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Foundations of digital signal processing — sampling, aliasing, the Nyquist criterion, quantization, convolution, the discrete Fourier transform, FFT, FIR and IIR filter design, windowing, spectral leakage, and practical issues in fixed-point versus floating-point implementation. Use when designing filters, analyzing spectra, choosing sample rates, reasoning about aliasing, or implementing DSP algorithms on a microcontroller, DSP chip, or host CPU.

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Systematic analysis of DC and AC linear circuits using Ohm's law, Kirchhoff's laws, node and mesh methods, Thevenin and Norton equivalents, phasor analysis, and Bode plots. Covers series and parallel reduction, superposition, source transformation, impedance in the frequency domain, first and second order transient response, and the conversion between time domain and phasor representations. Use when quantitatively predicting voltages, currents, power, gain, phase, or time response of any lumped-element linear circuit.

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Economics of low-income countries and the structural transformation from agrarian poverty to industrial prosperity. Covers growth models (Solow, endogenous growth, unified growth theory), the role of institutions (inclusive vs. extractive), inequality measurement and dynamics (Gini, Lorenz curve, Kuznets), poverty traps and their mechanisms (nutritional, financial, geographical), foreign aid debates, and the capability approach as an alternative development metric. Use when analyzing why some countries are rich and others poor, evaluating development interventions, or reasoning about the relationships between growth, inequality, institutions, and human well-being.

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Classical control and system dynamics for engineered systems — feedback and closed-loop control, transfer functions and block diagrams, poles/zeros and stability, time-domain response (rise time, overshoot, settling time), PID controllers and tuning, and frequency response (Bode plots, gain and phase margin). Traces feedback control from the flyball governor to modern controllers. Use when analyzing feedback loops, designing or tuning a PID controller, assessing stability from poles or margins, or characterizing transient response of a dynamic system.

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Techniques for generating novel ideas, reframing problems, and escaping fixed mental models. Covers lateral thinking (de Bono), Six Thinking Hats, random stimulation, provocation operators (PO), analogical transfer, assumption challenging, and divergent-then-convergent thinking cycles. Use when the goal is to produce new options or perspectives rather than evaluate existing ones.

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Celestial coordinate systems and sky positioning. Covers horizon (altitude-azimuth), equatorial (right ascension-declination), ecliptic, and galactic systems; epoch and precession; coordinate transformations; planisphere use; and practical sky-locating from any latitude and date. Use when locating objects, planning observations, converting catalog coordinates, or teaching the geometry of the sky.

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Transform a user's builder vision into a complete, executable GSD mission package. Use this skill whenever a user has described what they want to BUILD (a product, tool, feature, system, educational pack, or ecosystem component) and wants it structured for GSD execution. Triggers include: 'structure this for GSD', 'make this into a milestone', 'turn this vision into a mission', 'package this up for Claude Code', 'create the mission files', 'I want to hand this to GSD', 'make me a mission package', or any request to decompose a described system into wave-based executable tasks. Also trigger when the user has a vision doc already written and needs mission decomposition. Prefer this skill over generic document creation whenever the GSD ecosystem is mentioned alongside building something.

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Classical orbital mechanics from Kepler to Hohmann. Covers the six orbital elements, Kepler's three laws, vis-viva, orbit types (circular, elliptical, parabolic, hyperbolic), transfer orbits, gravity assists, the two-body problem, and practical methods for computing ephemerides. Use when reasoning about planet motion, spacecraft trajectories, comet orbits, exoplanet transits, or binary star dynamics.

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Thermal engineering for infrastructure: heat transfer (conduction, convection, radiation), cooling load analysis for data centers, heat exchanger sizing via LMTD and e-NTU, PUE/TUE/WUE efficiency metrics, and airflow management patterns. Activates for thermal analysis, data center cooling design, heat exchanger sizing, efficiency calculations, and airflow management.

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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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Electrical power distribution design for infrastructure: load calculations (NEC 220), conductor sizing (NEC 310.16), transformer/UPS/PDU selection, redundancy architectures (N through 2N+1), DC distribution, and voltage classes 120V-480V. Activates for electrical load calculations, conductor sizing, power equipment selection, data center power design, and redundancy architecture planning.

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Linear algebra and higher-dimensional thinking. Vectors, matrices, transformations — the architecture of mathematical space.

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当用户写出的内容读起来像产品公告/官方更新(如"我们发布了X""支持Y功能""效果很好")，需要翻译成读者能拿走的外部语言时调用。也适用于:用户问"怎么把公告式表达改成强推文""这条推文为什么没人理"(若原因是只讲自己不讲读者)、"怎么把功能介绍写得吸引人"。Trigger 词:公告式表达/内部语言/外部语言/帮助式表达/announcement tone/helpful expression/show don't tell/translate to reader value。不适用于:从零起草新内容(用 x-short-content-craft)、检查内容五件套完备性(用 x-five-piece-checklist)、评估内容值不值得发(用 x-four-saves)。

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Convert Chinese provinces, municipalities, autonomous regions, cities, counties, ancient cities, and cultural regions into restrained contemporary posters led by one culturally transformed Chinese character. Supports direct one-shot final image generation and layered production. Use when the user asks for a 中国省域文化海报、城市文化海报、地域文化视觉、极简大字海报、地区系列海报、展览主视觉、出版或社交封面，requests 直接生成、一次成图、不合成、不要后期、direct generation, or wants cultural analysis, art direction, image prompts, rendered poster images, or a coherent batch series for places such as 北京、广东、福建、江南、岭南、巴蜀 or 关中.

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当用户需要为产品或品牌引入权威背书以建立信任时调用此 skill。适用场景：新品上市缺乏认知度、高客单价产品需要信任支撑、功效型产品需要专业认可。不适用于：已有强品牌认知的成熟产品、低价快消品（权威背书反而显得过度包装）。关键 trigger 信号：用户提到"认证""获奖""合作机构""专家推荐""权威背书"。核心方法：树立权威的高地位，再描述权威的严格标准，将权威的光环嫁接到产品上。

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This skill should be used when the user asks to "plan chunks", "break this down", "plan the implementation", or when a story has status planning and needs implementation details before building. Required before any story can be implemented. Transforms story sparks into detailed chunk-by-chunk implementation plans with full technical specifics, file lists, and risk analysis. Supports parallel planning of multiple stories via batch mode.

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Conformal Geometric Algebra (CGA) for circles, spheres, and Möbius transformations

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Assists in writing high-quality content by conducting research, adding citations, improving hooks, iterating on outlines, and providing real-time feedback on each section. Transforms your writing process from solo effort to collaborative partnership.

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Transform ChatGPT ZIP exports into ACSets (Attributed C-Sets) for:

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Deploy serverless applications on Cloudflare Workers. Covers project setup, JavaScript handler patterns, routing, deployment with Wrangler, and API token configuration. Suitable for APIs, proxies, edge computing, and request transformation.

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Automatically creates user-facing changelogs from git commits by analyzing commit history, categorizing changes, and transforming technical commits into clear, customer-friendly release notes. Turns hours of manual changelog writing into minutes of automated generation.

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Categorical Rewriting: Triad 4 (World Transformation)

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Category-theoretic pipes with GF(3) flow balance checking. Validates data transformation pipelines using triadic trit algebra.

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CapTP: Capability Transfer Protocol

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