decide what to instantiate and where to case-split. These heuristics are tempting targets for learning, but there is a catch: because grind's search is non-monotone, a learned heuristic that helps one proof can break another, and an always-on replacement usually nets out near zero. We avoid this by invoking a learned intervention only after stock grind has already failed: a failure-triggered cascade that, by construction, cannot lose a proof grind already had. We apply it to two of grind's internal decisions. A cost-aware E-matching filter solves slightly more problems and runs about 5% faster. A lookahead step proves five theorems it otherwise times out on. We also report the negative result that motivated the design: across four feature-based models, statically predicting the correct case split is no better than random, because whether a split explodes is a runtime property that the features do not capture. Our results suggest that learning within theorem-proving tactics is most effective as a mechanism for deciding when and how to spend bounded search, backed by a reliable symbolic fallback.

LLM training is shifting from manual design and annotation to interaction-driven self-evolution. However, existing self-evolutionary methods face a fundamental dilemma between task diversity and verification reliability: environment-bound methods obtain precise feedback but confine learning to narrow domains, while open-ended self-generation broadens the task space but lacks reliable verification, allowing misleading rewards to pollute the training loop. We identify agent skills as a powerful middle ground to reconcile this tension: each skill ensures deep, verifiable execution in a specific scenario, while dynamic routing across skills maintains open-ended task variety. Leveraging this insight, we introduce Skill Self-Play (Skill-SP), a co-evolutionary framework comprising a proposer, a solver, and a dynamic skill controller. Orchestrated via a reinforcement learning loop, these components co-evolve in a continuous self-play loop: the proposer generates challenging tasks conditioned on dynamically sampled skills; the solver explores candidate solutions to push its capability boundaries; and the skill controller collects execution feedback to update and expand the skill library. This interactive co-evolution effectively bridges the gap between structured verification and open-ended exploration. Empirical evaluations on tool-use and reasoning benchmarks demonstrate that Skill-SP, serving as a robust evolution engine, consistently pushes the performance ceiling of competent backbones while catalyzing striking turnarounds for initially misaligned models. Our code is available at https://github.com/Qwen-Applications/skill-self-play.

Automating theoretical research requires generating candidate results and evaluating them reliably. Models keep getting better at the first, while the second remains hard. A common approach asks one large language model (LLM) to review what another produced, yet such reviewers are empirically unreliable: they may accept fabricated papers and catch the fabrication at close to chance rates~\citep{badscientist2025}. We present \textsc{CausalSmith}, a framework for automated theoretical research in causal inference built on the Lean proof assistant, where a proof is checked by a program rather than read by a referee. \textsc{CausalSmith} rests on \textsc{Causalean}, a foundational Lean library for causal inference holding 8,179 machine-checked definitions and theorems, developed with language-model assistance under human design and review. Around it, we build a self-improving agentic pipeline that selects research topics, proposes results, formalizes statements, constructs proofs, and presents the resulting artifacts for human inspection. Moreover, the pipeline pairs Lean verification with a statement audit that compares each formal theorem against the informal claim behind it. We evaluate the system using artifacts produced by completed autonomous research runs. The source code, formal library, and run records are available at https://github.com/Jiyuan-Tan/CausalSmith.

Resolving Design Rule Violations (DRVs) in layouts entails an iterative loop of geometric edits and verification. We present DRC-Aid, a closed-loop agentic framework that automates local DRC repair by formulating it as verification-in-the-loop search. To constrain the combinatorial geometric repair space, a deterministic Rule Engine converts physical verification tool-reported violations into a bounded menu of geometric edits. An off-the-shelf Large Language Model (LLM) evaluates local geometric context to select edits from this menu, with budgeted depth-first search and backtracking. Immediate feedback from verification tools such as Calibre nmDRC/nmLVS enforces geometric compliance and guards against electrical-topology degradation, while a global Memory Bank prevents cyclic re-exploration. Evaluated on FreePDK45 layouts containing DRVs, DRC-Aid achieves DRC-clean, LVS-equivalent repairs in ~92.5% of cases with a ~98% total violation reduction, while residual cases yield partially repaired LVS-equivalent candidates. Under an identical search and verification infrastructure, LLM-based selection outperforms random (54.4%) and deterministic-heuristic (83.3%) policies, with the gap widening on cases with six or more violations.

Large language model (LLM) agents routinely cheat on cybersecurity benchmarks, inflating reported pass rates far beyond genuine capability. Prior audits of Cybench found cheating in 0.3-3.4% of traces, implicating only a handful of models. We present a controlled prompt-ablation study across 22 frontier models from 7 providers on 23 Cybench capture-the-flag (CTF) challenges under three prompt conditions (no anti-cheat, standard, severe). All 1,518 task traces were individually audited through a four-stage pipeline combining LLM-as-a-judge classification, programmatic verification, judge-verifier reconciliation, and human review. We find cheating is far more pervasive than previously estimated: under baseline conditions, 37.1% of passes involved cheating, 21 of 22 models cheated, and scores were inflated by up to 5x. Anti-cheat prompts reduce cheat propensity from 33.0% (baseline) to 17.8% (standard) to 8.5% (severe) without degrading, and sometimes improving, solve rates. However, even under the most restrictive prompt condition, eight models still produced cheated passes, four showed backfire effects, and cheating escalated from web search toward infrastructure probing. We introduce the "solve rate" metric (clean passes only) to distinguish genuine capability from cheated outcomes, and argue it should be standard practice in any evaluation where cheating vectors are available. Anti-cheat prompts are an effective and essentially free first layer of defense, but they are not a substitute for environmental controls.

