The bottleneck in AI-assisted computational science is rarely the model. It is the knowledge underneath. A numerical method written in a 1998 paper may be mathematically sound, but an agent cannot reuse it unless the statement, the algorithm, and the error bound are all connected to something it can cite. FARMS — a Verifiable Foundation for Automated Computational Science — proposes a pipeline for building exactly that layer.
The Pipeline
FARMS has three stages. Source preparation turns scattered computational mathematics into structured source material. Reusable representations capture algorithmic meaning rather than prose. Semantic review checks that what was extracted is faithful to what the source actually says.
The pipeline was run against 171 targets in randomized numerical linear algebra and numerical partial differential equations. 157 were accepted, at mean estimated costs of US $0.85–2.29 per target across sources — cheap enough that the approach can be applied at scale rather than to a hand-picked shortlist.
The Verification Layer
What separates FARMS from a documentation project is the proof obligation. Lean-checked implications derived from explicit source premises connect each selected statement to the computational skill it licenses, so a downstream agent can trace why a method is valid rather than merely that a paper claims it is. The paper illustrates this with two cases: a heat-flow solve and wave-response compression.
That distinction matters for agents that write code. A method whose error guarantee is machine-checked against a stated premise is a method an agent can reason about. A method lifted from prose is a method an agent can only pattern-match.
Why It Matters
The interesting claim is not that FARMS works on 171 numerical targets. It is that provenance can be made cheap enough to be routine. Most knowledge-curation pipelines fail on economics: the review cost per item scales with how carefully you check it, so the corpus stays small and only covers what someone cared to curate.
At roughly a dollar per target, verification stops being a bottleneck and becomes a default. That is the precondition for a different class of agent: one that discovers numerical methods, checks them, and reuses them without a human in the loop deciding what counts as trustworthy.
The caveats are ordinary ones. The evaluation domains are numerical linear algebra and PDEs — both mature fields with well-typed quantities, which flatters a pipeline built around formal statements. Symbolic or data-dominated computational science would be harder. And “semantic review” still carries a human-judgment component whose cost the per-target figure only partly captures.
Still, the direction is a real one: from models that know about methods to agents that can prove why a method holds.
Related: arXiv:2610.40560