'math' 검색 결과

Review academic papers for correctness, quality, and novelty using OpenJudge's multi-stage pipeline. Supports PDF files and LaTeX source packages (.tar.gz/.zip). Covers 10 disciplines: cs, medicine, physics, chemistry, biology, economics, psychology, environmental_science, mathematics, social_sciences. Use when the user asks to review, evaluate, critique, or assess a research paper, check references, or verify a BibTeX file.

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Universal LaTeX document skill: create, compile, and convert any document to professional PDF with PNG previews. Supports resumes, reports, cover letters, invoices, academic papers, theses/dissertations, academic CVs, presentations (Beamer), scientific posters, formal letters, exams/quizzes, books, cheat sheets, reference cards, exam formula sheets, fillable PDF forms (hyperref form fields), conditional content (etoolbox toggles), mail merge from CSV/JSON (Jinja2 templates), version diffing (latexdiff), charts (pgfplots + matplotlib), tables (booktabs + CSV import), images (TikZ), Mermaid diagrams, AI-generated images, watermarks, landscape pages, bibliography/citations (BibTeX/biblatex), multi-language/CJK (auto XeLaTeX), algorithms/pseudocode, colored boxes (tcolorbox), SI units (siunitx), Pandoc format conversion (Markdown/DOCX/HTML ↔ LaTeX), and PDF-to-LaTeX conversion of handwritten or printed documents (math, business, legal, general). Compile script supports pdflatex, xelatex, lualatex with auto-detection, latexmk backend, texfot log filtering, PDF/A output, and verbosity control (--verbose/--quiet). Empirically optimized scaling: single agent 1-10 pages, split 11-20, batch-7 pipeline 21+. Use when user asks to: (1) create a resume/CV/cover letter, (2) write a LaTeX document, (3) create PDF with tables/charts/images, (4) compile a .tex file, (5) make a report/invoice/presentation, (6) anything involving LaTeX or pdflatex, (7) convert/OCR a PDF to LaTeX, (8) convert handwritten notes, (9) create charts/graphs/diagrams, (10) create slides, (11) write a thesis or dissertation, (12) create an academic CV, (13) create a poster, (14) create an exam/quiz, (15) create a book, (16) convert between document formats (Markdown, DOCX, HTML to/from LaTeX), (17) generate Mermaid diagrams for LaTeX, (18) create a formal business letter, (19) create a cheat sheet or reference card, (20) create an exam formula sheet or crib sheet, (21) condense lecture notes/PDFs into a cheat sheet, (22) create a fillable PDF form with text fields/checkboxes/dropdowns, (23) create a document with conditional content/toggles (show/hide sections), (24) generate batch/mail-merge documents from CSV/JSON data, (25) create a version diff PDF (latexdiff) highlighting changes between documents, (26) create a homework or assignment submission with problems and solutions, (27) create a lab report with data tables, graphs, and error analysis, (28) encrypt or password-protect a PDF, (29) merge multiple PDFs into one, (30) optimize/compress a PDF for web or email, (31) lint or check a LaTeX document for common issues, (32) count words in a LaTeX document, (33) analyze document statistics (figures, tables, citations), (34) fetch BibTeX from a DOI, (35) convert a Graphviz .dot file to PDF/PNG, (36) convert a PlantUML .puml file to PDF/PNG, (37) create a one-pager/fact sheet/executive summary, (38) create a datasheet or product specification sheet, (39) extract pages from a PDF (page ranges, odd/even), (40) check LaTeX package availability before compiling, (41) analyze citations and cross-reference with .bib files, (42) debug LaTeX compilation errors, (43) make a document accessible (PDF/A, tagged PDF), (44) create lecture notes or course handouts, (45) fill an existing PDF form (fillable fields or non-fillable with annotations), (46) extract text or tables from a PDF (pdfplumber, pypdf), (47) OCR a scanned PDF to text (pytesseract), (48) create a PDF programmatically with reportlab (Canvas, Platypus), (49) rotate or crop PDF pages (pypdf), (50) add a watermark to an existing PDF, (51) extract metadata from a PDF (title, author, subject).