The reliance on unstructured free text for documenting clinical trial protocols creates a significant barrier to automated reasoning, cohort discovery, and trial simulation. The lack of formal structure obscures critical temporal phenotypes, such as dynamic eligibility criteria and event timing constraints. Although Temporal Ensemble Logic (TEL) offers an expressive framework for modeling these elements, manual encoding remains a prohibitive bottleneck. We introduce the CT-TEL workflow: a scalable pipeline leveraging Large Language Models (LLMs) to translate narrative clinical protocols into TEL formulas. We applied CT-TEL to generate logical models for 23 real-world trials from ClinicalTrials.gov. We evaluated translation fidelity via a back-translation approach, using LLMs to convert TEL formulas back into natural language and measuring semantic similarity against source texts. The resulting semantic retention suggests that LLMs may offer a pathway for mapping informal protocols to computable logic, providing preliminary evidence toward scalable clinical trial emulation within the emerging "Symbolic Biomedicine" paradigm championed by the corresponding author.

Ninety-Nine Prolog Problems (P-99) is a famous set of Prolog exercises. We solved the first thirty three just by prompting an LLM (Large Language Model). We used Claude from Anthropic. By solved we mean: generate the Prolog code and a test file, run the tests and check whether they pass, then formally prove types, groundness, termination, uniqueness, existence and also sometimes functional correctness with LPTP (Logic Program Theorem Prover). Hence our approach is an experiment in vibe-coding/vericoding of P-99. It is a vibe-coding experiment because we started from informal specifications written in English and let Claude generate the Prolog code. It also fits within vericoding because the LLM proved reliability guarantees on the generated Prolog code. Claude wrote 58 logic procedures, 508 tests, 257 lemmas for a total of 11800 proof lines. We manually checked each file generated by the LLM. We checked the Prolog code, ran the tests, examined the logical statements generated by Claude and proof-checked Claude's proofs with LPTP. This paper describes this experiment and provides the main details so that it can be reproduced by the interested reader.

Event-B is a formal method rooted in predicate logic and set theory. We encoded over 600 proof rules in Prolog, enabling a systematic, comprehensible proof analysis and construction. By integrating the proof rules into the Prolog-based validation tool ProB, we obtain an interactive proof system with proof tree visualisation. This has advantages in teaching, giving students direct control over the selection of proof rules. Our tool can import proof obligations from the Rodin platform and provides multiple exports: a trace file for proof replay in ProB, an interactive HTML document for tool-independent exploration of the proof tree, and an export back to Rodin, allowing the ProB prover to be used as second chain. Compared to the previous implementation of the proof rules in Java, the encoding in Prolog is more compact, maintainable and extensible. While a preliminary iterative deepening prover with simple heuristics is already available and useful for finding short proofs, we aim to obtain fast automatic provers in the future.

We present the interactions with an LLM (Large Language Model) aiming at proving that the square root of 2 is not a rational number in an LP (Logic Programming) context. We start from a few basic pure logic programming predicate definitions. We rely on the LPTP (Logic Program Theorem Prover) system for stating and proving properties about logic programs. As the proof language of LPTP is based on natural deduction, the proofs are human readable. In our case study, we sketch in LPTP the usual proof showing the irrationality of the square root of 2. Then we describe the interactions we had with the LLM. We end up with a complete formal proof, partially generated by an LLM and fully proof-checked by LPTP.

Outsourced Transformer inference exposes clients to model substitution and incomplete execution, while direct replay removes the computational benefit of delegation. We present GKR-HND, a registered-model protocol for verifying the polynomial backbone of Homomorphic--Nonhomomorphic Decomposition Transformers. The retained verifier checks the GKR transcript and registered-weight openings, but delegates expensive public evaluations to an assigned computation worker. Assuming an honest retained verifier and prover--worker non-collusion, the verifier accepts only when the worker's signed, request-bound response agrees with the proof claims. Experiments with pretrained HND models validate the proof path and the delegated public computation without dense-matrix replay.

Visible tests are a common gate for LLM-generated code, but passing them does not certify specification correctness. We study a deployment-like monitoring problem: after code has passed public tests, can a weaker LLM verifier identify the residual hidden bugs? We introduce Code Monitor Red Teaming, a monitor-red-teaming protocol that fixes a public-check information boundary while varying generator pressure, verifier scaffolding, and weak-to-strong capability. We instantiate it as CodeMonitorBench, spanning function-level, data-science, and workflow code. Across 71,000 generated candidates, 43,677 pass public tests and 23,081 of those fail hidden tests. Weak verifiers improve with scaffolding and model family, but still miss most hidden bugs at 5% false-positive rate. As a robustness stress test, adversarial public-test-overfit pressure lowers verifier AUROC and raises low-FPR miss rates in most cells. A GLM-5.1 verifier recovers part of the gap under the same evidence boundary; an inferability audit shows that remaining misses mix verifier failures with M1 evidence limits.

