Math Research Lab

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

Skills (14)

• concept-disambiguation

  Use to prevent renaming, concept substitution, terminology inflation, and false novelty in candidate research concepts.

• concept-miner

  Use to detect recurring empirical or theoretical patterns and formulate cautious candidate concepts without claiming novelty.

• concept-registry

  Use to create and update auditable markdown records for candidate concepts under research_notes/concept_registry/.

• experiment-audit

  Use to audit data splits, duplicates, provenance, configs, checkpoints, evaluators, seeds, resource budgets, and reproducibility risks.

• formalize-problem

  Use when a vague mathematical idea, anomaly, algorithm, result, or research claim must be turned into precise objects, assumptions, claims, proof obligations, falsification tests, and minimal validation experiments.

• geometry-audit

  Use to analyze vector geometry, embeddings, prototypes, margins, distances, drift, clusters, and boundary crossings.

• metric-audit

  Use to audit any reported metric, especially generic metrics computed from matrices, sequences, grouped results, checkpoints, or decompositions.

• notation-audit

  Use to find ambiguous mathematical notation, overloaded symbols, dimension mismatches, unclear indices, inconsistent terminology, and undefined objects.

• numerical-validation

  Use to run reproducible numerical tests for mathematical or algorithmic claims, including property tests, gradient checks, finite differences, stability sweeps, and sensitivity checks.

• optimization-audit

  Use to analyze loss curves, convergence, gradients, plateaus, sensitivity, instability, additional optimization exposure, and hyperparameter-driven artifacts.

• proof-audit

  Use to critically inspect derivations, proof sketches, lemmas, equivalence arguments, convergence arguments, gradient derivations, or mathematical explanations.

• research-judge

  Use after a claim, result, mechanism, metric, explanation, or candidate concept has been produced and needs balanced evidence-bound adversarial judgment.

• spectral-audit

  Use to analyze SVD, eigenvalues, spectral energy, entropy, effective rank, low-rank reconstruction, and subspace coverage.

• statistical-audit

  Use to assess empirical evidence strength, uncertainty, confidence intervals, effect sizes, permutation tests, bootstrap tests, and seed sensitivity.

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