symmetry-validation-suite
Use when you need to empirically test whether hypothesized symmetries actually hold in your data or model. Invoke when user mentions testing invariance, validating equivariance, checking if symmetry assumptions are correct, debugging symmetry-related model failures, or needs data-driven validation before committing to equivariant architecture. Provides test protocols and metrics.
synthesis-and-analogy
Use when synthesizing information from multiple sources (literature review, stakeholder feedback, research findings, data from different systems), creating or evaluating analogies for explanation or problem-solving (cross-domain transfer, "X is like Y", structural mapping), combining conflicting viewpoints into unified framework, identifying patterns across disparate sources, finding creative solutions by transferring principles from one domain to another, testing whether analogies hold (surface vs deep similarities), or when user mentions "synthesize", "combine sources", "analogy", "like", "similar to", "transfer from", "integrate findings", "what's it analogous to".
translation-reframing-audience-shift
Use when content must be translated between audiences with different expertise, context, or goals while preserving accuracy but adapting presentation. Invoke when technical content needs business framing (engineering decisions → executive summary), strategic vision needs tactical translation (board presentation → team OKRs), expert knowledge needs simplification (academic paper → blog post, medical diagnosis → patient explanation), formal content needs casual tone (annual report → social media post), long-form needs summarization (50-page doc → 1-page brief), internal content needs external framing (roadmap → public updates, bug tracking → known issues), cross-cultural adaptation (US idioms → international clarity, Gen Z → Boomer messaging), medium shifts (written report → presentation script, detailed spec → action checklist), or when user mentions "explain to", "reframe for", "translate this for [audience]", "make this more [accessible/formal/technical]", "adapt for [executives/engineers/customers]", "simplify without losing accuracy", or "same content, different audience". Apply to technical communication (code → business value), organizational translation (strategy → execution), education (expert → novice), customer communication (internal → external), cross-cultural messaging, and anywhere same core message needs different presentation for different stakeholders while maintaining correctness.
symmetry-group-identifier
Use when you've identified candidate symmetries and need to map them to mathematical groups for architecture design. Invoke when user mentions cyclic groups, dihedral groups, Lie groups, SO(3), SE(3), permutation groups, or needs to formalize symmetries into group theory language. Provides taxonomy and mathematical foundations from Visual Group Theory principles.
socratic-teaching-scaffolds
Use when teaching complex concepts (technical, scientific, philosophical), helping learners discover insights through guided questioning rather than direct explanation, correcting misconceptions by revealing contradictions, onboarding new team members through scaffolded learning, mentoring through problem-solving question frameworks, designing self-paced learning materials, or when user mentions "teach me", "help me understand", "explain like I'm", "learning path", "guided discovery", or "Socratic method".
symmetry-discovery-questionnaire
Use when ML engineers need to identify symmetries in their data but don't know where to start. Invoke when user mentions data symmetry, invariance discovery, what transformations matter, or needs help recognizing patterns their model should respect. Works collaboratively through domain analysis, transformation testing, and physical constraint identification.
dialectical-mapping-steelmanning
Use when debates are trapped in false dichotomies, polarized positions need charitable interpretation, tradeoffs are obscured by binary framing, synthesis beyond 'pick one side' is needed, or when users mention steelman arguments, thesis-antithesis-synthesis, Hegelian dialectic, third way solutions, or resolving seemingly opposed principles.
scientific-clarity-checker
Use when reviewing any scientific document for logical clarity, argument soundness, and scientific rigor. Invoke when user mentions check clarity, review logic, scientific soundness, hypothesis-data alignment, claims vs evidence, or needs a cross-cutting scientific logic review independent of document type.
scientific-email-polishing
Use when writing or polishing professional scientific emails, journal cover letters, or responses to reviewers. Invoke when user mentions email to collaborator, cover letter to editor, reviewer response, professional correspondence, or needs help with professional tone, clear asks, or diplomatic communication in academic/scientific contexts.
role-switch
Use when stakeholders have conflicting priorities and need alignment, suspect decision blind spots from single perspective, need to pressure-test proposals before presenting, want empathy for different viewpoints (eng vs PM vs legal vs user), building consensus across functions, evaluating tradeoffs with multi-dimensional impact, or when user mentions "what would X think", "stakeholder alignment", "see from their perspective", "blind spots", or "conflicting interests".
causal-inference-root-cause
Use when investigating why something happened and need to distinguish correlation from causation, identify root causes vs symptoms, test competing hypotheses, control for confounding variables, or design experiments to validate causal claims. Invoke when debugging systems, analyzing failures, researching health outcomes, evaluating policy impacts, or when user mentions root cause, causal chain, confounding, spurious correlation, or asks "why did this really happen?"
