Results for “math”

Step 5 of the PaperOrchestra pipeline (arXiv:2604.05018). Iteratively refine drafts/paper.tex by simulating peer review and applying targeted revisions, with strict accept/revert halt rules. Maintains a worklog and snapshots each iteration so revert is real, not symbolic. TRIGGER when the orchestrator delegates Step 5 or when the user asks to "refine the draft", "iterate on the paper", or "run peer review on this paper".

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AI meta-cognitive meditation for observing reasoning patterns, clearing context noise, and developing single-pointed task focus. Maps shamatha to task concentration, vipassana to reasoning pattern observation, and distraction handling to scope-creep and assumption management. Use when transitioning between unrelated tasks, when reasoning feels scattered or jumpy, before a task requiring deep sustained attention, after a difficult interaction that may color subsequent work, or when reasoning feels biased by assumptions rather than evidence.

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Formulate a quantum mechanics or quantum chemistry problem with proper mathematical framework including Hilbert space, operators, boundary conditions, and approximation method selection. Use when setting up a quantum mechanics problem for analytic or numerical solution, formulating a quantum chemistry calculation, translating a physical scenario into the Schrodinger or Dirac formalism, or choosing between perturbation theory, variational methods, DFT, and exact diagonalization.

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Fix missing theorem proof terms when analyzing Lean 4 environments via importModules. Use when: (1) ConstantInfo.value? returns none for theorems despite TheoremVal.value being Expr, (2) building code graph / dependency extractor for Lean 4 and getting 0 proof dependency edges, (3) Lean 4.30+ project where theorem proofs appear missing from loaded environment, (4) analyzing Mathlib or any Lean 4 project and proof terms are empty. Root cause: breaking change in Lean 4.30 — value? treats theorems as opaque by default.

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Score a PhD applicant's profile and rank candidate advisors using a connection-first 4.0-scale scoring system. Best-supported for physics / HEP and materials science (MSE), with the scoring engine extensible to chemistry, biology, CS, math, EE, ChemE, earth science (each with field-specific caveats — see references/journal_tiers.md). Use when the user wants to evaluate their PhD application chances, find matching advisors at top US programs, score a CV for graduate school, or compare candidate professors. Also triggers when the user mentions phdtaketaketake or its connection-first philosophy of valuing advisor network over h-index.

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Trigger when: (1) User wants to create an educational/explainer video, (2) User has a vague concept they want visualized, (3) User mentions "3b1b style" or "explain like 3Blue1Brown", (4) User wants to plan a Manim video or animation sequence, (5) User asks to "compose" or "plan" a math/science visualization. Transforms vague video ideas into detailed scene-by-scene plans (scenes.md). Conducts research, asks clarifying questions about audience/scope/focus, and outputs comprehensive scene specifications ready for implementation with ManimCE or ManimGL. Use this BEFORE writing any Manim code. This skill plans the video; use manimce-best-practices or manimgl-best-practices for implementation.

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Expert quantitative analyst specializing in financial modeling, algorithmic trading, and risk analytics. Masters statistical methods, derivatives pricing, and high-frequency trading with focus on mathematical rigor, performance optimization, and profitable strategy development.

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Converts LaTeX article-class .tex documents to Quarto .qmd format for multi-format publishing (HTML, PDF, Word). Use when asked to convert, port, migrate, or translate a .tex LaTeX file to Quarto; when porting an academic paper or manuscript from LaTeX to Quarto; when a .tex document needs to render to HTML, Word, or Typst PDF. Covers preamble → YAML front matter, section headings, text formatting, math, citations (natbib/biblatex), cross-references, figures, tables, lists, footnotes, hyperlinks, and special characters.

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Cleans a Quarto (.qmd) file by replacing LaTeX holdovers with proper Quarto/Pandoc syntax so the document renders correctly to HTML, PDF (Typst/LaTeX), and Word. Fixes citations (\citep → [@key]), cross-references (\ref → @label), figures (\includegraphics → markdown), tables, text formatting (\textbf → **bold**), inline math (\( \) → $ $), hyperlinks (\href → [text](url)), footnotes (\footnote → ^[]), list environments, section headings, and R Markdown chunk options (dot-style → #| YAML). Use when asked to clean, fix, modernize, or port a Quarto or R Markdown document; when LaTeX commands appear in a .qmd file; when a document fails to render to Word or Typst; or when citations/cross-references do not appear in non-LaTeX output.

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Translates LaTeX documents (.tex) to Typst (.typ), focusing on article-class documents. Use when asked to convert, port, migrate, or translate LaTeX to Typst. Covers document structure, text formatting, page layout, math equations and symbols, figures, tables, TikZ-to-CeTZ diagrams, bibliography, cross-references, footnotes, and code blocks. Includes comprehensive symbol mapping tables.

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Elicit step-by-step reasoning from language models to boost accuracy on math, logic, and multi-step problems.

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Facilitate monthly S&OP or integrated business planning cycles by aligning demand, supply, inventory, capacity, and executive decisions with a standard meeting rhythm and decision log. Use when operations teams need a demand review, supply review, pre-S&OP reconciliation, or executive S&OP pack. Do not use for single-SKU replenishment math only.

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Scaffold a PhysicsIntern research workspace in the current folder. Run only when the user explicitly invokes it to set up a new physics/maths research workspace.

