On October 6, 2026, OpenAI published mathematical results from an internal frontier model. The openai/math repository contains 722 manuscripts organized into 372 families, with Lean formalizations for many of the results.
For engineers building AI agents, the release suggests a concrete experiment: apply its separation between proposing a result and independently checking it to the rules that update persistent memory.
For Symptomato, the target is a familiar failure: a corrected patient record arrives, an old document is uploaded again, and the current value silently goes backward. Every extracted field can be correct while the update rules fail.
The published Lean artifacts make many of the proofs available for machine checking. Verification status varies across the collection, and some results still lack formalizations. The model itself remained internal at publication.
The repository also includes verification instructions using Comparator, an existing tool from Lean FRO. OpenAI's release shows how these established tools can accompany AI-generated research results.
OpenAI additionally shares reasoning summaries, attempted-problem counts, and compute estimates. That transparency suggests another practice to carry into our experiment: report the effort required to obtain a checked result.
The transferable component is the verification workflow. Our patient-memory specification and proofs would be new application work.
Consider a synthetic sequence for one weight observation: Revision 1 records 72.4 kg. Revision 2 explicitly corrects that observation to 72.1 kg. Revision 1 arrives again.
Bind each accepted structured event to an organization, patient, encounter, and assertion. Store its source lineage, source-issued revision, operation, value, and immutable provenance. Compare revisions only within that lineage. Independent sources need separate reconciliation rules.
Corrections carry complete replacement values, allowing revision 2 to be accepted before revision 1. Arrival order never determines precedence.
The ledger stores distinct structured events. Equality includes stable payload and provenance; transport delivery timestamps and delivery IDs stay outside it. Reusing a version-specific event ID with different content produces an ingestion conflict, with both candidates preserved.
Derive the current view from the highest revision for each scoped assertion and source. A consistent assertion becomes active; a retraction removes its active value while preserving history. Incompatible operations or values at the highest revision become a visible conflict.
These statements reuse existing Mathlib finite-set laws. The model covers evidence insertion only. Event validation and the current-record projection still need their own definitions and proofs.
The third obligation is essential: a function that ignores every event would also be idempotent and independent of delivery order.
Implement the projection next, with explicit obligations: Consistent assertions at the highest revision produce the current value and its provenance. A strictly older revision cannot replace the current value or resurrect a retracted assertion within its lineage. Incompatible highest revisions produce a conflict regardless of delivery order. Every displayed value has stored evidence for the exact organization, patient, encounter, and assertion. Previously accepted events remain in the ledger after a correction.
A reviewer freezes the schema, reducer definitions, theorem statements, imports, and build configuration. The agent fills in proof bodies, using Lean diagnostics to guide bounded retries.
Give Comparator a trusted Challenge and an agent-produced Solution. Under its documented environment assumptions, it checks statement and definition agreement, permitted axioms, and acceptance of the proofs by the Lean kernel. Changes to the contract require a separate review.
Keep a minimal repository with the reviewed model, candidate proofs, generated histories, and the CI check. Pin Lean and Mathlib versions so every proof attempt runs against the same environment.