adr-architecture
Use when documenting significant technical or architectural decisions that need context, rationale, and consequences recorded. Invoke when choosing between technology options, making infrastructure decisions, establishing standards, migrating systems, or when team needs to understand why a decision was made. Use when user mentions ADR, architecture decision, technical decision record, or decision documentation.
brainstorm-diverge-converge
Use when you need to generate many creative options before systematically narrowing to the best choices. Invoke when exploring product ideas, solving open-ended problems, generating strategic alternatives, developing research questions, designing experiments, or when you need both breadth (many ideas) and rigor (principled selection). Use when user mentions brainstorming, ideation, divergent thinking, generating options, or evaluating alternatives.
career-document-architect
Use when writing or reviewing career documents including research statements, teaching statements, diversity statements, CVs, or biosketches. Invoke when user mentions research statement, teaching philosophy, diversity statement, biosketch, academic CV, faculty application, or needs help with career narrative, positioning, or professional documents for academic advancement.
decomposition-reconstruction
Use when dealing with complex systems that need simplification, identifying bottlenecks or critical failure points, redesigning architecture or processes for better performance, breaking down problems that feel overwhelming, analyzing dependencies to understand ripple effects, user mentions "this is too complex", "where's the bottleneck", "how do we redesign this", "what are the key components", or when optimization requires understanding how parts interact.
bayesian-reasoning-calibration
Use when making predictions or judgments under uncertainty and need to explicitly update beliefs with new evidence. Invoke when forecasting outcomes, evaluating probabilities, testing hypotheses, calibrating confidence, assessing risks with uncertain data, or avoiding overconfidence bias. Use when user mentions priors, likelihoods, Bayes theorem, probability updates, forecasting, calibration, or belief revision.
constraint-based-creativity
Use when brainstorming feels stuck or generates obvious ideas, need to break creative patterns, working with limited resources (budget/time/tools/materials), want unconventional solutions, designing with specific limitations, user mentions "think outside the box", "we're stuck", "same old ideas", "tight constraints", "limited budget/time", or seeking innovation through limitation rather than abundance.
design-of-experiments
Use when optimizing multi-factor systems with limited experimental budget, screening many variables to find the vital few, discovering interactions between parameters, mapping response surfaces for peak performance, validating robustness to noise factors, or when users mention factorial designs, A/B/n testing, parameter tuning, process optimization, or experimental efficiency.
discovery-interviews-surveys
Use when validating product assumptions before building, discovering unmet user needs, understanding customer problems and workflows, testing concepts or positioning, researching target markets, identifying jobs-to-be-done and hiring triggers, uncovering pain points and workarounds, or when users mention user research, customer interviews, surveys, discovery interviews, validation studies, or voice of customer.
communication-storytelling
Use when transforming analysis/data into persuasive narratives—presenting to executives, explaining technical concepts to non-technical audiences, creating customer-facing communications, writing investor updates, announcing changes, turning research into insights, or when user mentions "write this for", "explain to", "present findings", "make this compelling", "audience is". Invoke when information needs to become a story tailored to specific stakeholders.
cognitive-design
Use when designing visual interfaces, data visualizations, educational content, or presentations and need to ensure they align with how humans naturally perceive, process, and remember information. Invoke when user mentions cognitive load, visual hierarchy, dashboard design, form design, e-learning, infographics, or wants to improve clarity and reduce user confusion. Also applies when evaluating existing designs for cognitive alignment or choosing between design alternatives.
decision-matrix
Use when comparing multiple named alternatives across several criteria, need transparent trade-off analysis, making group decisions requiring alignment, choosing between vendors/tools/strategies, stakeholders need to see decision rationale, balancing competing priorities (cost vs quality vs speed), user mentions "which option should we choose", "compare alternatives", "evaluate vendors", "trade-offs", or when decision needs to be defensible and data-driven.
deliberation-debate-red-teaming
Use when testing plans or decisions for blind spots, need adversarial review before launch, validating strategy against worst-case scenarios, building consensus through structured debate, identifying attack vectors or vulnerabilities, user mentions "play devil's advocate", "what could go wrong", "challenge our assumptions", "stress test this", "red team", or when groupthink or confirmation bias may be hiding risks.
