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Carbon allotropes and nanoscale materials — graphite, diamond, fullerenes (C60 and family), carbon nanotubes, graphene, and the broader class of low-dimensional materials. Covers synthesis routes (arc discharge, laser ablation, CVD, exfoliation), structural characterization, exceptional mechanical and electronic properties, and the gap between laboratory demonstrations and structural-scale applications.

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Understanding and integrating multiple perspectives in historical analysis. Covers historical empathy (reconstructing how past actors understood their world), analyzing events from multiple viewpoints, constructing inclusive narratives that recover marginalized voices, and avoiding presentism (the imposition of contemporary values on past societies). Use when interpreting historical actors' motivations, assessing whose stories are told and whose are silenced, or guarding against anachronistic judgment.

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Analysis of aggregate economic phenomena -- GDP measurement, inflation dynamics, unemployment theory, monetary policy (central banks, interest rates, money supply), fiscal policy (government spending, taxation, debt), and the business cycle. Covers Keynesian, monetarist, and new classical perspectives. Use when analyzing national or global economic conditions, policy debates, economic growth, recessions, or the interaction between monetary and fiscal authorities.

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Ecological organization, energy flow, food webs, biodiversity, succession, and species interactions. Covers trophic structure, primary productivity, nutrient transfer efficiency, keystone and foundation species, ecosystem services, carrying capacity, disturbance regimes, primary and secondary succession, and resilience metrics. Use when analyzing how living communities are organized, how energy and matter move through ecosystems, how disturbance and recovery shape landscapes, or why biodiversity matters for ecosystem function.

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Statics, dynamics, stress-strain analysis, materials selection, failure modes, and finite element analysis concepts for engineered structures. Covers free-body diagrams, equilibrium, internal forces (shear and moment), beam deflection, column buckling, material properties, factor of safety, fatigue, fracture mechanics, and FEA workflow. Use when analyzing loads on structures, selecting materials, predicting failure, or interpreting structural behavior.

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Systems engineering covering requirements management, the V-model lifecycle, integration planning, verification and validation (V&V), interface control, trade studies, and the NASA Systems Engineering Handbook. Spans the full lifecycle from concept through operations and disposal. Includes requirements decomposition, traceability matrices, configuration management, and technical performance measures. Use when managing complex system development, writing requirements, planning integration, or conducting V&V activities.

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Economic analysis of government intervention -- taxation (incidence, efficiency, optimal design), regulation (cost-benefit, market failure correction), externalities (Pigouvian taxation, cap-and-trade, Coasian bargaining), and public goods provision (non-rivalry, non-excludability, free-rider problem). Covers welfare analysis of policy interventions, government failure, and the institutional context of policy-making. Use when evaluating policy proposals, analyzing tax effects, assessing regulatory design, or reasoning about the appropriate scope of government action.

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Design of active analog circuits built around operational amplifiers and discrete gain stages — inverting, non-inverting, difference, and instrumentation topologies, negative feedback and loop stability (gain-bandwidth product, phase margin, compensation), active filters (Sallen-Key, multiple-feedback biquad), sinusoidal and relaxation oscillators, comparators and Schmitt triggers, voltage references (bandgap, shunt, series), and linear versus switching voltage regulators. Covers how to pick a topology, close a feedback loop that stays stable, set gain and bandwidth, and choose a power-conversion approach. Use when designing an amplifier, filter, oscillator, reference, comparator, or regulator, or when reasoning about feedback stability, loop gain, phase margin, or op-amp non-idealities.

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Ionic, covalent, and metallic bonding, Lewis structures, VSEPR theory, molecular geometry, polarity, and intermolecular forces. Covers octet rule and exceptions, formal charge, resonance, sigma/pi bonds, orbital hybridization, electronegativity-driven bond classification, VSEPR electron-domain and molecular geometries, dipole moments, and the four intermolecular force types (London dispersion, dipole-dipole, hydrogen bonding, ion-dipole). Use when predicting molecular shapes, bond properties, or physical behavior from molecular structure.

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Color theory principles for art education. Covers the three color properties (hue, saturation, value), color mixing systems (subtractive and additive), color relationships (complementary, analogous, triadic, split-complementary), color temperature, simultaneous contrast and the relativity of color perception, and practical palette construction. Use when analyzing color in artworks, planning color schemes, understanding optical phenomena in painting, or investigating Albers's Interaction of Color experiments.

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Calculus and continuous transformation — derivatives, integrals, ODEs, Taylor series, and optimization. Computes rates of change, accumulates quantities over intervals, solves differential equations, and classifies critical points. Use when computing derivatives or integrals, solving ordinary differential equations, performing Taylor series approximations, finding critical points, or analyzing continuous change and motion.

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Guide for creating effective skills. This skill should be used when users want to create a new skill (or update an existing skill) that extends Claude's capabilities with specialized knowledge, workflows, or tool integrations.

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Apply modern web development best practices for security, compatibility, and code quality. Use when the task involves `apply best practices`, `security audit`, `modernize code`, `code quality review`, or `check for vulnerabilities`.

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Detects timing side-channel vulnerabilities in cryptographic code. Use when implementing or reviewing crypto code, encountering division on secrets, secret-dependent branches, or constant-time programming questions in C, C++, Go, Rust, Swift, Java, Kotlin, C#, PHP, JavaScript, TypeScript, Python, or Ruby.

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Analyze code changes for security vulnerabilities using LLM reasoning and threat model patterns. Use for PR reviews, pre-commit checks, or branch comparisons.

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Scans Cosmos SDK blockchains for 9 consensus-critical vulnerabilities including non-determinism, incorrect signers, ABCI panics, and rounding errors. Use when auditing Cosmos chains or CosmWasm contracts. (project, gitignored)

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The **Commitment Tracker** skill extracts and makes explicit the **ontological commitments** that agents make implicitly through their code and behavior. It enables detection and resolution of silent incompatibilities between systems that use different underlying assumptions about what exists and ho

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。

Colored stochastic six-vertex model with rainbow initial data, projection properties, and height functions tracking particle counts by color.

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。

CatColab Schemas - database schema modeling distinguishing entities (tables) from attributes (columns). Foundation for ACSets (Attributed C-Sets) and AlgebraicJulia data structures.

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Query NCBI ClinVar for variant clinical significance. Search by gene/position, interpret pathogenicity classifications, access via E-utilities API or FTP, annotate VCFs, for genomic medicine.

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Query ChEMBL's bioactive molecules and drug discovery data. Search compounds by structure/properties, retrieve bioactivity data (IC50, Ki), find inhibitors, perform SAR studies, for medicinal chemistry.

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。

Scans Cairo/StarkNet smart contracts for 6 critical vulnerabilities including felt252 arithmetic overflow, L1-L2 messaging issues, address conversion problems, and signature replay. Use when auditing StarkNet projects. (project, gitignored)

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。

GitHub interactome explorer for bmorphism/plurigrid ecosystem. Maps collaborations across AlgebraicJulia, Topos Institute, Anthropic, and MCP servers. Use for discovering cobordisms between research communities.

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。

BDD-Driven Mathematical Content Verification Skill Combines Behavior-Driven Development with mathematical formula extraction, verification, and transformation using: - Cucumber/Gherkin for specification - RSpec for implementation verification - mathpix-gem for LaTeX/mathematical content extraction - Pattern matching on syntax trees for formula validation Enables iterative discovery and verification of mathematical properties through executable specifications.

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。