Skill UI

A specialized tool for polishing pure mathematics manuscripts, designed to enhance the rigor and overall flow of academic writing. It guides authors to eliminate soft language (e.g., "clearly," "obviously"), ensure precise quantification, explicitly state constant dependencies, and structure hypotheses meticulously. Ideal for late-stage proof refinement before journal submission.

This detailed guide outlines the structure and scientific rigor required for publishing high-quality papers in the domain of Computer Aided Verification (CAV). It instructs authors to transition their work from mere system demonstrations or benchmark reports to formally guaranteed, mathematically precise contributions, emphasizing clear scope definition, stated theorems, and proof ideas.

This comprehensive guide provides detailed instructions for revising academic papers, specifically in the field of learning theory, for the COLT conference. It teaches authors how to structure the argument rigorously, ensuring the model is unambiguous, mastering the informal-to-formal theorem pairing, and maintaining mathematical precision (quantifier and constant hygiene).

This skill serves as a comprehensive guide for authors submitting papers to Communications on Pure and Applied Mathematics (CPAM). It helps authors assess the theoretical depth, mathematical rigor, and suitability of their work—especially in PDEs, analysis, and mathematical physics—for a top-tier journal. It covers scope fitting, proof standards, and submission best practices.

This comprehensive guide outlines the necessary theoretical rigor for algorithms and models submitted to top-tier computational journals. It instructs authors on how to formally state mathematical formulations, rigorously prove model validity, establish convergence, and quantify complexity (e.g., approximation ratios, finite termination). It provides specialized paths for exact methods, metaheuristics, and ML-enhanced OR, ensuring that the theoretical advancements fully support and rationalize the experimental findings.

A guide for authors submitting to theoretical computer science venues (ITCS). It strictly defines what constitutes valid evidence for a mathematical claim, emphasizing that complete proofs are paramount. The guidelines detail how to use worked examples, separating objects, and appropriately scoped computations, while strongly advising against using empirical benchmarks or performance metrics.

This skill is a comprehensive guide for authors targeting the Journal of the American Mathematical Society (JAMS). It outlines the journal's extremely high standards for pure and applied mathematics, covering required levels of mathematical rigor, novelty, general significance, and specific formatting guidelines (AMS LaTeX, MSC codes, arXiv). Use this tool to assess the suitability of your manuscript for top-tier academic publication.

This guide outlines the rigorous standards for presenting 'evidence' in highly theoretical computing venues. It emphasizes that results must be supported by deep mathematical proofs, establishing matching upper and lower bounds (tightness), and meticulously auditing all underlying model assumptions (e.g., timing, failure modes). It shifts focus from empirical benchmarks to formal correctness.

A comprehensive guide for computer graphics researchers detailing how to achieve result-level reproducibility, especially for major conferences like SIGGRAPH. It emphasizes pinning all provenance—including assets, random seeds, hardware stacks, and hyperparameters—and methodologies for handling non-determinism in floating-point math and stochastic simulations, ensuring that the reported figures and timings can be regenerated by any reader.

This skill provides a comprehensive framework for ensuring the mathematical verifiability of advanced algorithms papers (like those submitted to SODA). It guides authors to establish a complete, checkable argument, documenting every claim, explicit model assumption, constant status, and providing machine-checkable steps. It moves beyond simple claims of accuracy to mandate full, reproducible proof structures.

A comprehensive guide for authors submitting to UAI (Uncertainty in Artificial Intelligence). It details how to position research by ensuring coverage across diverse academic communities, including Machine Learning, Statistics, Causal Inference, and foundational mathematics. Focuses on establishing the technical 'delta' rather than merely listing citations, helping authors avoid common review failures.

SymPy is a powerful Python library designed for symbolic mathematics. Unlike numerical solvers, it performs exact calculations using mathematical symbols, allowing users to model and solve complex problems across various domains. Core capabilities include symbolic calculus (derivatives, integrals, limits), advanced algebra, solving systems of equations, linear algebra (determinants, eigenvalues), and specialized modules for physics and number theory. It can also generate executable code in languages like C and Fortran, making it invaluable for academic research and scientific computing.