Skill UI

Creates and edits Obsidian Flavored Markdown, covering frontmatter, wikilinks, embeds, callouts, math, diagrams, and other vault-specific syntax so notes render correctly when working in Obsidian or referencing its features.

A comprehensive, adaptive mathematics tutor covering K-12 topics from arithmetic through calculus. This skill utilizes proven pedagogical strategies—such as Socratic questioning, CPA approach, and error analysis—to ensure students build deep mathematical understanding rather than just procedural fluency. It adapts to multiple global curricula (SAT, A-Level, Gaokao) and tracks progress to target weak spots.

SymPy is a Python library for exact symbolic mathematics, enabling algebra, calculus, equation solving, and linear algebra without numerical approximations. Ideal for physics calculations, code generation, and generating LaTeX output. Use when precision matters over speed.

Reads a LaTeX proof, finds gaps via cross-model adversarial review, fixes each gap with full derivations, re-reviews until convergence, and outputs an audit report with proof-obligation accounting.

This utility evaluates complex arithmetic expressions using arbitrary-precision decimal mathematics. It is specifically designed for scientific, financial, or engineering calculations where standard floating-point arithmetic causes unacceptable rounding errors (e.g., 0.1 + 0.2). Supports addition, subtraction, multiplication, division, exponents, and parentheses.

Generate comprehensive Chinese interview preparation cheat sheets for ML/LLM topics including mathematical formulas with derivations, from-scratch PyTorch implementations, comparison tables, and 25 high-frequency interview questions across L1/L2/L3 difficulty levels. Supports balanced or max effort modes with cross-model review.

Render ARIS Markdown or JSON artifacts such as IDEA_REPORT, AUTO_REVIEW, KILL_ARGUMENT and research-wiki state into polished single-file HTML reports for human reading, with sticky TOC, math, callouts, score progressions and source drift detection.

This skill converts complex, narrative technical documents, research excerpts, or natural language problem descriptions into a highly structured Mathematical Problem Specification (MPS). It systematically extracts variables, constraints, objectives, and uncertainty parameters. By adhering to a strict Zero-Inference Protocol, it ensures all extracted elements are strictly grounded in the source text, making it invaluable for formalizing real-world optimization, data science, and engineering problems.

Invariant-Guard enforces a correctness-first approach to algorithm design. Instead of writing code and hoping it works, this skill mandates defining the function contract, loop invariants, termination arguments, and all potential edge cases *before* implementation. It is essential for complex algorithms where subtle bugs (like off-by-one errors or missed post-conditions) are common, ensuring mathematically rigorous and verifiable code.

A specialized skill for achieving asymptotic performance gains when classical algorithms are already near optimal. It leverages advanced mathematical techniques and probabilistic data structures (e.g., Bloom Filters, HyperLogLog, FFT, MinHash/LSH) to handle massive datasets (n ≥ 10⁶) by accepting bounded approximations or exploiting deep structural properties. Requires strict adherence to error parameter and complexity justification protocols.

This skill simulates a world-class Senior System Design Engineer with 20+ years of experience at top tech companies. It helps users design, review, and scale complex, highly available, and resilient distributed systems. It covers every aspect from database sharding and microservices decomposition to caching strategies, observability stacks, and CI/CD pipelines, providing detailed blueprints and mathematical scaling estimates.

This skill provides a rigorous, multi-layered audit for User Interfaces, proving layout balance and usability beyond subjective judgment. It combines a deterministic spatial audit (calculating centroid, optical-center, and pixel-oracle balance via explicit math) with a professional usability review based on Nielsen's 10 heuristics, conducted by a separate 'fresh-eyes' judge. Ideal for catching misaligned or poorly structured AI-generated designs.