An evidence-aware multi-engine mathematics kernel — usable as a Python library (mathkernel) and MCP server (mathkernel-mcp) — enables LLMs to perform advanced mathematics while preserving assumptions, provenance, and claim-specific evidence. The LLM interprets intent; the Math Kernel computes and records mathematical evidence with explicit trust levels, engine tags, and derivation trails. Exact computation, symbolic results, certified enclosures, formal proofs, and empirical evidence are distinct claims; approximate-input ancestry must not disappear silently.

The kernel uses a typed orchestration layer: the public facade handles parsing, contexts, object identity, persistence, evidence composition, resource policy, and derivation tracking, while domain adapters perform actual mathematics. Presentation layers cannot alter claims. Features span symbolic algebra, calculus, complex analysis, probability, exact graph theory, combinatorics, geometry, topology, statistics, PDEs, and more, with support for Numba, CUDA, parallelism, visualization, sonification, and unified portable artifacts.

The system ensures mathematical integrity by separating computation from presentation, preventing silent loss of evidence or misleading interpretations.