Introducing MathKernel, an evidence-aware multi-engine mathematics runtime for LLMs, available as a Python library (mathkernel) and as an MCP server (mathkernel-mcp), designed to enable applications and LLMs to perform advanced mathematics with explicit provenance, trust labels, and claim-specific evidence.

The project provides detailed documentation of its typed functionality surface, listing domain objects, operations, and outputs, and emphasizes replayability of provenance through derivation traces and replayable source ancestry for complex artifacts.

A nuanced trust model uses multiple evidence types—formal Lean certificates, exact arithmetic, symbolic checks, interval-certified numerics, and numeric/empirical evidence—and propagates provenance explicitly; overall trust is determined by the weakest required evidence for a claim.

The feature matrix covers a broad range of domains and operations (including algebra, calculus, graphs, combinatorics, topology, statistics, PDEs, optimization, geometry, and more), with outputs that provide separate evidence bundles for each conclusion rather than a single aggregated trust score.

A core design goal separates the LLM's mathematical intent from the kernel's computations, ensuring results carry explicit trust levels, engine tags, and derivation trails, including exact computations, symbolic results, certified certificates, and empirical proofs.

The architecture is a typed orchestration layer where MathKernel coordinates parsing, contexts, object identity, persistence, evidence composition, and derivation tracking, while domain adapters perform mathematics through multiple engines (symbolic, exact, certified, formal, numerical).

Practical usage paths include installation and quickstart guides for both MCP server usage and the Python library, with examples spanning symbolic solving, exact arithmetic in GF(2^m), finite dynamics, and various verification workflows.

The trust model cautions against treating engine agreement as proof and notes that decimal literals reduce trust to numeric; for proof-grade results, exact rationals or interval certifications are required, with Lean/SMT certificates available for formal proofs.