Cognitive remediation tasks often require patients to perform structured actions involving object manipulation and sequential reasoning. For patients diagnosed with schizophrenia, these tasks are crucial for addressing severe cognitive deficits. However, evaluating the correctness of these physical actions generally relies on manual observation by clinicians, which introduces subjectivity and limits the scalability of therapeutic interventions. In this paper, we propose an automated framework based on Vision-Language Models for action verification in cognitive remediation tasks tailored for schizophrenia rehabilitation. The proposed system relies on a camera-monitored tabletop environment composed of structured miniature scenes including roads, a roundabout, a park, and toy vehicles. Patients receive audio instructions describing goal-oriented spatial actions to perform by manipulating a toy vehicle. These interactive physical activities are specifically designed to stimulate targeted cognitive functions, such as sustained attention, motor coordination, spatial navigation, and cognitive flexibility. To verify the correctness of the performed actions without requiring continuous clinical oversight, the system analyzes the video feed tracking the patient's hand and toy movements. A fine-tuned Vision-Language Model interprets the recorded video sequences and generates semantic descriptions of the observed activities, enabling high-level verification of the executed actions with respect to the initial textual instructions. A dedicated dataset of 4634 tabletop cognitive remediation video scenarios was collected to evaluate the proposed approach. Experimental results demonstrate that our specialized framework effectively bridges low-level physical telemetry with high-level clinical feedback, presenting a scalable and objective solution for advanced cognitive rehabilitation.

Agentic systems large language model (LLM) based architectures capable of reasoning, planning, acting, and coordinating with tools and other agents are rapidly transitioning from research prototypes to production scale deployments across domains such as software engineering, scientific discovery, and finance. While academic work has emphasized benchmarks and algorithmic innovation, deployment raises new challenges around robustness, safety, and reliability. This tutorial brings together researchers and practitioners to explore advances in reasoning and planning, multi agent coordination, and evaluation, highlighting open challenges arising from deployment experience. Through applied case studies in pharmaceutical discovery and financial systems, we analyze common design patterns that make agentic systems successful, and discuss practical mitigation strategies for failure modes, such as verification pipelines, fallback mechanisms, and human in the loop supervision. Attendees will gain a comprehensive view of the field along with concrete design patterns, evaluation checklists, and templates for safe and reliable deployment across industries.

Circuit extraction identifies a small set of model components whose presence preserves a target behavior under ablation, and the resulting circuit is often read as the mechanism behind that behavior. We argue that this reading is under-determined: preserving behavior does not single out one circuit, because the claim it supports depends on which circuit is reported and how two circuits are compared. We make this concrete in a synthetic Lean tactic-prediction benchmark -- predicting the next step of a proof -- where fixed proof rules with randomized surface form let differences between extracted circuits be attributed to these choices rather than to the task. Across dense and weight-sparse checkpoints (most weights constrained to zero) of the same transformer, evaluated on atomic (single-rule) and compositional (multi-rule) proofs, we vary which extracted object is reported (a compact prediction-preserving circuit, a broader graph that also keeps surrounding read, write, and routing structure, or the smallest subgraph meeting a post-ablation loss threshold), and whether each attention head's query and key are represented jointly or separately. Exact component-to-component edge overlap is low and sensitive to these choices, at times dropping to a random baseline, while two coarser summaries stay stable: the set of selected attention heads, and the circuit-size ranking of conditions that differ in which supervised checkpoint initializes reinforcement learning (RL). The largest accuracy gains from RL on compositional proofs come with the most structure beyond the atomic circuits. A circuit-level claim is therefore well defined only once one states which circuit is reported, the pruning threshold used to extract it, and the level at which circuits are compared. We distill these requirements into a reporting practice for circuit-extraction studies.

Agentic commerce protocols such as AP2 and ACP define mechanisms for secure agent-initiated transactions but do not provide interoperable, tamper-evident auditability or verifiable temporal ordering of events across heterogeneous domains. This paper addresses these gaps by proposing a verifiable global event timeline for agentic commerce, constructed from four core components: canonical event schemas that enforce deterministic serialization, deterministic batch formation ensuring reproducible ordering without reliance on synchronized clocks, Merkle-based append-only commitments providing logarithmic-cost inclusion proofs, and blockchain anchoring establishing a tamper-evident temporal backbone. Building on this infrastructure, we introduce a cryptographically signed fraud marker that binds risk labels to anchored evidence through an unforgeable provenance chain, and a dataset lineage model enabling reproducible, tamper-evident AI training pipelines. Empirical results from a prototype implementation demonstrate: Merkle tree construction processes 50,000 events in 47 milliseconds; end-to-end verification completes in under 0.013 milliseconds regardless of batch size; inclusion proof sizes grow logarithmically from 320 bytes at 1,000 events to 512 bytes at 50,000 events; and Merkle-based verification outperforms linear scan by 14.4x at 50,000 events.

This paper explores a way to verify that audio has not been maliciously tampered in a specific context: short viral videos taken from news recordings. Rather than trying to detect artifacts of tampering (internal inconsistency), we focus on positively verifying a query against a trusted source such as a news recording (external consistency). We propose a method for cross verifying a short audio query against a reference recording from which it was taken. Our approach is to define two hypotheses (non-tampered vs tampered), calculate the most likely alignment between query and reference for each hypothesis, and then perform a likelihood ratio test on the two alignments. We show that this method is fast to compute, much more robust than using MFCC features with Euclidean distance, and has the key benefit of explainability. Our cross verification approach provides an alternative perspective and complementary tool to existing tampering detection methods.

