64 件 ・ 関連度順
概要と使いどころ
Use when designing or auditing AISTATS experiments, simulations, baselines, statistical tests, uncertainty estimates, ablations, random seeds, hyperparameters, compute, dataset handling, and claim-to-evidence fit, with emphasis on experiments that validate theorems rather than chase leaderboards.
日本語の概要は準備中です。原文の説明を表示しています。
Use when revising an AISTATS paper for concise AI-statistics framing, theorem-and-experiment clarity, 8-page two-column compression, double-blind wording, reproducibility clarity, statistically careful claims, and assumption-labeling discipline that survives statistician reviewers.
日本語の概要は準備中です。原文の説明を表示しています。
Use when the contribution of an American Economic Journal: Microeconomics (AEJ: Micro) manuscript is fuzzy or oversold relative to the closest existing results. Stakes the theorem-relative delta against the nearest theory; it does not build the model (see aejmic-theory-model) or frame the prose (see aejmic-writing-style).
日本語の概要は準備中です。原文の説明を表示しています。
Use when the model setup, equilibrium concept, or proof architecture is the bottleneck for an American Economic Journal: Microeconomics (AEJ: Micro) manuscript — the central skill for a theory-first paper. Builds the model to the AEJ: Micro bar (clean, general, well-motivated result); it does not check whether your theorem is correct.
日本語の概要は準備中です。原文の説明を表示しています。
Core distributed systems patterns - load balancing, caching, sharding, consistent hashing, message queues, rate limiting, CDN, Bloom filters, ID generation, replication, conflict resolution, CAP theorem
日本語の概要は準備中です。原文の説明を表示しています。
Formal theorem proving with research, testing, and verification phases
日本語の概要は準備中です。原文の説明を表示しています。
When designing distributed systems for scalability, reliability, and consistency. Covers CAP/PACELC theorems, consistency models (strong, eventual, causal), replication patterns (leader-follower, multi-leader, leaderless), partitioning strategies (hash, range, geographic), transaction patterns (saga, event sourcing, CQRS), resilience patterns (circuit breaker, bulkhead), service discovery, and caching strategies for building fault-tolerant distributed architectures.
日本語の概要は準備中です。原文の説明を表示しています。
Translate Python programs to equivalent Lean4 code while preserving semantics and ensuring type safety. Use when users ask to convert, translate, or port Python code to Lean4, or when they need to verify Python algorithms using Lean4's theorem proving capabilities. Handles functions, classes, data structures, control flow, and ensures the generated Lean4 code is well-typed, executable, and can successfully run.
日本語の概要は準備中です。原文の説明を表示しています。
Recommend relevant Isabelle/HOL or Coq standard library theories, lemmas, and tactics based on proof goals. Use when: (1) Users need library lemmas for their proof, (2) Proof goals match standard library patterns, (3) Users ask what libraries to import, (4) Specific lemmas are needed for list/set/arithmetic operations, (5) Users are stuck and need to know what library support exists, or (6) Guidance on find_theorems/Search commands is needed. Supports both Isabelle/HOL and Coq standard libraries.
日本語の概要は準備中です。原文の説明を表示しています。
Debug proof failures using counterexamples from Nitpick (Isabelle) or QuickChick (Coq) to identify specification errors, missing preconditions, and proof strategy issues. Use when: (1) A proof attempt fails and you need to understand why, (2) Counterexamples are generated by Nitpick or QuickChick, (3) Specifications may be incorrect or incomplete, (4) Theorems need validation before proving, (5) Missing preconditions or lemmas need identification, or (6) Proof failures need explanation and correction suggestions. Supports both Isabelle/HOL and Coq equally.
日本語の概要は準備中です。原文の説明を表示しています。
Think and work like an expert Mathematical Analyst. Use when a task calls for Mathematical Analyst judgment. Reasons from function-space topology, convergence modes, and constant-dependent inequalities (Hölder, Sobolev, Gronwall) through compactness theorems (Rellich-Kondrachov, Banach-Alaoglu), Calderon-Zygmund and Schauder estimates, and Lax-Milgram while treating limit-integral swaps without dominated convergence, boundary-degenerating constants, weak-versus-classical regularity gaps, and concentration-compactness loss as first-class failure modes.
日本語の概要は準備中です。原文の説明を表示しています。
Think and work like an expert Algebraist. Use when a task calls for Algebraist judgment. Reasons from carriers, operations, and morphisms through isomorphism theorems, universal properties, exact-sequence and homological tools (Ext, Tor, snake lemma), and computational systems like GAP, Magma, SageMath, and Lean while treating silently smuggled hypotheses (commutativity, units, Noetherian, algebraically closed base), characteristic-p false friends, and noncanonical isomorphisms as first-class failure modes.