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Use when the user wants to run a full ad-campaign pipeline on top of Higgsfield Marketing Studio — 'create a campaign', 'build a content plan', 'run the content pipeline', 'generate 100 UGC videos', 'plan and schedule a launch', 'make a batch of ads from my product', or 'how much did this save vs traditional production'. Covers the 5-stage orchestration (Research → Plan → Generate → Publish → Report), the UGC-first 5-format campaign mix (UGC Entertainment, Street Interview, Unboxing, Product Review, ASMR), the even-split allocation math, button-driven onboarding, the per-batch generation gate, and the publish + cost-report tail (satellite). Defers all Marketing Studio API ground-truth (presets, params, hooks, avatars) to higgsfield-marketing-studio.

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Builds lead generation systems using Alex Hormozi's Core Four framework (warm outreach, content, cold outreach, paid ads), lead magnets, and Rule of 100. Use when designing customer acquisition, scaling advertising, choosing marketing channels for revenue stage, building referral programs, or fixing low lead flow. Covers lead magnets, LTGP:CAC math, More Better New scaling, and Lead Getters (referrals, employees, agencies, affiliates).

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Guided trip planning workflow. Asks destination, dates, travelers, class, and flexibility, then runs parallel flight/hotel search with cpp math and booking plan.

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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 the user is launching or running a DROPSHIPPING business end to end — the full 12-phase pipeline: product research with winning criteria, Minea and PiPiAds, supplier sourcing on AliExpress, CJ, Spocket, and Zendrop, Shopify store and app setup, the 10-ads-per-week creative pipeline, interest and lookalike targeting, 3-5x markup and BE-ROAS math, customer service, and scaling. Trigger on 'start dropshipping', 'winning product research', 'Shopify store setup', 'AliExpress supplier', 'scale my dropshipping store', 'my store gets traffic and no sales'. Not for — only the ad copy, see `05-ad-copy-global`; only the product page, see `12-landing-page-brief-global`; only the account audit, see `21-ads-audit-global`; only pricing, see `17-pricing-strategy-global`.

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Use when a marketing BUDGET has to be planned or managed in USD — allocation by bucket, channel, and month, test versus scale split, scale-up and stop-loss thresholds, reserve, a plan-versus-actual tracker, and a review cadence. Trigger on 'budget planning', 'marketing budget', 'split the budget across channels', 'stop loss threshold', 'quarterly budget', 'we keep overspending and nobody notices'. Also use when a number has been approved and nobody has divided it up. Not for — the revenue-backward math that produces the number, see `10-reverse-kpi-global`; paid media allocation only, see `54-media-plan-global`; paying an external vendor, see `67-agency-vendor-brief-global`.

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Use when persuasion principles have to be applied to a specific asset — reciprocity, scarcity, authority, social proof, liking, commitment, and unity mapped onto copy, a landing page, an email, or an ad, each with a hypothesis and a test plan. Trigger on 'marketing psychology', 'Cialdini', 'persuasion principles', 'how do I add urgency', 'make this more convincing', 'behavioral triggers for this page'. Also use when the user asks why people read the whole page and still do not buy. Not for — price framing and margin math, see `17-pricing-strategy-global`; building the offer itself, see `31-offer-design-global`; running the experiment properly, see `19-ab-test-setup-global`.

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Use when the user wants a VALID experiment instead of a guess — hypothesis, one variable, sample size and runtime math, statistical significance, primary versus secondary metrics, multi-arm designs, and a results template, across Optimizely, VWO, and native Meta and Google tests. Trigger on 'A/B test', 'split test', 'how long should I run the test', 'is this result significant', 'test two versions', 'which creative is actually better'. Also use when a winner was declared after two days on tiny numbers. Not for — scaling the proven winner, see `55-scaling-ads-global`; analyzing data already collected, see `13-data-analysis-global`; auditing the account, see `21-ads-audit-global`.

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Use when a PAID MEDIA plan is needed — work backward from revenue to max CPA and required budget, split spend across channels, funnel stages, and campaign types, build a ramp-up timeline, set KPI targets per channel, and prepare a contingency plan. Trigger on 'media plan', 'paid media budget', 'how much should I spend on ads', 'channel mix for the campaign', 'plan the ad budget', 'we have 10k a month and no plan'. Also use when a budget number exists and nobody has decided where it goes. Not for — the pure revenue-to-budget math, see `10-reverse-kpi-global`; the whole marketing budget including non-paid, see `61-budget-planning-global`; the next period plan built from results, see `57-next-ads-plan-global`.

