Automatically send Claude Code conversations and tool calls to Braintrust. View nested activity records that connect each session, conversation exchange, and operation, including file reads, edits, and terminal commands, to inspect how coding work unfolded.
Work through topology problems about connectedness, the property of a space having no separation into two nonempty open parts. It outlines proof strategies, path construction, and connected components, with command examples for symbolic calculation and proof tools.
Plan solutions to topology problems involving open sets and continuous maps. Choose criteria based on distances or preimages, the points mapping into a set, and organize reasoning about interiors, closures, boundaries, and epsilon-delta conditions.
Work through limits in real analysis by choosing among substitution, algebraic manipulation, derivative-based methods, and bounding arguments. The skill also guides rigorous epsilon-delta proofs and provides commands for symbolic calculations and proof checks.
Organize topology problems about compactness, a property defined through finite selections from open covers. Choose tests suited to the space, examine products, and apply compactness to continuous images and maximum or minimum values.
Work through matrix eigenvalue problems, from the characteristic polynomial, whose roots give the eigenvalues, to finding eigenvectors. Follow a structured process to check the results and examine algebraic and geometric multiplicities.
Plan solutions to modular arithmetic problems, which involve integer remainders. Choose methods for modular inverses, simultaneous congruences, powers, quadratic residues, and primitive roots, with example commands for symbolic calculations and checking mathematical claims.
Work through matrix problems in linear algebra by identifying matrix types and choosing suitable calculations. The skill covers multiplication, inverses, determinants, linear systems, and decompositions that express a matrix as simpler components.
Work through natural transformation problems in category theory by checking component maps and compatibility conditions. The skill outlines strategies for natural isomorphisms, composition, and the Yoneda lemma, with references for expressing and checking work in Lean 4.
Review progress while solving a math problem by organizing previous attempts, checking intermediate results, and assessing growing complexity. The skill recommends whether to continue, adjust the approach, switch strategies, or tackle a smaller problem first.
Work through operator theory problems in functional analysis with structured steps for boundedness, adjoints, spectra, and compactness. Includes example commands for symbolic calculations and proof checks using SymPy and Z3.
Helps select graph algorithms for shortest paths, minimum spanning trees, network flow, and coloring. Provides decision guides and example commands for symbolic calculations and checking mathematical properties.
Choose approaches for prime number problems, including primality testing, factorization, and prime distribution. The skill outlines relevant algorithms and theorems, with commands for symbolic calculation and checking mathematical claims.
Study source coding, the information theory behind data compression. The skill guides problems involving Huffman codes, average code length, prefix-code constraints, arithmetic coding, and the tradeoff between compression rate and distortion, with calculation and proof command examples.
Solve complex analysis problems by choosing residue calculations for different singularities, points where a function is not analytic. The skill covers limits, derivatives, Laurent series, and contour integrals using the residue theorem, with Sympy and Z3 command examples.
Review the technology choices in an implementation plan using past project outcomes and web research. Produce a report that identifies outdated approaches, deprecated tools, and security concerns, with supporting sources and suggested alternatives.
Give new users a practical introduction to what the agent can help with, including coding, memory, research, and planning. Explain natural ways to ask for work, recall earlier lessons, and prepare handoffs for later sessions.
Check whether infrastructure code actually runs when a user triggers it. Trace calls from hooks or commands through scripts and modules, verify registration and permissions, and test the complete path to uncover unreachable code.
Build understanding of mathematical ideas before calculating. The skill guides you through concrete examples, diagrams, simpler cases, and analogies, then summarizes the intuition and suggests a next step with a check.
Choose a mathematical approach for a problem you do not yet know how to model. Guided questions clarify change, uncertainty, optimization goals, and required precision, leading to a recommended framework, starting equations, tools, and related skills.
Work through graduate-level problems using Rudin's Real and Complex Analysis. The skill guides theorem selection for measure theory, integration, and complex analysis, with commands for textbook searches, symbolic calculations, and verification.
Guides work on categories and functors by checking definitions, composition rules, and structure-preserving properties. Explains common functor types and provides examples for verifying proofs with Lean 4 and Mathlib.
Choose approaches to Hilbert space problems in functional analysis using orthogonal decomposition, projection, and representation theorems. The skill provides a decision tree and command examples for inner product calculations and proof tasks.
Match code investigation questions to the appropriate tldr command. Find ways to inspect files, function calls, branching, variable flow, and line dependencies, helping you explore a project or investigate a bug.
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