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Multi-layer cognitive stack for machine-verified mathematical problem solving across 14 sub-disciplines.
Passed 22 of 22 test cases with the skill, and 21 of 22 without it.
1 fixed21 passed either way0 still failing0 broke
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A test case the skill fixed. Same model, same prompt, with and without the skill.
I have a complex real-world problem involving tracking fluid flow, network traffic congestion, and probabilistic customer churn, but I'm unsure which mathematical domain or framework I should use to model it. What step or module should be used first to select the appropriate mathematical framework?
| Checked | Without skill | With skill |
|---|---|---|
| Recommends using math-model-selector to choose the appropriate mathematical framework. | Missed | Passed |
The instructions your model reads when the skill loads.
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.
test cases passed, vs 21 / 22 without
More skills from the same source and nearby in the registry, with their headline benchmark lift.