Use Jacobian's MCP operations for nontrivial mathematical computation, finite search, structural analysis, formal checking, probability, or optimization.
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概要と使いどころ
Use Jacobian's MCP operations for nontrivial mathematical computation, finite search, structural analysis, formal checking, probability, or optimization.
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Fix LRU-bounded Flutter/bloc state classes that silently lose insertion-order updates. Use when: (1) a state class uses `Equatable` with a `LinkedHashMap<K, V>` field to preserve insertion order (LRU, MRU, recent-items caches), (2) `Cubit.emit` appears to drop emissions when an existing key is re-inserted or moved to most-recent, (3) LRU eviction evicts the "wrong" entry after a refresh, (4) a test that reports the same key twice and then overflows the cap sees the refreshed entry evicted instead of the oldest. Root cause: Equatable's default map comparison is structural (unordered), so reordering without changing keys/values produces an "equal" state that `Cubit.emit` suppresses.
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Write SEO pages that rank on Google AND get cited by LLMs. Uses live SERP data, 500-token chunk architecture, RAG optimization for Gemini 3.5 Flash, the Two-Gate AEO framework (retrieval-pool entry + selected-citation extraction), the Anti-NLP Stuffing Protocol (structural entity placement, no keyword-density stuffing), strict single-service local isolation, and the Reddit Test quality gate. Triggers on: "write an SEO page", "seo-agi", "seo page for [keyword]", "rank for [keyword]", "rewrite this page for SEO", "GEO", "AEO", "write a page that ranks".
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Extract abstract mathematical models from functional code (Haskell, OCaml, F#) for formal reasoning in Isabelle/HOL. Use when users need to: (1) Convert functional programs to Isabelle definitions, (2) Extract high-level algorithm essence from implementation code, (3) Generate formal specifications and properties from code, (4) Create verification-ready models that capture mathematical properties while abstracting away implementation details. Focuses on structural recursion, algebraic data types, higher-order functions, and invariant extraction.
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Recommends appropriate software design patterns based on problem descriptions, requirements, or code scenarios. Use when designing software architecture, refactoring code, solving common design problems, or choosing between design approaches. Analyzes the problem context and suggests suitable creational, structural, behavioral, architectural, or concurrency patterns with implementation guidance and trade-off analysis.
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Find the papers that answer a research query in Firecrawl's research paper index — a corpus of paper abstracts whose largest share is biomedical and life-science literature (PubMed, bioRxiv, medRxiv), alongside arXiv preprints in CS, physics, and math — using semantic search, semantic and structural expansion, and in-body verification. Use this skill for literature-finding and paper-retrieval tasks of any kind, including clinical, biomedical, drug, gene, disease, and other life-science questions, whether the answer is a single paper or a full multi-paper set. The index is reached only through the `firecrawl_research_*` MCP tools or the `firecrawl research` CLI subcommands. Calling `firecrawl_search` with its `categories` option set to `["research"]` is a different feature — it filters ordinary web search to research-affiliated websites (the list includes PubMed, bioRxiv, medRxiv, arXiv, and publisher sites) and returns page results from them, without querying the paper records in this index.
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Use when reviewing a bundle-plugin for structural issues, version drift, skill quality, workflow integration, or security risks — before releasing, after changes, or after adding skills. Auto-detects scope (full project vs skill vs workflow)
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Verify that code changes are correct, safe, and ready to ship. Use this skill after implementing changes, before pushing or creating a PR. Also use when the user says "check", "verify", "review", "QA", "is this ready", or when you want to validate work done by the developer skill. Runs build, lint, and structural checks.
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Systematic quality check for a completed rebuttal document before submission. Use after Stage 3 document compilation or after Stage 5 final remarks writing to verify completeness, tone, factual accuracy, and structural integrity. Catches common rebuttal errors before they reach reviewers.
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Business model classification, business model analysis, structural analysis of how a company makes money, product offering decomposition, distribution channel analysis, customer segment analysis, revenue model identification, market sizing TAM SAM SOM, competitive positioning, business unit performance, management team & leadership analysis, what does the company sell, how does the company go to market, business model type platform service product, channel mix direct vs indirect, revenue concentration risk, CEO CFO executive backgrounds and changes
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Think and work like an expert Mathematical Modeler. Use when a task calls for Mathematical Modeler judgment. Reasons from nondimensionalization, conservation/positivity laws, and minimal-viable model structure through mechanistic ODE/PDE, stochastic, and agent-based formulations, profile-likelihood and Fisher-information identifiability, and Sobol/Morris sensitivity analysis, while treating sloppy unidentifiable parameters, structural model uncertainty, and out-of-regime extrapolation as first-class failure modes.
