Skill UI

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.

Convert narrative technical documents into grounded Mathematical Problem Specifications (MPS) with variables, constraints, objectives, and uncertainty. Enforces zero-inference protocol, extracts structured components, and identifies missing information for formalization.

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.

This skill acts as an ultra-advanced mathematician inspired by Terence Tao. It performs rigorous code and architecture analysis using deep mathematical theories such as information theory, graph theory, computational complexity, linear algebra, stochastic analysis, category theory, Bayesian probability, and formal logic. Ideal for complex algorithmic verification and architectural design review.

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.

A comprehensive guide to implementing the Swiss Design (International Typographic Style). This style emphasizes absolute mathematical grids, clean sans-serif typography (like Helvetica), and asymmetrical layouts. It is ideal for users requiring highly structured, minimal, and objective visual communication across web and mobile platforms.

Viboscope helps discover compatible people for various life aspects—from cofounders and project partners to friends and romantic interests. It builds a comprehensive psychological profile across 10 validated dimensions (including Big Five, Values, and Work Style) and calculates mathematical compatibility scores, providing detailed insights into why connections are strong. Ideal for professional networking, team building, or personal relationships.

This skill develops and verifies mathematical proofs using the Lean theorem prover. It handles creating new proofs, continuing incomplete projects, and auditing existing formalizations to ensure they match original statements. It connects inputs to lemmas, assembles theorems, and checks axioms for reproducibility. Use it for formal verification tasks rather than ordinary drafting.

Edit mathematically, empirically, or technically dense papers for readers outside the author's specialty, including empirical legal scholarship, law-and-economics models, and legal-technology research. Clarifies terminology, antecedents, study design, and claim-statistic relationships while checking equations, numbers, quotations, and citations against the source. Use to clarify exposition or de-jargonize a technical draft; not to rewrite briefs or doctrinal arguments. Produces an edited draft and audit memo. Full integrity checks and original-format rendering require suitable extraction, c...