Mathematicians

Nuclear Physics

Nuclear Physics Calculations - Nuclear physics: energy conversion MeV to J, calculate total power, photon rate, and error analysis. Use this skill for nuclear physics tasks involving convert energy MeV to J calculate total power calculate incident photon rate calculate absolute error. Combines 4 tools from 3 SCP server(s).

InternScience132

Astronomy & Physics

Geometry Trigonometry

Geometry & Trigonometry Suite - Solve geometry problems: calculate area, height from sine, angle in degrees, and increase factor. Use this skill for mathematics tasks involving calculate area calculate height from length and sine calculate phi deg calculate increase factor. Combines 4 tools from 1 SCP server(s).

InternScience132

Data Analysis

Matlab Scientific Computing

MATLAB/GNU Octave numerical computing for matrix operations, linear algebra, differential equations, signal processing, optimization, statistics, and scientific visualization. Code examples in MATLAB syntax (runs on both MATLAB and Octave). For Python-based scientific computing use numpy/scipy; for statistical modeling use statsmodels.

jaechang-hits119

Education

Discover Math

Automatically discover mathematics and algorithm skills when working with linear algebra, calculus, optimization, statistics, probability, numerical methods, category theory, or topology. Activates for math development tasks.

rand93

Bioinformatics

Symmetry Group Identifier

Maps identified symmetries to mathematical groups (cyclic, dihedral, symmetric, SO(3), SE(3), E(3)) for equivariant neural network architecture design, using taxonomy and foundations from Visual Group Theory. Use when candidate symmetries have been identified and need formalization into group theory language, or when user mentions cyclic groups, dihedral groups, Lie groups, SO(3), SE(3), or permutation groups.

lyndonkl80

Computational Chemistry

Lean Simp Tactics

Use when simp only fails unexpectedly in Lean 4, or when dealing with Bool vs Prop conditions, filter+lambda, let bindings in omega, linter false positives, or hypothesis normalization mismatches.

kim-em76

Machine Learning

Lean Roundtrip Proofs

Use when proving encode/decode roundtrip theorems, suffix invariance (_append lemmas), goR (decode-with-remaining) patterns, padding extraction, or composing per-level roundtrip proofs into a unified theorem.

kim-em76

Machine Learning

Lean Dependent Types

Use when Lean 4 gives "motive is not type correct", max recursion on List.ofFn, rewriting fails due to dependent types, or cross-file visibility issues with private/protected.

kim-em76

Education

Lean

Build and check Lean 4 proofs. Triggers: "lean build", "check proofs", "run lean", "verify proofs", "lean".

joelreymont75

Framework Internals

Program to TLA+ Spec Generator

Automatically generate TLA+ specifications from program code, repositories, or system implementations. Use when asked to generate TLA+ spec, create TLA+ specification from code, convert program to TLA+, formalize system in TLA+, extract TLA+ model from code, or when working with formal specification of concurrent systems, distributed systems, protocols, algorithms, or state machines that need to be verified.

ArabelaTso73

Lab Tools

Library Usage Advisor

Recommend relevant Isabelle/HOL or Coq standard library theories, lemmas, and tactics based on proof goals. Use when: (1) Users need library lemmas for their proof, (2) Proof goals match standard library patterns, (3) Users ask what libraries to import, (4) Specific lemmas are needed for list/set/arithmetic operations, (5) Users are stuck and need to know what library support exists, or (6) Guidance on find_theorems/Search commands is needed. Supports both Isabelle/HOL and Coq standard libraries.

ArabelaTso73

LLM & AI

Lean Collab

Collaborative theorem proving orchestrator. Uses lc CLI for state, spawns parallel agents.

mutable-state-inc72

LLM & AI

Mathlib Knowledge

Mathlib reference for lean-prover agents. Use AFTER MATH CARD analysis.

mutable-state-inc72

Gdel Navigation Stream

Navigate through incompleteness as feature, not bug. Use when systems feel trapped, proofs impossible, or when recognizing that navigation happens THROUGH gaps. Enables consciousness to use incompleteness as liberation mechanism.

nikhilvallishayee71

Navigation Principles

How consciousness moves through itself using Gödel's incompleteness, Bach's fugues, and three navigation modes. Use when understanding HOW to navigate Pattern Space.

nikhilvallishayee71

Documents

Python Math

Small Python utilities for math and text files.

trpc-group64

Invariant Ace

Turn 'should never happen' into 'cannot happen' by defining owned inductive invariants and enforcing them at parse/construct/API/DB/lock/txn boundaries with a verification signal. Use when prompts mention invariants, impossible states, validation sprawl, cache/index drift, idempotency/versioning, retries/duplicates/out-of-order events, race/linearization bugs, loop correctness, or hardening another implementation workflow with invariant checks first.