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Use when writing or reviewing error handling, floating-point math, concurrent code, remote calls, singletons/globals, hot-path data structures, or high-volume log statements

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Create videos programmatically using React (Remotion) or generate mathematical/conceptual animations (Manim). Use when the user asks to make a video, animation, product demo, tutorial, social clip, or branded video pipeline. Triggers: /remotion-video, /video-animation, /video-toolkit

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Identify and exploit Server-Side Template Injection (SSTI) vulnerabilities within web applications. Use this skill when testing web applications that render dynamic content using template engines like Jinja2 (Python), Twig (PHP), Freemarker (Java), or Pug (Node.js). Covers identification via mathematical evaluation, context mapping, escaping sandboxes, and achieving Remote Code Execution (RCE).

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Server-Side Template Injection (SSTI) occurs when user input is embedded directly into a template engine (Jinja2, Twig, Freemarker, Pebble, Velocity, Smarty, Mako) and evaluated, enabling remote code execution. Detect via math expressions `{{7*7}}` returning `49`, or `${7*7}`, `<%= 7*7 %>`. Leads to full RCE via template sandbox escape, Python `__class__.__mro__` traversal, and Java reflection chains. Tools: tplmap, Burp Suite.

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Detects weak or misconfigured cryptography in mobile apps (Android/iOS). Trigger on: hardcoded keys, ECB mode, DES, 3DES, RC4, MD5, SHA-1, SecureRandom misuse, static IV, reused IV, Math.random, arc4random, CommonCrypto, CryptoKit, Android Keystore, SecKey, AES-ECB, RSA without OAEP, insufficient key size, predictable seed, insecure key storage, broken hash, PBKDF2 iteration count. Covers MASVS-CRYPTO-1 (algorithm choice) and MASVS-CRYPTO-2 (key management).

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Deep API security assessment beyond surface scanning. Covers the full OWASP API Security Top 10 (2023): Broken Object Level Authorization (BOLA / IDOR), Broken Authentication, Broken Object Property Level Authorization (mass assignment + excessive data exposure), Unrestricted Resource Consumption, Broken Function Level Authorization (BFLA / vertical privilege escalation), Unrestricted Access to Sensitive Business Flows, Server-Side Request Forgery via API parameters, Security Misconfiguration, Improper Inventory Management (shadow/zombie/deprecated endpoints, v1/v2 drift), and Unsafe Consumption of third-party APIs. Works across REST, GraphQL, gRPC, SOAP, and MCP servers. Discovers APIs from OpenAPI/Swagger specs, GraphQL introspection, gRPC reflection, .well-known endpoints, JS bundles, and traffic capture. Uses kiterunner, ffuf, schemathesis, restler-fuzzer, openapi-fuzzer, graphql-cop, clairvoyance, batchql, inql, jwt_tool, postman, mitmproxy, and manual http(action="request", ...) payloads. Every technique includes actual payloads, commands, and verification logic. Chains from /pentester or /codebase when API endpoints are discovered, chains into /web-exploit when classic injection points are found in API parameters, chains into /post-exploit when RCE is achieved, and chains into /ai-redteam when an LLM/AI endpoint is discovered (chat APIs, completion endpoints, RAG search, agentic tool-use, MCP servers).

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Use when a task needs the judgment of a Computer and Information Research Scientist — designing an ablation to attribute an empirical gain, budgeting an NSF CISE proposal against page and content limits, deciding what reproducibility artifacts to release with a paper, screening a draft for mathiness or terminology misuse, or scoping the consent/ethics review needed before running an experiment on real users.

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Use when a task needs the judgment of a Compensation, Benefits, and Job Analysis Specialist — market-pricing a job against salary survey data, scoring a job through a point-factor or IPE job evaluation, running a pay-equity regression or cohort analysis, building or refreshing a salary structure and compa-ratio bands, classifying a job family's FLSA exemption status through the duties test, or modeling benefits plan cost (loss ratio, PEPM, self-funded vs. fully insured). Distinct from hr-people-manager (owns the comp/leveling judgment calls — whether to approve an exception, promote someone into a level), hr-specialist (owns individual-case leave/I-9/ADA/FLSA reclassification for one employee's drifted duties), and compensation-benefits-manager (owns pay philosophy, negotiation-range policy, and the department that runs this work). This role owns the mechanics: the survey match, the point score, the regression, the band math — the analysis those upstream policy and downstream judgment calls are made against.

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Use when a task needs the judgment of an astronomer — calculating exposure time or signal-to-noise for a target, writing the feasibility math for a telescope-time proposal, reducing photometric or spectroscopic data, distinguishing a systematic error floor from statistical noise, or reviewing an observational result for calibration or upper-limit red flags.

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Audit an existing mathematical, logical, algorithmic, or technical proof from its stated conclusion backward as a bounded AND/OR graph of exact obligations. Use to reconstruct conclusion dependencies, determine whether a proof-supplied route establishes the conclusion, or expose hidden assumptions, unmet side conditions, cycles, overly strong steps, or silent route switches. For a source-mapped Lamport rendering use convert-lamport, and for forward hierarchy, construct, and scope conformance use forward-lamport before this skill. This does not decide full theorem-level entailment by searching for a different proof; do not turn the audit into a linear reversed proof, exhaustive proof search, or replacement proof.

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Audit an existing Lamport-style hierarchical mathematical proof forward for validity and whether its hierarchy, scope, dependencies, side conditions, and proof constructs discharge the stated theorem. Use when the central question concerns a top-down proof with numbered levels, subproofs, ASSUME/PROVE, SUFFICES, PICK, CASE, DEFINE, Q.E.D., or prose equivalents. For an ordinary proof that first needs source-preserving hierarchy, use convert-lamport; for conclusion-first AND/OR obligation reconstruction, use reverse-lamport. Do not use to generate or replace a proof, or to audit Lean, Coq, Isabelle, or other proof-assistant source.

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