日本語の概要は準備中です。原文の説明を表示しています。
Build the deterministic evidence ledger (artifact_manifest.json + claims.json) that every other Anti-Autoresearch auditor reads. One pass inventories artifacts, derives the observability level (L0 PDF-only / L1 +LaTeX / L2 +repo+results) by fixed rule, and extracts span-anchored, hashed, checkable claims (numbers, comparisons, scope, method, baselines, citations, captions, table cells) into claims.json. An OPTIONAL additive cross-model pass ADDS span-anchored semantic claims — method, theorem statements with their assumptions, definitions, proof/derivation steps and equations, scope, baselines, conclusions, the motivation span, and reproducibility-artifact references (the proof, derivation, and structure anchors the family B/D/G auditors need) — it never invents a number, emits a finding, or computes a verdict. Run FIRST, before any audit skill. Triggers: "build the ledger", "extract claims", "prep for integrity audit", "evidence ledger", "建证据账本".
日本語の概要は準備中です。原文の説明を表示しています。
Expert guide for mathematical formal verification, SMT solver constraints (Z3, Dafny, TLA+), invariant theorem proving for FinTech billing state machines, RBAC/ABAC authorization, and zero-violation architecture / Panduan ahli verifikasi formal matematis, SMT solver (Z3, Dafny, TLA+), pembuktian invarian state machine billing FinTech, otorisasi RBAC/ABAC, dan arsitektur zero-violation.
日本語の概要は準備中です。原文の説明を表示しています。
First-order logic with quantifiers, predicates, functions, and identity. Covers syntax, interpretation over a domain, the universal and existential quantifiers, quantifier scope and binding, translation from natural language with multi-variable predicates, natural deduction for quantifiers, undecidability at first order, and the soundness/completeness theorems. Use when propositional logic is insufficient -- whenever "for all" or "there exists" matters to the argument.
日本語の概要は準備中です。原文の説明を表示しています。
Spatial reasoning, coordinate geometry, transformations, and trigonometry for geometric problem solving. Covers Euclidean geometry (points, lines, angles, congruence, similarity), triangle geometry (Pythagorean theorem, laws of sines and cosines), circle geometry (tangent lines, inscribed angles, power of a point), coordinate geometry (distance, midpoint, slope, conic sections), transformations as functions (rotation, reflection, translation, dilation), trigonometry (unit circle, identities, inverse functions), and geometric proof techniques. Use when reasoning about shapes, angles, spatial relationships, coordinate problems, or trigonometric computations.
日本語の概要は準備中です。原文の説明を表示しています。
Real-world problem formulation, mathematical abstraction, and applied mathematics for translating between practical problems and mathematical frameworks. Covers the modeling cycle (problem identification, assumptions, formulation, analysis, validation, interpretation), Polya's framework adapted for modeling, common model types (linear, exponential, logistic, periodic, power-law), dimensional analysis (Buckingham Pi theorem), optimization (linear programming, gradient descent, constraint satisfaction), probability models (Markov chains, queuing theory, Monte Carlo simulation), statistical modeling (regression, hypothesis testing, model selection), model criticism (overfitting, underfitting, sensitivity analysis), and real-world case studies. Use when formulating mathematical models, performing dimensional analysis, optimizing systems, running simulations, or evaluating model validity.
日本語の概要は準備中です。原文の説明を表示しています。
The logical structure of mathematical proof -- how first-order logic, natural deduction, and semantic reasoning combine to produce rigorous mathematical arguments. Covers the logical skeleton of direct proof, contraposition, contradiction, cases, and induction; the role of definitions, lemmas, and theorems; how informal mathematical prose maps to formal deductive structure; and the difference between proof-as-object and proof-as-activity. Use when the question is "why is this a valid proof?" rather than "what proof technique applies?"
日本語の概要は準備中です。原文の説明を表示しています。
Design and analysis of combinational and sequential digital circuits using Boolean algebra, truth tables, K-maps, CMOS gate implementation, flip-flops, registers, counters, and finite state machines. Covers De Morgan's theorems, canonical sum-of-products and product-of-sums forms, minimization techniques, propagation delay, setup and hold times, metastability, synchronous design discipline, and FSM encoding. Use when designing, minimizing, verifying, or debugging any circuit whose signals take only discrete logic values.
日本語の概要は準備中です。原文の説明を表示しています。
Distributed storage systems design and operation for cloud platforms. Covers the GFS/HDFS block-and-master pattern, object storage (Swift/S3) with consistent hashing and eventual consistency, block storage semantics, replication vs erasure coding, the CAP theorem in practice, read-repair and anti-entropy, snapshot chains, and the GFS/BigTable/Spanner evolution. Use when designing a storage subsystem, choosing between object/block/file, or reviewing a replication and consistency strategy.
日本語の概要は準備中です。原文の説明を表示しています。
Mathematical verification for physical calculations: unit tracking algebra (exponent maps), PhysicalQuantity pattern for compound units, SI/Imperial mixed-unit handling, Buckingham pi theorem for dimensionless groups, and common engineering dimensionless numbers. Activates for unit verification, dimensional consistency checks, scaling analysis, and calculation validation across all infrastructure domains.
日本語の概要は準備中です。原文の説明を表示しています。
Machine learning environment for automated theorem proving with Coq.
日本語の概要は準備中です。原文の説明を表示しています。
Safe proof ↔ theorem navigation with non-backtracking constraint.
日本語の概要は準備中です。原文の説明を表示しています。
IMO Gold Medal level Lean4 theorem proving via Harmonic API
日本語の概要は準備中です。原文の説明を表示しています。