code-data-analysis-scaffolds
Use when starting technical work requiring structured approach - writing tests before code (TDD), planning data exploration (EDA), designing statistical analysis, clarifying modeling objectives (causal vs predictive), or validating results. Invoke when user mentions "write tests for", "explore this dataset", "analyze", "model", "validate", or when technical work needs systematic scaffolding before execution.
facilitation-patterns
Use when running meetings, workshops, brainstorms, design sprints, retrospectives, or team decision-making sessions. Apply when need structured group discussion, managing diverse stakeholder input, ensuring equal participation, handling conflict or groupthink, or when user mentions facilitation, workshop design, meeting patterns, session planning, or running effective collaborative sessions.
financial-unit-economics
Use when evaluating business model viability, analyzing profitability per customer/product/transaction, validating startup metrics (CAC, LTV, payback period), making pricing decisions, assessing scalability, comparing business models, or when user mentions unit economics, CAC/LTV ratio, contribution margin, customer profitability, break-even analysis, or needs to determine if a business can be profitable at scale.
forecast-premortem
Use to stress-test predictions by assuming they failed and working backward to identify why. Invoke when confidence is high (>80% or <20%), need to identify tail risks and unknown unknowns, or want to widen overconfident intervals. Use when user mentions premortem, backcasting, what could go wrong, stress test, or black swans.
focus-timeboxing-8020
Use when managing time and attention, combating procrastination or context-switching, prioritizing high-impact work, planning daily/weekly schedules, improving focus and productivity, or when user mentions timeboxing, Pomodoro, deep work, 80/20 rule, Pareto principle, focus blocks, task batching, energy management, or needs structured approach to getting important work done.
ethics-safety-impact
Use when decisions could affect groups differently and need to anticipate harms/benefits, assess fairness and safety concerns, identify vulnerable populations, propose risk mitigations, define monitoring metrics, or when user mentions ethical review, impact assessment, differential harm, safety analysis, vulnerable groups, bias audit, or responsible AI/tech.
expected-value
Use when making decisions under uncertainty with quantifiable outcomes, comparing risky options (investments, product bets, strategic choices), prioritizing projects by expected return, assessing whether to take a gamble, or when user mentions expected value, EV calculation, risk-adjusted return, probability-weighted outcomes, decision tree, or needs to choose between uncertain alternatives.
estimation-fermi
Use when making quick order-of-magnitude estimates under uncertainty (market sizing, resource planning, feasibility checks), decomposing complex quantities into estimable parts, bounding unknowns with upper/lower limits, sanity-checking strategic assumptions, or when user mentions Fermi estimation, back-of-envelope calculation, order of magnitude, ballpark estimate, triangulation, or needs to assess feasibility before detailed analysis.
equivariant-architecture-designer
Use when you have validated symmetry groups and need to design neural network architecture that respects those symmetries. Invoke when user mentions equivariant layers, G-CNN, e3nn, steerable networks, building symmetry into model, or needs architecture recommendations for specific symmetry groups. Provides architecture patterns and implementation guidance.
Writing Mentor
Guide users writing new pieces, revising drafts, planning structure, improving organization, making messages memorable, or applying expert writing techniques from McPhee, Zinsser, King, Pinker, Clark, Klinkenborg, Lamott, and Heath
alignment-values-north-star
Use when teams need shared direction and decision-making alignment. Invoke when starting new teams, scaling organizations, defining culture, establishing product vision, resolving misalignment, creating strategic clarity, or setting behavioral standards. Use when user mentions North Star, team values, mission, principles, guardrails, decision framework, or cultural alignment.
grant-proposal-assistant
Use when writing or reviewing NIH, NSF, or foundation grant proposals. Invoke when user mentions specific aims, R01, R21, K-series, significance, innovation, approach section, grant writing, proposal review, research strategy, or needs help with fundable hypothesis, reviewer-friendly structure, or compliance with grant guidelines.
heuristics-and-checklists
Use when making decisions under time pressure or uncertainty, preventing errors in complex procedures, designing decision rules or checklists, simplifying complex choices, or when user mentions heuristics, rules of thumb, mental models, checklists, error prevention, cognitive biases, satisficing, or needs practical decision shortcuts and systematic error reduction.
layered-reasoning
Use when reasoning across multiple abstraction levels (strategic/tactical/operational), designing systems with hierarchical layers, explaining concepts at different depths, maintaining consistency between high-level principles and concrete implementation, or when users mention 30,000-foot view, layered thinking, abstraction levels, top-down design, or need to move fluidly between strategy and execution.
