Math Research Lab

Plugin math-research-lab in bytetiff/SolanumCL. Commands read from the repo's manifest — 1 month ago.

Skills (16)

• concept-disambiguation

  Use this skill when a candidate concept, new term, renamed effect, theoretical interpretation, or unusual empirical pattern may overlap with existing mathematical or machine-learning concepts.

• concept-miner

  Use this skill when searching for new, underexplored, or weakly formalized mathematical concepts from experimental patterns, algorithmic behavior, or repeated empirical anomalies.

• domain-adapter-router

  Use this skill when a mathematical audit should be specialized to a domain such as continual learning, PDE/PINN, hypernetworks, simplex decompositions, quantization, or optimization.

• continual-learning-adapter

  Use this adapter with Math Research Lab when analyzing continual learning, Class-IL, BWT, forgetting, replay buffers, task-balanced sampling, or SGFR-like methods.

• hypernetwork-adapter

  Use this adapter with Math Research Lab when analyzing hypernetworks, generated parameters, task-conditioned networks, or mappings from problem parameters to model weights.

• optimization-adapter

  Use this adapter with Math Research Lab when analyzing optimizers, convergence claims, gradient alignment, curvature, stability, or hybrid optimization schedules.

• pde-pinn-adapter

  Use this adapter with Math Research Lab when analyzing PDE solvers, PINNs, residual losses, boundary conditions, parameterized PDEs, or hybrid optimizers.

• quantization-adapter

  Use this adapter with Math Research Lab when analyzing vector quantization, codebooks, product quantization, learned quantizers, or memory-accuracy trade-offs.

• simplex-decomposition-adapter

  Use this adapter with Math Research Lab when analyzing simplex decompositions, triangulations, barycentric coordinates, coverage claims, or piecewise-linear approximations.

• formalize-problem

  Use this skill when a research idea, algorithm, mathematical claim, or experimental result must be converted into precise mathematical objects, assumptions, definitions, and proof obligations.

• geometry-spectral-audit

  Use this skill when analyzing SVD, PCA, rank, effective dimension, feature margins, prototype geometry, subspace overlap, or spectral explanations of a method.

• novelty-scan

  Use this skill when positioning a candidate mathematical concept, method, theorem, or empirical phenomenon against nearby literature and known terminology.

• numerical-validation

  Use this skill when a mathematical claim needs randomized numerical tests, finite-difference checks, stability tests, or synthetic counterexample searches.

• proof-audit

  Use this skill when checking a derivation, theorem, lemma, proposition, convergence argument, complexity claim, or mathematical explanation.

• research-judge

  Use this skill after a mathematical, empirical, conceptual, or algorithmic research result has been produced and must be critically judged for overclaiming, weak evidence, alternative explanations, concept substitution, protocol artifacts, missing decisive tests, and next research forks.

• statistical-audit

  Use this skill when checking confidence intervals, seed sensitivity, bootstrap estimates, permutation tests, metric stability, or experimental significance.

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