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Get Started Free →Multi-layer cognitive stack for machine-verified mathematical problem solving across 14 sub-disciplines.
| Test case | Without → With | Effect | Δ tokens | Δ turns |
|---|---|---|---|---|
| case-01 | ✗→✓ | ▲ Improved | -22% | 0% |
| case-20 | ✓→✓ | ＝ Same ✓ | 2% | 0% |
| case-02 | ✓→✓ | ＝ Same ✓ | 11% | 0% |
| case-03 | ✓→✓ | ＝ Same ✓ | -6% | 0% |
| case-04 | ✓→✓ | ＝ Same ✓ | -7% | 0% |
A structured collection of skills for mathematical reasoning, proof construction, and problem solving.
| Directory | Topic | |-----------|-------| | abstract-algebra | Groups, rings, fields, homomorphisms | | category-theory | Functors, natural transformations, adjoints | | complex-analysis | Holomorphic functions, contour integration | | functional-analysis | Banach/Hilbert spaces, operators | | graph-number-theory | Graph theory and number-theoretic results | | information-theory | Entropy, channel capacity, coding | | linear-algebra | Vector spaces, matrices, eigenvalues | | math-intuition-builder | Build intuition before formalization | | math-model-selector | Choose the right mathematical model | | math-progress-monitor | Track proof progress and open goals | | mathematical-logic | Propositional and first-order logic, proofs | | measure-theory | Sigma-algebras, integration, probability foundations | | numerical-methods | Approximation, error analysis, algorithms | | odes-pdes | Ordinary and partial differential equations | | optimization | Convex, combinatorial, gradient-based optimization | | real-analysis | Limits, continuity, differentiation, integration | | rudin-real-complex-analysis | Guided work through Rudin's textbooks | | topology | Open sets, continuity, compactness, connectedness |
Activate the appropriate sub-skill based on the mathematical domain in the user's question. Use math-model-selector when the domain is unclear.
Other measured skills in the registry, with their headline benchmark lift.