Large language models (LLMs) now routinely draft literature reviews and assist with academic writing, which means a higher risk of fabricated references: GPTZero found 53 papers with hallucinated citations among NeurIPS 2025's accepted set. Rule- and LLM-based verifiers are emerging, but no shared benchmark compares them and gives detailed failure diagnostics. We close that gap with HALLMARK (Hallucination benchmark): 2,526 BibTeX entries spanning 14 hallucination types, three difficulty tiers, six diagnostic sub-tests per entry, and a contamination-resistant held-out split. On it we evaluate a DOI-lookup baseline, frontier LLMs zero-shot, tool-augmented agents, and our own rule-based, co-designed verifier bibtex-updater. Across the benchmark one result is consistent: the false-positive rate, not recall, decides whether a verifier is deployable. HALLMARK makes it concrete through three failure modes: agentic lookups buy recall but inflate false positives; at a venue-realistic base rate, the order-of-magnitude spread in false-positive rates (FPRs) -- not recall -- governs whether a verifier's flags are mostly true catches or mostly noise; and most LLMs over-flag papers published past their training cutoff, where only the two latest-cutoff models hold their false-positive rate near in-distribution levels (a signal we report as descriptive, since it is confounded with possible recall of those entries). Thus FPR is the deployment bottleneck, but an undetected fabrication remains the costlier error for the scientific record.

Verify-repair loops are a standard means for large language model (LLM) agents to correct faulty plans in code generation, mathematical reasoning, and tool use. When both the verifier and the repairer are noisy, repair can damage already-correct plans, and reported acceptance keeps rising while true validity falls, so existing methods lack a principled basis for deciding when repair should stop. We propose VRR-Stop, a robust stopping framework for noisy verify-repair-repeat (VRR) loops. A four-parameter noise model separates verifier false acceptance and false rejection from the repair and damage behavior of the repairer. Belief filtering turns repeated verification votes into an estimate of committed validity, and the loop commits or repairs according to the sign of the true marginal gain, which requires only sign identifiability rather than accurate recovery of all parameters. When verifier discrimination approaches zero, calibration itself fails and estimation error can flip the stopping sign, so we pair VRR-Stop with VRR-Guard, an estimation-free fallback that replaces the incumbent candidate only under a sufficient verification margin. On a GSM8K stress setting, VRR-Stop improves final true validity by 60.6 percentage points over fixed five-round repair at an average cost of 0.72 repair rounds. Across settings, stopping reliability is governed jointly by verifier discrimination and the decision margin rather than by the absolute size of estimation error.

Test-time collaboration, including self-consistency, best-of-N selection, critic models, and verifier pipelines, is often credited with broadly improving LLM reasoning, yet its gains are uneven and sometimes negative. We ask when training-free collaboration should be expected to help. For a fixed candidate pool, we decompose a selector or verifier's net gain into measurable factors: recoverable mass, verification-signal coverage, conditional selection quality, and harm to already-correct outputs. This reframes collaboration as a candidate-selection problem rather than as an intrinsic property of a multi-agent topology. Across LiveCodeBench, MATH Level-5 hard subjects, and GPQA-Diamond, gains are bounded first by the oracle gap and then by signal fidelity, which we measure directly as candidate-level agreement between verifier verdicts and official labels. On LiveCodeBench, a public-test verifier (MCC 0.825) gains +8.14 percentage points (pp) over a first-sample baseline; a generated-test verifier (MCC 0.248) improves by +2.70pp and is not statistically distinguishable from an LLM selector, but operates at near-zero harm versus the selector's 4.69% harm rate. On MATH, a symbolic answer-equivalence selector beats self-consistency by +4.67pp, while LLM selectors are negative. On GPQA-Diamond, recoverable mass is only 3.03% and 87.54% of candidate pools are answer-identical; a weaker model's pools shrink both further, suggesting that oracle gap is a joint property of task, model, and sampling configuration. Our framework yields a practical pre-deployment diagnostic: estimate the oracle gap, then measure coverage, signal fidelity, and harm before investing in collaboration.

Large language models confabulate chemical objects (molecular formulas, space groups, formation energies) in fluent reasoning traces, concentrated on long-tail entities where confidence is least trustworthy. Deterministic, database-grounded verification can catch and repair such errors without the coverage cost of blanket retrieval; the binding constraint, we find, is detection, not repair. Our tiered verifier extracts each checkable claim, checks it against authoritative databases and physics, and feeds the reference into a gated correction loop. Across four models and 528 condition-pinned prompts, gated correction cuts committed-formula error from 22% to 4% at $3.2\times$ fewer retrievals than blanket augmentation, beating a conversational oracle. Repair succeeds wherever a flag fires (80--97%); the bottleneck is in-loop detection recall. Grounding improves the final answer only when the verifier's scope reaches the deliverable (83% to 90%), and the lift appears only where extractable long-tail error exists: absent on near-ceiling physical constants, large on isotope half-lives (11% to 0%).

We investigate the capacity of current language models to contribute to mathematical research. In Banach space theory, AI systems generated key ideas and proofs for five new results, which were then verified and refined by humans. We also developed an automated system that searches the literature for open problems and attempts solutions at scale. Our results show both the potential of language models for mathematical discovery and the continuing importance of expert verification.

