Formal Foundations
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Formal Foundations and Proof-Carrying Certificates for q-ary Covering Codes in Lean 4
Announce Type: new Abstract: Covering codes in finite Hamming spaces ask for small sets of words whose Hamming balls cover the whole space. This paper presents a Lean 4 formalization of the elementary theory of q-ary covering codes, centered on certificate predicates for upper bounds, lower bounds, and exact covering numbers $K_q(n,r)$. The formalization proves the q-ary Hamming-ball volume formula, the sphere-covering lower bound, elementary exact cases, product and relation rules, and...
LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworks
Announce Type: replace Abstract: Large Language Models (LLMs) exhibit strong informal mathematical reasoning but struggle to generate mechanically verifiable proofs in formal languages like Lean. We present LEAP, an agentic framework that enables general-purpose foundation models to achieve state-of-the-art performance on automated formal theorem proving. LEAP leverages foundation model capabilities, such as informal reasoning, instruction following, and iterative self-refinement.
LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworks
arXiv:2606.03303v1 Announce Type: new Abstract: Large Language Models (LLMs) exhibit strong informal mathematical reasoning but struggle to generate mechanically verifiable proofs in formal languages like Lean. We present LEAP, an agentic framework that enables general-purpose foundation models to achieve state-of-the-art performance on automated formal theorem proving. LEAP leverages foundation model capabilities, such as informal reasoning, instruction following, and iterative self-refinement.
The Sim-to-Real Gap of Foundation Model Agents: A Unified MDP Perspective
arXiv:2606.07017v1 Announce Type: new Abstract: Foundation model agents are increasingly deployed for real-world decision-making, but suffer from the sim-to-real gap. While robotics and classical control have mature frameworks to address this gap, the foundation model community is treating agent robustness as an entirely novel phenomenon. Our paper proposes formalizing the foundation model agent evaluation and training gap as a classical sim-to-real problem structured entirely around the...
Modeling the Diachronic Evolution of Legal Norms: An LRMoo-Based, Component-Level, Event-Centric Approach to Legal Knowledge Graphs
arXiv:2506.07853v5 Announce Type: replace Abstract: Representing the temporal evolution of legal norms is a critical challenge for automated processing. While foundational frameworks exist, they lack a formal pattern for granular, component-level versioning, hindering the deterministic point-in-time reconstruction of legal texts required by reliable AI applications. This paper proposes a structured, temporal modeling pattern grounded in the LRMoo ontology.
Short-Term Developmental Trajectories of Dorsal-Ventral Pathways and Their Relationships with First-Grade Learning
The first year of formal schooling is a year of foundational reading and math learning, and individual differences emerging within this single year predict academic achievement decades later. Yet, how brain changes throughout this critical year relate to individual differences in reading and math learning remains uncharacterized. In this pre-registered study (https://osf.io/97ybe), we acquired monthly both behavioral assessments of reading- and math-learning, and diffusion-weighted MRI scans...
Daily briefing: Trial to ‘de-age’ cells treats first person
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Overlaying Governance: A Compositional Authorization Framework for Delegation and Scope in Agentic AI
Announce Type: new Abstract: As AI systems evolve from passive models into autonomous active agents capable of initiating actions, collaborating, and delegating tasks, the traditional boundaries of software systems blur. Traditional authorization and delegation frameworks, built around fixed principals, explicit requests, and static scopes, are insufficient to govern agentic systems. Agentic AI demands richer authorization semantics: agents must inherit and delegate permissions, act under...
Formal Semantics for Agentic Tool Protocols: A Process Calculus Approach
arXiv:2603.24747v2 Announce Type: replace Abstract: The emergence of large language model agents capable of invoking external tools has created urgent need for formal verification of agent protocols. Two paradigms dominate this space: Schema-Guided Dialogue (SGD), a research framework for zero-shot API generalization, and the Model Context Protocol (MCP), an industry standard for agent-tool integration. While both enable dynamic service discovery through schema descriptions, their formal...
Muses: Designing, Composing, Generating Nonexistent Fantasy 3D Creatures without Training
arXiv:2601.03256v2 Announce Type: replace Abstract: We present Muses, the first training-free method for fantastic 3D creature generation in a feed-forward paradigm. Previous methods, which rely on part-aware optimization, manual assembly, or 2D image generation, often produce unrealistic or incoherent 3D assets due to the challenges of intricate part-level manipulation and limited out-of-domain generation. In contrast, Muses leverages the 3D skeleton, a fundamental representation of...