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在Python中复现C#的Quaternion.AngleAxis方法，根据角度和旋转轴计算四元数，且不使用numpy.quaternion库。

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Converts Markdown to styled HTML with WeChat-compatible themes. Supports code highlighting, math, PlantUML, footnotes, alerts, and infographics. Use when user asks for "markdown to html", "convert md to html", "md转html", or needs styled HTML output from markdown.

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Creates a lesson plan, student-facing materials, and observation template. Load this skill BEFORE asking the teacher any clarifying question about grade, subject, topic, standard, or timing. Use when a K-12 teacher needs a math, ELA, science, or social studies lesson built from scratch — even if grade, subject, or topic isn't yet stated. Do NOT load for grading, a rubric, assessment feedback, a quiz, or a standards lookup — answer those directly. Triggers on explicit requests (lesson plan, mini-lesson, unit plan, daily plan) and implicit teacher intent: "I'm teaching long division to 5th graders," "need to teach photosynthesis tomorrow." Core signal: teacher needs new instructional content created. A new lesson that asks for differentiated, tiered, or leveled materials is still ONE planning request — this skill produces those materials inside the lesson package; do not also invoke k12-lesson-differentiation. Not for differentiating an existing lesson (use k12-lesson-differentiation) or passage rewrites.

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Helps a teacher prepare to teach an existing K-12 lesson (math / ELA / science / social studies) — a prep partner that thinks through the lesson's key student task with the teacher and leaves a short teacher-only prep note. Triggers on asks to internalize, prepare for, get ready to teach, or understand a lesson, including implicit ones ("help me get ready for tomorrow's lesson"), and right after another skill built a lesson, which it can follow. Not for building or adapting a lesson, grading, rubrics, assessment feedback, or generating quizzes or student-facing material, and not for single-fact lookups a sentence would answer ("what standard is this?", "how long is this lesson?").

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Adapts an existing K-12 lesson (math, ELA, science, or social studies) for students at different proficiency levels (below / at / above grade level). Load this skill BEFORE asking the teacher any clarifying question about the lesson, tiers, or student levels. Triggers on explicit asks to differentiate, tier, or scaffold a lesson, and on implicit signals like "my students are at different levels". Produces 1 teacher-facing differentiation plan + 3 student-ready tier documents as editable, printable documents in a single output turn (shared content is written once, so tiers cannot drift). Uses the Learning Commons Knowledge Graph when connected; works without it. This skill adapts a lesson the teacher brings or names. Not for creating a new lesson from scratch — a new-lesson request that asks for differentiated or leveled materials is k12-lesson-plan-creation's job, one package. Not for grading, rubrics, assessment feedback, or quizzes.

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Metacognitive check-ins during problem solving - detects when to pivot or persist

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Search Mathlib for lemmas by type signature pattern using Loogle.

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Mathematically rigorous Socratic interview system that drives ambiguity below 20% before any code is written. One question per message, weighted ambiguity scoring, brownfield-aware, outputs a complete PRD. Replaces discovery-interview with a stricter protocol.

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Manages persistent memory. Invoke to read active context or archive old tasks. Structure: Long-term Principles (Rules) + Short-term Workbench (Tasks).

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自动清洗赛题或爬取的数据（处理缺失/异常/格式），并生成可视化图表。Invoke when 用户需要处理原始数据、清洗数据或生成数据分析图表。

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根据 model_route.json、数据计划和清洗数据，为数学建模论文生成结果证据契约和 q1/q2/q3 建模代码脚手架。Invoke when 需要把模型输出、评价指标、结构化结论、论文表格和当前赛题专用建模代码沉淀到 paper_output/results/、paper_output/tables/ 和 paper_output/code/modeling/，供 QA 与正文生成读取。

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按常见评分点生成建模论文结构与写作清单，并根据题目类型与数据条件给出模型选择与对照实验路线。Invoke when需要“论文格式/评分对齐/模型选型/路线不确定”。

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强制审计论文生成质量，防止模型偷换、逻辑断链、内容空洞。Invoke when 用户提出检查/审计/验收/确保/verify/QA，或合并前需要把关。

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