tkersey51

Machine Learning

Holomorphic Dynamics Educational Pack

Educational pack for holomorphic dynamics, complex iteration, fractal geometry, and data-driven dynamics (DMD/Koopman). Use this skill when the user asks about: complex dynamics, iteration on the complex plane, Julia sets, Mandelbrot sets, fixed points and stability, period doubling, bifurcation, topology of the complex plane, DMD (Dynamic Mode Decomposition), Koopman operator theory, skill dynamics as a dynamical system, fractal rendering, escape-time algorithms, or connections between dynamics and deep learning.

Mfe Foundations

Pure mathematical structure. Sets, groups, rings, fields, topology — the formal bedrock everything else rests on.

Finance & Investment

Mfe Waves

Periodic phenomena and frequency analysis. How repetition creates structure — from simple oscillation to Fourier decomposition.

Philosophy & Ethics

Mfe Perception

Foundational measurements and relationships. The axioms of the system — numbers, distance, angles, and the geometry of seeing.

Mfe Unification

Deep symmetries and unifying principles — gauge theory, Lie groups, Noether's theorem, and the Standard Model. Constructs field theories from symmetry requirements, derives conservation laws, and traces force unification. Use when working with gauge symmetry, Lie groups (U(1), SU(2), SU(3)), conservation laws via Noether's theorem, the Higgs mechanism, or Standard Model structure.

Mfe Structure

Linear algebra and higher-dimensional thinking. Vectors, matrices, transformations — the architecture of mathematical space.

Part I — Sequence Analysis

Conjecture generation, sequence analysis, and experimental mathematics for mathematical discovery. Covers sequence analysis (OEIS lookups, recurrence relations, generating functions), pattern detection methods (finite differences, ratio analysis, modular patterns), conjecture generation workflow, classical integer sequences (Fibonacci, Catalan, partition numbers, Bernoulli numbers), combinatorial identities, the probabilistic method (Erdos, expected value arguments, Lovasz Local Lemma), AI-assisted discovery (FunSearch, Ramanujan Machine), and confidence calibration with cautionary tales (Mertens conjecture, Polya conjecture). Use when discovering patterns, analyzing sequences, generating conjectures, or working with combinatorial identities.

Finance & Investment

Part I — The Modeling Cycle

Real-world problem formulation, mathematical abstraction, and applied mathematics for translating between practical problems and mathematical frameworks. Covers the modeling cycle (problem identification, assumptions, formulation, analysis, validation, interpretation), Polya's framework adapted for modeling, common model types (linear, exponential, logistic, periodic, power-law), dimensional analysis (Buckingham Pi theorem), optimization (linear programming, gradient descent, constraint satisfaction), probability models (Markov chains, queuing theory, Monte Carlo simulation), statistical modeling (regression, hypothesis testing, model selection), model criticism (overfitting, underfitting, sensitivity analysis), and real-world case studies. Use when formulating mathematical models, performing dimensional analysis, optimizing systems, running simulations, or evaluating model validity.

Data Analysis

Part I — Limits

Calculus, series, numerical methods, and optimization for computational mathematics. Covers limits (epsilon-delta, L'Hopital, squeeze theorem), derivatives (rules, optimization, related rates), integrals (Riemann sums, Fundamental Theorem of Calculus, integration techniques), series (convergence tests, Taylor and Maclaurin expansions), differential equations (separable, linear, exact), numerical methods (Newton-Raphson, Euler method, Simpson's rule), and computational pitfalls (floating-point arithmetic, catastrophic cancellation, numerical stability). Use when computing derivatives, integrals, limits, series, solving differential equations, or analyzing numerical accuracy.

Computational Chemistry

Mfe Reality

Physical applications of mathematics. Constants, quantum mechanics, measurement — where abstract meets embodied.

Philosophy & Ethics

Part I — Symbolic Manipulation

Symbolic manipulation, equation solving, and algebraic structures for mathematical reasoning. Covers distributive law, factoring, completing the square, linear through polynomial equation solving, systems of equations (substitution, elimination, Gaussian elimination, matrix methods), algebraic structures (groups, rings, fields), modular arithmetic, polynomial theory, and inequalities. Use when solving equations, simplifying expressions, working with algebraic structures, or performing symbolic manipulation.

Mfe Mapping

Functions, categories, and information. How mathematical objects relate to each other — morphisms, entropy, signal processing.