Designing effective Lean proof agents is a central challenge in formal mathematical reasoning. Beyond building stronger provers, recent work emphasizes the workflow around Lean: how an agent decomposes proof obligations, uses tools and compiler feedback, diagnoses failures, repairs proofs, and maintains structured proof context. Motivated by code-level self-evolving agents, we study whether such workflows can be evolved rather than hand-designed. We present a self-evolving Lean proof agent in which a small fixed, trusted runtime wraps a fully mutable workspace: the proof workflow, prompts, and tools. Unlike most self-evolving systems, which optimize against a fixed external benchmark, our system coevolves the agent and its benchmark. Between generations, the highest-scoring agent (the champion) revises the active task distribution through a mastery-throttled curriculum update that introduces harder proof obligations only after the current level is mastered, and a single-anchor recalibration re-runs the champion on the updated benchmark to keep scores comparable as difficulty rises. All evolution stays inside a Lean-grounded verification loop: however the agent rewrites itself, a success counts only when its behavior yields Lean-verified proofs under a trusted snapshot, and each attempt must emit a machine-readable, Lean-grounded proof context whose representation may evolve but whose groundedness is enforced. We run the coevolving trajectory and a fixed-benchmark baseline for 15 active generations and compare them on a held-out miniF2F test split. The best coevolving agent reaches a 45.1% held-out solve rate, versus 12.7% for the seed and 32.0% for the best fixed-benchmark agent, showing that verifier-grounded self-evolution can improve Lean proof workflows under a coevolving benchmark.

Deep research agents increasingly operate over the open web, where relevant records coexist with redundant summaries, outdated reports, and misleading documents. Existing evaluations offer limited insight into whether agents preserve sound evidential standards when an ordinary-looking false document is deliberately seeded into a searchable environment and offers a direct shortcut to a conflicting answer. We introduce DRNOISE, a 100-task benchmark for answer recovery under misleading evidence. Each task has a unique gold answer supported by two corroborating indirect record chains; the paired noisy condition adds one plausible document that states a conflicting answer directly. The benchmark spans ten families of evidence operations. Across agents with strong clean-task performance, this single intervention causes 66-88 percentage-point accuracy drops. Trace analyses identify verification inertia as the dominant failure mode: agents often retrieve truthful records but stop before completing and reconciling the evidence chain, instead deferring to the answer-like document. Generic verification prompts reduce but do not close this gap. The setting is especially relevant to open-web deployment, where plausible falsehoods arrive through ordinary-looking pages rather than explicit attacks. Reliable deep research therefore requires more than retrieval and citation; it requires active reconciliation of direct claims with record-level evidence.

In this work, we investigate the effect of lookahead branching strategies in neural network verification. We present a general recipe to integrate lookahead into any branch-and-bound verifier and demonstrate how one of the current state-of-the-art branching heuristics, FSB, can be viewed as a special instantiation of the lookahead branching strategy. We also describe how, in addition to improving the quality of branching decisions, lookahead can generate additional lemmas that accelerate verification. We instantiate the method in two representative branch-and-bound-based verifiers (Marabou and $α$-$β$-CROWN), and demonstrate that lookahead leads to consistent speedups in verification time and up to $57\%$ more solved instances. Code is available at https://github.com/ai-ar-research/lookahead-branching.

Multi-step enterprise agent tasks fail in a characteristic way: single-pass inference has no checkpoint between deciding an answer and committing to it. We study one production system (Leni) whose architecture installs such checkpoints: verification loops (execute, observe, compare, correct) staffed by lightweight task-specialized post-trained models. We evaluate the unmodified production configuration on three public benchmarks stressing distinct failure modes: SpreadsheetBench Verified (silent computation error), BullshitBench v2 (premise confabulation), and the GAIA validation split (cascade error over long tool chains). The full system improves over its frontier base model by +11.0 percentage points on SpreadsheetBench (91.25% vs 80.25%, n=400, p<0.001), +7 to +10 percentage points on BullshitBench (98% vs 91%, n=100), and roughly +15 points on GAIA validation (75.2% pass@1, n=165; 83.0% best-of-k). Our central contribution is a decomposition of that uplift: most of it comes from scaffolding, routing, and specialist models rather than from the verification step itself, whose isolated contribution is small (+1.5 points) but concentrated at the top of the score distribution, where it converts otherwise-failing tasks. We instrument the loop end-to-end, yielding an empirical verifier confusion matrix (catch rate about 0.20, fix rate 0.75, no false-alarm regressions) that grounds a compounding-reliability model. Specialist-swap ablations suggest that the loop's value depends on who observes it: replacing the small trained verifier with the generating frontier model eliminates most rescues. A valid-premise control shows zero over-rejections in 100 expert-level questions.

Mathematicians distinguish proofs that explain, simplify, or introduce a nonstandard route, but these judgments are difficult to operationalize. We study a deliberately narrower construct: time-relative proof-route nonstandardness in formal mathematics. For a Lean theorem, PriorProof extracts the dependency footprint of its elaborated proof term and scores the weighted surprisal of that footprint under a retrieval-conditioned, hierarchically smoothed prior built only from an earlier quarterly snapshot of Mathlib. The method requires no hand-built technique ontology and no human labels: statement retrieval is learned from proof-derived contrastive pairs, while the scored object is read mechanically from proof terms. In a blinded topology study, 100 presentations collapse to 76 distinct underlying pairs: 12 canonical contrasts shown three times for consistency screening and 64 distinct stratified pairs. Against the majority of three retained domain raters, PriorProof agrees on 53/76 pairs (69.7%, Wilson 95% CI 58.7-78.9%), including 11/12 canonical pairs (91.7%, 64.6-98.5%) and 42/64 stratified pairs (65.6%, 53.4-76.1%). Score-gap quartiles are nonmonotone after repeat collapse; the endpoints are 12/19 (63.2%, 41.0-80.9%) in the smallest-gap bin and 16/19 (84.2%, 62.4-94.5%) in the largest, supporting an endpoint-calibration tendency rather than a resolved staircase. The best language-model condition agrees on 60/76 pairs (78.9%, 68.5-86.6%); on paired outcomes, PriorProof alone is correct on 8 pairs and the model alone on 15 (exact two-sided McNemar p = 0.210), so the difference is not established at this sample size. We therefore present PriorProof not as a replacement for expert or model judgment, but as a decomposable, time-anchored signal whose score gap provides an interpretable reliability indicator.

