Paper → Proof → Code
Ingest a published paper, extract its theorems, formalize them in Lean 4, and compile the proofs to executable code. One pipeline, three verified stages.
Visual Models
CAB-certified visualizations parameterized by Lean 4 proofs. Every shader constant traces back to a machine-checked theorem.
Proof Explorer
Navigate the dependency graph of our entire verified codebase. Search declarations, inspect proof terms, trace upstream and downstream dependencies.
Lean Blueprint
Interactive blueprint of all HeytingLean modules. View proof status, dependency structure, and completion progress across the formalization program.
Structure tames probability.
Large language models are stochastic. Every response is a sample from a distribution—useful, often brilliant, never guaranteed. The way to harness this power is not to fight the randomness but to channel it through persistent, deterministic artifacts that survive the session that produced them.
A well-designed tool converts probabilistic generation into reproducible output. It defines the input contract, constrains the transformation, and writes the result to a format that can be verified, versioned, and reused—independent of the model that created it. The artifact becomes the source of truth, not the conversation.
This is how we build with AI at apoth3osis: every tool below produces a concrete, auditable artifact—a proof tree, a translation ledger, a certified export, a formal conjecture. The model proposes; the tool constrains; the artifact persists. What remains is not a chat log but a verified contribution to the codebase.
Define the input schema, the valid transformations, and the output invariants before the model touches anything. The tighter the contract, the more useful the output.
Write the result to disk in a format that outlives the session. JSON proof trees, Lean source, translation ledgers, certified binaries—artifacts that version-control and diff cleanly.
Run the artifact through a deterministic checker—a type checker, a kernel, a test harness. If the model got it wrong, the tool catches it. Correctness is a gate, not a hope.
Artifact-producing tools
Each tool below defines a clear input, applies a structured transformation, and outputs a persistent artifact. They are designed to be used by humans and AI agents alike—the interface is the contract.
Sheaf Transport Engine
Machine-verified proof transport across algebraic lenses via differentiable sheaf-theoretic ATP. Proves in one representation, transports to another with kernel-checked correctness.
Have a workflow that should produce a verified artifact instead of a chat response? We build tools that make AI outputs deterministic, persistent, and auditable. Reach out at rgoodman@apoth3osis.io.