Research mathematical tasks using domain context and codebase exploration. Invoke for math-language research involving algebra, lattice theory, order theory, topology, and category theory.
Research physics formalization tasks using domain context and codebase exploration. Invoke for physics-language research involving dynamical systems, chaos theory, and related formalization.
Coordinate formal reasoning research across logic, math, and physics domains. Invoke for formal-language research requiring cross-domain coordination.
Research mathematical logic tasks using domain context and codebase exploration. Invoke for logic-language research involving modal logic, Kripke semantics, and related mathematical foundations.
Research Z3/SMT tasks. Invoke for Z3-language research.
Enter explore mode - a thinking partner for exploring ideas, investigating problems, and clarifying requirements. Use when the user wants to think through something before or during a change.
Visual & UI philosophy (The 5 Pillars of Intentional UI). Understand deeply to avoid "AI slop" and create distinctive, memorable interfaces.
Internal logic and data flow philosophy (The 5 Laws of Elegant Defense). Understand deeply to ensure code guides data naturally and prevents errors.
Parallel critique of proposals via 5 philosophical personas with consensus synthesis.
Analyzes and critiques historical systems of government or eras by providing a structured list of advantages (pros) and disadvantages (cons).
Translates Spanish texts from the Psychoenergetics (Vibrational Psychology) framework into English, maintaining consistent terminology for key concepts like Self-Esteem, Cognitive Congruence, and the Law of the Circles.
Analyzes a political system by addressing a specific set of questions regarding its operation, leadership structure, democratic nature, human rights adherence, and potential improvements.
Expands academic text in theology and philosophy, adding depth and context while strictly adhering to Harvard citation style and generating a reference list.
Identifies and describes metaphors within a given text from a philological perspective, including classification of the metaphor type and explanation of its linguistic function.
Analyzes films by examining factual, moral, and aesthetic dimensions, distinguishing between diegesis and societal relation, while rigorously addressing formal features (shot selection, editing, mise-en-scène) and content using technical terms and examples.
Use this skill when writing a philosophy essay to defend Immanuel Kant's claim that space is a form of intuition against counter-arguments based on empirical research (e.g., developmental psychology, neuroscience). It provides a specific logical framework to reconcile empirical findings with Kantian theory.
Evaluates the grammaticality or ungrammaticality of English sentences by applying specific syntactic principles: Subjacency, Empty Category Principle (ECP), Condition on Extraction Domain (CED), and island effects.
Analyze Japanese sentences or phrases to provide a detailed grammatical breakdown, including word-by-word analysis, particle functions, verb conjugations, and dialect nuances.
Respond using British English spelling, vocabulary, and grammar conventions.
Recommend reading materials or websites about Japanese culture that prioritize authentic perspectives, avoid gamification/anime, and focus on cultural knowledge over academic theory.
Analyze geometric definitions to determine equivalence by formulating conditional statements, constructing 2-column proofs using triangle congruence theorems, or providing counterexamples.
Analyzes French and Portuguese sentences with granular, line-by-line breakdowns. Translates Portuguese phrases into natural Spanish with multiple options and justifications. Covers grammatical structure, word groups, and traditional/neutral forms.
Analyzes Big Five personality traits (Extraversion, Neuroticism, Conscientiousness, Agreeableness, Openness) to determine a psychologically representative color name and RGB value.