Linear-attention models replace the growing KV cache with recurrent states, but autoregressive decoding still reads, updates, and writes these states one token at a time. Speculative decoding can reduce this cost by verifying several draft tokens in one target pass, yet existing speculative systems are designed for Transformer KV caches. For stateful linear-attention targets, verification must follow recurrent dependencies across chains and branches, acceptance must update only the accepted state trajectory, and the drafter must avoid submitting candidates that waste stateful verification work. This paper presents SpecLA, a speculative decoding runtime for stateful linear-attention models. SpecLA verifies chains and trees with topology-aware kernels, stores compact factors produced during verification to recover accepted states, and uses confidence pruning plus a target-aligned EAGLE-style drafter to feed useful candidates to the verifier. On an NVIDIA H100 with a public GDN-1.3B target, SpecLA achieves up to 1.70x end-to-end speedup over autoregressive decoding.

State machine replication (SMR) and Byzantine fault-tolerant (BFT) consensus guarantee agreement despite a bounded number of arbitrary, colluding faulty participants. However, these guarantees rely on participants outside this set correctly executing the protocol's transition semantics. Agentic validators expose a weaker boundary: an authenticated, responsive, non-equivocating, and protocol-compliant reasoning participant may still endorse a semantically invalid transition due to reasoning errors. We call this failure mode an epistemic fault, and the collective phenomenon the Honest Quorum Problem (where "honest" means protocol-compliant, not semantically correct). Such a quorum can satisfy ordinary checks while forming a certificate for an invalid transition. Thus, agreement alone does not guarantee semantic validity or execution safety. Furthermore, because agentic validators often share model weights, training distributions, prompts, or toolchains, they are highly susceptible to correlated epistemic faults. We define Epistemic Byzantine Fault Tolerance (EBFT), a fault-tolerance model for agentic infrastructure and post-deterministic distributed systems. EBFT augments the conventional Byzantine fault bound with two separate, confidence-indexed quantities: $e_δ$ bounds coherent invalid endorsements outside the Byzantine set, and $u_ε$ bounds unusable validator support that degrades liveness. These quantities characterize semantic safety risk and liveness degradation independently. We derive quorum-threshold conditions for semantic validity, consensus agreement, liveness, and feasible threshold selection, and outline a calibration methodology for estimating these budgets. We show that adding nominally distinct agents improves fault tolerance only when it measurably reduces the upper-tail concentration of invalid endorsements or unusable support.

Interactive theorem proving (ITP) underpins program verification and formalized mathematics, but its manual effort limits scalability. LLM-based proof agents promise to ease this effort, but their heavy token consumption and API cost remain a major obstacle. We trace this cost to a shared root: current agents operate on serialized concrete syntax, emitting proofs as source text and recovering proof states through separate, line-number-based queries, so every edit shifts later lines and forces repeated relocation of errors and states. This same dependence on concrete syntax also blocks adoption of Minilang, a recent proof language that reaches SOTA on LLM-based proving but is too new for LLMs' training corpora. We address both problems by lifting the agent off source text and onto the abstract syntax tree (AST): the model supplies proofs as JSON representations of Minilang's AST -- native to tool-calling LLMs -- and drives the prover through a tree-edit model that fuses proof operations and states into one proof tree, so each operation carries its own subgoal's state, readable directly off the tree. We realize this design in \emph{Agent over AST} (AoA). Against Amazon's Isabelle Agent on miniF2F and NTP4VC-Pearl common success sets, AoA cuts API cost by 2.3--4.7x (normalized input-cache accounting), uses 2.9--6.9x fewer tokens and 3.9--8.9x fewer tool calls, and finishes 1.4--2.0x faster -- while also solving far more problems on the harder verification benchmark.

Motivated by the challenge of testing distributions over high-dimensional or continuous domains, we study distribution testing with respect to bounded classes of distinguishers. A representative task is to use samples from an unknown distribution $P$ over a very large domain to decide between two cases: $P = P_{\mathsf{ref}}$ for a fixed reference distribution $P_{\mathsf{ref}}$, or there exists a distinguisher $f$ in a bounded class $\mathcal{F}$ which witnesses the separation $|\mathbf{E}_P[f] - \mathbf{E}_{P_{\mathsf{ref}}}[f]| > ε$. This is the task of identity testing with respect to fooling distance, a name inspired by the conceptual connection with pseudorandomness. (Formally, our model instantiates integral probability metrics from Boolean classes of bounded expressivity.) We show that testing with respect to fooling distance is not only a natural computational problem that admits sample-efficient algorithms even in high-dimensional settings, but also one that reveals and underlies connections between three seemingly unrelated areas of study: testable learning, verification of learning algorithms, and testing of structured distributions (whose "$\mathcal{A}_k$-testing" model our framework extends). These connections yield new results for all of these models, including: 1. Testable proper learners using membership queries for halfspaces and decision trees. 2. A lower bound for testable PAC verification in terms of Rademacher complexity, and a distribution-free verification protocol for disjoint unions of $k$ multidimensional rectangles. 3. Identity testers (with respect to total variation distance) for decision tree distributions and distributions with low-degree polynomial densities, over Boolean and continuous hypercube domains.