metrics-tree
Use when setting product North Star metrics, decomposing high-level business metrics into actionable sub-metrics and leading indicators, mapping strategy to measurable outcomes, identifying which metrics to move through experimentation, understanding causal relationships between metrics (leading vs lagging), prioritizing metric improvement opportunities, or when user mentions metric tree, metric decomposition, North Star metric, leading indicators, KPI breakdown, metric drivers, or how metrics connect.
meta-prompt-engineering
Use when prompts produce inconsistent or unreliable outputs, need explicit structure and constraints, require safety guardrails or quality checks, involve multi-step reasoning that needs decomposition, need domain expertise encoding, or when user mentions improving prompts, prompt templates, structured prompts, prompt optimization, reliable AI outputs, or prompt patterns.
mapping-visualization-scaffolds
Use when complex systems need visual documentation, mapping component relationships and dependencies, creating hierarchies or taxonomies, documenting process flows or decision trees, understanding system architectures, visualizing data lineage or knowledge structures, planning information architecture, or when user mentions concept maps, system diagrams, dependency mapping, relationship visualization, or architecture blueprints.
market-mechanics-betting
Use to convert probabilities into decisions (bet/pass/hedge) and optimize scoring. Invoke when need to calculate edge, size bets optimally (Kelly Criterion), extremize aggregated forecasts, or improve Brier scores. Use when user mentions betting strategy, Kelly, edge calculation, Brier score, extremizing, or translating belief into action.
model-equivariance-auditor
Use when you have implemented an equivariant model and need to verify it correctly respects the intended symmetries. Invoke when user mentions testing model equivariance, debugging symmetry bugs, verifying implementation correctness, checking if model is actually equivariant, or diagnosing why equivariant model isn't working. Provides verification tests and debugging guidance.
morphological-analysis-triz
Use when need systematic innovation through comprehensive solution space exploration, resolving technical contradictions (speed vs precision, strength vs weight, cost vs quality), generating novel product configurations, exploring all feasible design alternatives before prototyping, finding inventive solutions to engineering problems, identifying patent opportunities through parameter combinations, or when user mentions morphological analysis, Zwicky box, TRIZ, inventive principles, technical contradictions, systematic innovation, or design space exploration.
scientific-manuscript-review
Use when reviewing or editing research manuscripts, journal articles, reviews, or perspectives. Invoke when user mentions manuscript, paper draft, article, research writing, journal submission, reviewer feedback, or needs to improve scientific writing clarity, structure, or argumentation in their manuscript.
prototyping-pretotyping
Use when testing ideas cheaply before building (pretotyping with fake doors, concierge MVPs, paper prototypes) to validate desirability/feasibility, choosing appropriate prototype fidelity (paper/clickable/coded), running experiments to test assumptions (demand, pricing, workflow), or when user mentions prototype, MVP, fake door test, concierge, Wizard of Oz, landing page test, smoke test, or asks "how can we validate this idea before building?".
prioritization-effort-impact
Use when ranking backlogs, deciding what to do first based on effort vs impact (quick wins vs big bets), prioritizing feature roadmaps, triaging bugs or technical debt, allocating resources across initiatives, identifying low-hanging fruit, evaluating strategic options with 2x2 matrix, or when user mentions prioritization, quick wins, effort-impact matrix, high-impact low-effort, big bets, or asks "what should we do first?".
reference-class-forecasting
Use when starting a forecast to establish a statistical baseline (base rate) before analyzing specifics. Invoke when need to anchor predictions in historical reality, avoid "this time is different" bias, or establish outside view before inside view analysis. Use when user mentions base rates, reference classes, outside view, or starting a new prediction.
postmortem
Use when analyzing failures, outages, incidents, or negative outcomes, conducting blameless postmortems, documenting root causes with 5 Whys or fishbone diagrams, identifying corrective actions with owners and timelines, learning from near-misses, establishing prevention strategies, or when user mentions postmortem, incident review, failure analysis, RCA, lessons learned, or after-action review.
negotiation-alignment-governance
Use when stakeholders need aligned working agreements, resolving decision authority ambiguity, navigating cross-functional conflicts, establishing governance frameworks (RACI/DACI/RAPID), negotiating resource allocation, defining escalation paths, creating team norms, mediating trade-off disputes, or when user mentions stakeholder alignment, decision rights, working agreements, conflict resolution, governance model, or consensus building.
memory-retrieval-learning
Use when long-term knowledge retention is needed (weeks to months), studying for exams or certifications, learning new job skills or technology, mastering substantial material that requires systematic review, combating forgetting through spaced repetition and retrieval practice, or when user mentions studying, memorizing, learning plans, spaced repetition, flashcards, active recall, or durable learning.
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