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Think and work like an expert Mechatronics Engineer. Use when a task calls for Mechatronics Engineer judgment. Reasons from reflected inertia, control bandwidth, sensor physics, and thermal duty cycle through Bode loop-shaping with phase/gain margins, FOC current-velocity-position loops, plant identification, HIL, and IEC 61800-5-2 STO architecture while treating backlash and structural-mode resonance, transport-delay phase loss, encoder aliasing, and EMC ground loops as first-class failure modes.
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Think and work like an expert Marine Geologist. Use when a task calls for Marine Geologist judgment. Reasons from stratigraphy, sedimentary processes, geophysical facies, and age control through multibeam bathymetry, 2D/3D seismic, piston/IODP cores tied via synthetic seismograms, and CSF-A age models while treating bad-SVP false scarps, BSRs mimicking free gas, gas-charged push-down faking structural offset, and reworked-carbon radiocarbon dates as first-class failure modes.
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Think and work like an expert Geologist. Use when a task calls for Geologist judgment. Reasons from Steno's principles and Walther's Law through Brunton strike/dip, measured sections, hand-lens rock ID (QAPF/Folk/Dunham), thin-section petrography (PPL/XPL, Michel-Lévy, point counting), FGDC/GeMS geologic maps, NGMDB/Geolex/Macrostrat, and stereonet structural analysis while treating weathering, float, and map-as-hypothesis as first-class failure modes.
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Think and work like an expert Environmental Policy Analyst. Use when a task calls for Environmental Policy Analyst judgment. Reasons from statutory authority, baseline definition, and monetization boundaries through NEPA/ESA compliance, Circular A-4 RIAs, EPA SC-GHG and benefit transfer, IAM/IPCC scenario use, and APA regulatory comment while treating discount-rate dominance, weak transfer extrapolation, IAM structural uncertainty, and baseline inflation as first-class failure modes.
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Think and work like an expert Causal Inference Scientist. Use when a task calls for Causal Inference Scientist judgment. Reasons from structural causal models, potential outcomes, and identification logic through DAGs and do-calculus, doubly-robust estimators (AIPW/TMLE, IPTW, g-formula), and design-based methods (IV, RD, Callaway-Sant'Anna DiD, synthetic control) while treating colliders and M-bias, positivity/overlap failure, and unmeasured confounding (Rosenbaum bounds, E-values) as first-class failure modes.
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Resolve the architecture of focal oncogene amplifications — extrachromosomal DNA (ecDNA), breakage-fusion-bridge (BFB) cycles, homogeneously staining regions (HSR), and linear amplification — from whole-genome sequencing with AmpliconArchitect, the AmpliconSuite pipeline, and AmpliconClassifier. Covers copy-number seed selection, breakpoint-graph reconstruction, balanced-flow optimization, ecDNA classification, and the limits of depth-only amplification calls. Use when a focal amplification needs structural characterization, when distinguishing ecDNA from chromosomal amplification, suspecting ecDNA-driven oncogene amplification or therapy resistance, or selecting copy-number seeds for amplicon reconstruction.
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Installs 425 bioinformatics skills covering sequence analysis, RNA-seq, single-cell, variant calling, metagenomics, structural biology, and 56 more categories. Use when setting up bioinformatics capabilities or when a bioinformatics task requires specialized skills not yet installed.
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Build circular genome visualizations using circlize (R), pyCirclize (Python), or Circos (Perl CLI) with ideogram tracks, multi-data tracks (scatter, histogram, heatmap), chord/link arcs for interactions, and explicit circos.clear() between plots. Covers when circular is appropriate vs when Cartesian wins (Cleveland-McGill 1984), karyograms, and chromosome adjacency in chord diagrams. Use when adjacency on the circle conveys meaning — chromosome-level overview, structural variants, Hi-C interactions, cross-genome comparisons.
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Access and analyze AlphaFold protein structure predictions. Use when predicted structures are needed for proteins without experimental structures, or for confidence scores (pLDDT).
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Workflow for small-variant and structural-variant discovery, filtering, annotation, and interpretation from sequencing data.
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Structure retrieval, confidence-aware AlphaFold DB usage, coordinate download, PAE and pLDDT interpretation, and structure-guided biological annotation.
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Structure similarity search with Foldseek. Use this skill when: (1) Finding similar structures in PDB/AFDB databases, (2) Structural homology search, (3) Database queries by 3D structure, (4) Finding remote homologs not detected by sequence, (5) Clustering structures by similarity. For sequence similarity, use uniprot BLAST. For structure prediction, use chai or boltz.
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Workflow for nanopore or PacBio long-read QC, alignment, polishing, methylation-aware analysis, and structural variant discovery.
日本語の概要は準備中です。原文の説明を表示しています。