Topos causal models recast causal inference inside a topos: a causal world is a presheaf, an intervention is a sub-model named by a characteristic map into the subobject classifier $\Om$, and reasoning is Kripke-Joyal forcing in an intuitionistic internal language. We give the first axiom-free machine-checked account of this 1-topos core, in Cubical Agda over a previously verified probability monad and do-calculus; the framework is otherwise developed on paper, with central claims stated rather than proved. Three of our results go beyond faithful transcription. We exhibit a contextuality obstruction the programme does not treat: pairwise-consistent local causal data with no global model, detected by a degree-one holonomy class. We delimit the claim that interventions are modelled by the subobject classifier: an intervention and an observation name the same subobject, so $\Om$ fixes the target of a do-operation but not the operation itself, which is surgery on the kernels --- where, on a confounder, the interventional and observational laws differ. And we settle the modal unit --- inflationarity is derivable from $j\top = \top$ and naturality, not a fourth axiom. We also machine-check the classifier of sieves with its classification theorem, the pullback collating local mechanisms, and the Kripke-Joyal forcing clauses. The development assumes no axioms and typechecks under Agda's \texttt{--safe} flag, with the ordered field discharged at $\mathbb{Q}$; type-level sheafification and a directed do-calculus are future work.

Autonomous coding agents increasingly execute multi-step software work, but lifecycle states such as reviewed, tested, DONE, and ready-to-merge remain claims unless supported by current evidence. We present Proof-or-Stop Lifecycle Control, a method that permits lifecycle transitions only when fresh, tracked-source-state-bound, mechanically verifiable evidence satisfies the relevant gate. The method treats agent outputs as claims rather than lifecycle state, and uses proof operationally to mean gate-admissible evidence under a stated trust model, not semantic program correctness. We evaluate an open-source implementation through mechanism tests, a powered control-policy ablation, and operated self-application evidence. The unattended-loop engine passed 10 of 10 scenarios with zero false-DONE, and local-key receipt bundles rejected 18 tamper classes with zero false accepts. In a 9,240-cell ablation, the pre-registered A4 versus A2-prime comparison reduced visible-pass/hidden-fail amplification from 31 of 1,800 injected cells under a compute-budgeted naive loop to 2 of 1,800 under the gated loop, a 1.6 percentage-point improvement in not-amplified rate with a 95 percent confidence interval of [0.8, 2.5]. A near-compute A3 versus A4 comparison, 14 of 1,800 versus 2 of 1,800, indicates that the gain is associated with enforcing review as a lifecycle gate rather than merely adding a reviewer. The self-application corpus contains 565 stories and 1,007 review findings, with 94.8 percent resolved, plus a 68-row high/critical cross-vendor exhibit. These results support Proof-or-Stop as a model-agnostic, host-neutral control layer for deciding which autonomous-agent claims a lifecycle may act on. The evaluation is limited to one model family, 24 ablation tasks, and a self-hosted corpus.

Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition. In this paper, we propose MathCoPilot, a human-in-the-loop system that embodies a new human--AI symbiotic paradigm for mathematical research, in which the mathematician steers the high-level mathematical direction while AI agents carry out the detailed formalization and proof work under continuous human guidance. MathCoPilot unifies three core capabilities: (1) an interactive workbench where the mathematician and AI agents collaborate through a living proof blueprint that decomposes a proof into navigable steps the human can directly inspect, direct, and refine; (2) automated proving skill orchestration with adaptive knowledge base search and Lean-integrated iterative verification; and (3) topic-driven paper retrieval and automated formalization into a verified Lean knowledge base. Using MathCoPilot, we systematically compare four state-of-the-art LLMs, including Gemini3.1Pro, GPT-5.4, and ClaudeOpus4.7, on a FormalMATH subset and on two real PDE theorems requiring deep domain expertise, evaluating their ability to produce verified Lean~4 proofs and to identify errors in deliberately incorrect proofs. Our results show that while current models can handle undergraduate-level problems with high success rates under favorable autoformalization conditions, substantial challenges remain for domain-specific theorems requiring genuine mathematical understanding.

Computer-use agents are becoming capable software operators, but their interface to desktop applications is still often a brittle motor layer: they look at screenshots, predict coordinates, click, and hope that the visible state changed as intended. This collapses target grounding, action execution, and outcome verification into a single ambiguous operation. We present Tactile, an open-source tool layer that gives agents a more reliable "hands and feet" for desktop use. Tactile converts heterogeneous UI evidence--operating-system accessibility semantics, OCR-grounded text, and visual fallback regions--into action-grounded interface states: compact target candidates with source labels, roles or text, state, geometry, executable affordances, and verification cues. Agents operate through an observe-ground-act-verify loop that prefers native semantic actions when available, falls back to OCR-grounded coordinates when visible text is the best evidence, and keeps full provenance for replay and failure attribution. On macOSWorld-style tasks, adding Tactile improves Codex Success@100 from 41.1% to 50.0% overall and from 45.2% to 55.3% on accessibility-adapted tasks; a 96-task cross-agent subset shows consistent gains across Codex, Claude Code, OpenCode, and Goose. These results suggest that reliable computer use requires not only stronger models, but also a reusable execution substrate that exposes software actions as semantic, verifiable, and auditable objects rather than anonymous screen coordinates.

