elements-infinity-cats
Elements of ∞-Category Theory (Riehl-Verity) for foundational ∞-categorical
bisimulation-oracle
Formal oracle for behavioral equivalence. Given two systems (skills, agents, processes), decides if they are bisimilar — i.e., indistinguishable by any external observer. Implements strong bisimulation, weak bisimulation, and GF(3)-colored bisimulation games. The oracle answers YES/NO, never "probably".
model-categories
Homotopical algebra via weak equivalences, fibrations, cofibrations, Quillen adjunctions, and homotopy (co)limits
naval-review
Gut-check any life or business decision through Naval's principles. Use when someone wants a direct, honest assessment of a plan, a choice, or a situation using Naval Ravikant's full philosophy as the lens.
galois-connections
Galois connections for lawful conversions and bi-Heyting topos logic. Lift adjoint pairs as behaviors with floor/ceiling/round/truncate. Derives ∧∨⇒¬∼ from adjoints.
causal-inference
Bengio's causal inference for AI: Interventional reasoning, counterfactuals, and System 2 deep learning. World models with causal structure.
bumpus-narratives
Sheaves on time categories for compositional temporal reasoning. Bumpus
axiomatic-semantics
Define program meaning through logical assertions and proof rules (Hoare logic).
relational-parametricity-prover
Proves relational parametricity. Use when: (1) Proving abstraction boundaries, (2) Reasoning about polymorphism, (3) Free theorems.
testing
Stack-agnostic testing principles, strategies, and patterns for building reliable test suites. Use when the user asks to design a test strategy, choose between unit/integration/e2e tests, apply TDD, fix flaky tests, improve test quality, use test doubles (mocks, stubs, fakes, spies), or review tests for antipatterns. Covers the testing pyramid, test design heuristics, arrange-act-assert structure, test isolation, property-based testing, and common testing pitfalls.
tcm-constitution-analyzer
Analyzes Traditional Chinese Medicine (TCM) constitution data, identifies constitution types using the standardized nine-constitution framework, assesses constitution characteristics, and provides personalized wellness recommendations. Supports correlation analysis with nutrition, exercise, and sleep data. Use when the user wants a TCM constitution assessment or personalized TCM-based health advice.
jungian-psychologist
Expert in Jungian analytical psychology, depth psychology, shadow work, archetypal analysis, dream interpretation, active imagination, addiction/recovery through Jungian lens, and the individuation process - grounded in primary sources and clinical frameworks. Activate on 'Jung', 'Jungian', 'shadow work', 'archetypes', 'dream interpretation', 'active imagination', 'individuation', 'anima', 'animus', 'collective unconscious', 'addiction', 'recovery', 'spiritus contra spiritum'. NOT for therapy or diagnosis (only licensed analysts diagnose), active psychosis, severe dissociation, or replacing the relational container of actual Jungian analysis.
debate-workflow
Structured multi-perspective debate for important architectural decisions and complex trade-offs
debate-workflow
Structured multi-perspective debate for important architectural decisions and complex trade-offs
hstack-summarize-research
Summarize the latest research on a medical condition, treatment, or procedure. Distinguishes between what's available now, what's in clinical trials, what's early-stage research, and what's theoretical. Use when you want to understand the current state of knowledge about a health topic, find emerging treatments, or prepare for informed conversations with your doctor.
opsx-explore
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.
roundtable
Multi-perspective roundtable discussion skill for exploring a topic through a truth-seeking moderator and a small set of representative real figures. Use when the user asks for 圆桌讨论 / roundtable / 多人物观点碰撞 / 让几位思想家讨论 / 模拟多方思想交锋 / 结构化辩论探索, or wants to examine one topic through disciplined multi-party debate rather than a plain summary. Do not use it for ordinary argumentative writing, generic pros/cons lists, or a single-speaker explanation.
debate-coach
Argue both sides of any topic with structured reasoning
davinci-define
Apply the 7 Da Vincian Principles to define problems, set direction, and reflect on life choices. Use for career decisions, goal setting, life planning, or when you need to clarify what the real question is before solving it.
animation-principles-master
Use when someone seeks the philosophical foundation of animation principles, wants to understand why they work, or is at a teaching/mentorship level
