Research

Problem-solving strategies for propositional logic in mathematical logic

Problem-solving strategies for proof theory in mathematical logic

Problem-solving strategies for predicate logic in mathematical logic

Problem-solving strategies for source coding in information theory

Problem-solving strategies for entropy in information theory

Problem-solving strategies for prime numbers in graph number theory

Problem-solving strategies for modular arithmetic in graph number theory

Problem-solving strategies for operator theory in functional analysis

Problem-solving strategies for banach spaces in functional analysis

Problem-solving strategies for analytic functions in complex analysis

Problem-solving strategies for natural transformations in category theory

Rapid ideation skill adapted from obra/superpowers to kick off cortex sessions. Use when defining scope, aligning on goals, or exploring solution space before coding.

Flip, remove, or exaggerate assumptions to unlock new solution angles.

Technical research methodology using Context7, Exa, and Sequential Thinking for documentation, best practices, and complex investigations.

Use after 2 consecutive failed attempts at solving a problem - STOP guessing and research documentation, codebase, and online resources before resuming

Use before starting implementation - research repository documentation, codebase patterns, and external resources to inform the approach

Expert product discovery guidance for user research and problem validation. Use when conducting user interviews, validating problems, applying jobs-to-be-done framework, sizing opportunities, customer segmentation, competitive analysis, prototype testing, usability testing, designing surveys, or synthesizing research insights. Covers discovery sprints, continuous discovery, and research operations.

Problem analysis using Explore agents

Multi-agent research orchestration: split a research goal into parallel sub-goals, run each via headless `claude -p` subprocesses, aggregate results into a polished report file. Use for systematic web/document research, competitive or industry analysis, batch link/dataset processing, and long-form evidence synthesis. Triggers: "深度调研", "deep research", "wide research", "多 Agent 调研", "系统调研".

This skill should be used when the user asks to "research a topic", "deep research", "investigate thoroughly", "multi-source research", "comprehensive analysis", or needs to conduct research across web, documentation, and memory sources.

This skill calculates key financial ratios and metrics from financial statement data for investment analysis

"This skill should be used when the user asks to 'define quality requirements',

"This skill should be used when the user asks to 'model the domain',

Conduct preliminary research on a topic and generate research outline. For academic research, benchmark research, technology selection, etc.