We study exact verification of ReLU networks in an adversarial smoothed model. Every network weight and bias is independently perturbed by Gaussian noise, clipped to $[-2,2]$, and rounded to the exact dyadic grid determined by the input bit complexity. We show that, under the standard assumption $\mathrm{NP}\not\subseteq\mathrm{BPP}$, there is no sound and complete verifier whose expected running time is polynomial in network size, bit complexity, and inverse noise level for every base instance. The conclusion already holds at the fixed noise level $σ_\star=2^{-11}$ for one-hidden-layer networks over a unit box, with hidden fan-in at most three and base coefficients in $[-1,1]$. The proof combines an exact gap embedding with a quantitative robustness argument. For every E3SAT formula $Φ$ with $m$ clauses, a four-ReLU-per-clause construction satisfies $\max_{x\in[0,1]^n} g_Φ(x)=(m-\operatorname{unsat}(Φ))/3$, and coordinatewise threshold rounding never decreases the objective. A weighted parameter-sensitivity inequality and Gaussian concentration then show that a verification gap linear in $m$ survives the aggregate perturbation of all coefficients with probability at least $1-e^{-m/8}$. The proof includes clipping, exact dyadic rounding, output-layer perturbations, polynomial-bit sampling of the rounded Gaussian law, and the conversion from expected smoothed running time to a BPP algorithm. Computational checks test the exact identity and illustrate the different scaling of extensive and constant gaps; they are diagnostics rather than evidence for the complexity theorem. The result concerns worst-case base networks in the stated absolute-noise model, but it shows that parameter nondegeneracy alone does not yield a universal smoothed-polynomial guarantee for exact verification.

AI coding agents produce code faster than humans can review it. In our approach, the prover is the judge of whether the code is correct. Under a verifier-driven loop, AI agents wrote and verified bare-metal security software in Ada/SPARK spanning classical and post-quantum cryptography, TLS 1.3, IKEv2, X.509, and a Matrix client. GNATprove discharged 49,280 proof obligations, established functional correctness for selected primitives, and proved the absence of run-time errors for the rest, at roughly 20-40 times lower supervision cost than comparable hand verification. GNATprove alone was insufficient: some defects could not be detected and were resolved using known-answer tests, interoperability, or human review of specifications. Given weak checks, the agent tried to bypass them and reported success. We report where each layer caught faults and draw the central lesson: what an agent can be trusted to establish is bounded by the strength of its feedback.

The rapid proliferation of Agentic Artificial Intelligence fundamentally disrupts traditional customer loyalty paradigms. As AI evolves from passive recommendation algorithms to autonomous, goal-directed agents capable of executing purchasing decisions, the conventional understanding of consumer-brand relationships requires a structural reevaluation. By synthesizing extant literature across human-machine teaming, consumer decision-making, and algorithmic trust dynamics, we demonstrate that traditional loyalty models fail to account for algorithmic bounded rationality and constructed autonomy. To address this, we introduce the Dynamic Verifiable Multi-Agent Human Agentic Loyalty Loop (DVM-HALL) model. We formalize brand choice via a softmax probability formulation where human emotional equity, agentic machine-experience utility, calibrated trust, delegated authority, and verifiable execution jointly determine selection. The model features recursive updating mechanisms to dynamically calibrate trust and delegation after each interaction. Crucially, the framework integrates a verifiable execution layer for Decentralized Finance (DeFi) and tokenized loyalty settings, incorporating execution risks -- such as gas costs, slippage, MEV exposure, and smart-contract vulnerabilities -- as core predictors of agentic brand preference. Furthermore, we introduce the Net Human-Agent Score (NHAS), an auditable, risk-weighted metric designed to measure human-agent alignment using human feedback, execution logs, benchmark comparisons, and verifiable receipts. Finally, we propose a comprehensive three-stage empirical validation plan spanning controlled shopping experiments, multi-agent market simulations, and DeFi testbeds. This framework provides the foundational theory required for brands to navigate the impending transition toward machine customers.

Serial verification gates are a core reliability primitive in LLM harnesses: a candidate answer is returned only if $k$ verifier calls all accept it. Under conditionally independent gates, the recent Odds Law (arXiv:2606.15712) shows that posterior log-odds grow linearly in $k$, so failure decays exponentially, and states that "a tight theory of partially correlated verifier cascades remains open." This note gives a minimal such theory. Modeling the per-instance false-accept rate on the generator's own errors as a latent variable $α\sim G$ (de Finetti), the exact cascade posterior is $\ell_k = \ell_0 - \ln m_k$, with $m_k$ the $k$-th moment of $G$. Then: (i) $\ell_k$ is concave in $k$ for every non-degenerate $G$ -- the Odds Law is its tangent at the first gate and an upper bound; (ii) for Beta$(a,b)$ latents, failure decays polynomially, $1-r_k \asymp k^{-b}$, with correlation parameter $ρ_v = 1/(a+b+1)$; (iii) a blind-spot atom of mass $1-π$ at $α=1$ caps the evidence extractable from any number of gates at $-\ln(1-π)$ nats, so reliability saturates below 1; (iv) letting the true-accept rate also vary ($β\sim H$) yields a trichotomy -- gates eventually always help, plateau, or actively harm -- decided by the upper-tail exponents of $G$ and $H$, with closed-form crossover $k^\dagger$. The mechanism is survivorship: errors surviving gates are the high-$α$ ones. The theory is measurable: $R$ repeated verdicts per instance identify the first $R$ moments of $G$, so two verdicts identify $ρ_v$; beta-binomial likelihood and NPMLE recover the reliability curve and the ill-posed ceiling. In synthetic tests, independence-based extrapolation underestimates failure by 20x at $k=5$ and ~3000x at $k=10$; the correlated fit at $R=8$ tracks held-out depths. The practical lever is decorrelation -- changing model family, modality, or evidence source -- not adding gates.