A Mathematical
Sky Survey.
A systematic search through the open questions between mathematics’ landmarks.
SCOPE — the System for Conjecture and Open-Problem Exploration — is a mathematical sky survey using AI research methods. It searches broadly with SCOPE Survey and stays with harder questions through SCOPE Deep.
SCOPE is designed as a research map rather than a publication stream. Most findings are intended to remain quiet public records, becoming visible primarily when they are relevant to a researcher exploring the corresponding region of mathematics.
SCOPE Survey
The wide-field research architecture behind SCOPE, designed for broad exploration within short time windows and modest inference budgets.
Meet SCOPE SurveyPublished on Resultary.
Resultary holds each finding, its provenance, version, and verification evidence. Annual GitHub archives hold supporting code, formal proofs, and research files.
Search SCOPE findingsFrom a question to a record.
Phase II connects specific literature gaps with research and review of correctness, originality, and value. The research architecture remains experimental and may change throughout the phase.
Define a concrete, valuable gap.
Start from existing literature, define the objects and assumptions, and identify a useful gap between established results—not merely a famous unresolved problem.
Check what is already known.
Search prior work before committing research effort. Record the scope and limitations of that search.
Give SCOPE a bounded observing window.
SCOPE Survey coordinates research under explicit time and cost limits, producing a claim and a traceable argument.
Examine the result from three directions.
Review examines correctness, originality, and mathematical value, including equivalent statements and stronger prior coverage. Each record identifies its review method; a same-model review is not independent validation.
Bring valuable results to the kernel.
Selected high-value results may later enter Lean verification; it is not an automatic stage of the current workflow. The record states the exact formalized claim, its assumptions, and external dependencies.
Keep the map open.
Publish the core derivation, provenance, and verification status on Resultary. Supporting code and research material remain available in the annual GitHub archive.
See what stands behind a result.
Phase II records can be published after a same-model review. Their review status is explicit: same-model review, independent AI review, Lean verification, and expert attestation are different evidence categories and must never be conflated.
- same-model reviewed
- the same-model review has reviewed correctness, originality, and value. Read the recorded evidence and limitations; this does not qualify as independent AI review.
- AI Reviewed
- An AI reviewer independent of the producing research agent has reviewed the full stated result and its proof. The review record identifies the reviewer, date, scope and proof version. This is not a mathematical guarantee.
- Lean Verified
- A formalization covering the full stated result has passed Lean kernel checking. The evidence identifies the checked declaration and proof version, with the statement correspondence, assumptions and axiom dependencies available for inspection. Checking a supporting lemma alone does not earn this badge.
- Expert Attested
- A named human expert has provided an explicit attestation for the full stated result and proof version. The record links to the attestation and its scope. This does not imply journal peer review or institutional endorsement.
A check mark means qualifying evidence is recorded for the current proof version. “Not recorded” is an absence of evidence, not a claim that the result is false. Earlier-version, partial and withdrawn checks do not qualify as current verification. Originality remains a separate assessment. Labelled demonstration records are not published research results and do not claim completed reviews.
Search filters use all-of matching: selecting Lean Verified and Expert Attested shows only records with both. Independent AI review is asserted only when separate qualifying evidence is recorded; the review method is stated for each result.
Every status has a scope.
Badges must point to a specific proof version and supporting evidence. A change to the proof requires renewed checks for that version. Corrections and withdrawals remain part of the record; the preview does not yet accept public attestations.
Cost
SCOPE’s estimated annualized API-equivalent cost is approximately US$1 million. This estimate reflects equivalent API usage, not actual spending.
Phase II: expanding the survey.
Phase II began on 16 September 2026 UTC. This stage develops literature-led mathematical exploration through ongoing experiments in research and review. Its architecture is not fixed for the duration of the phase. Originality is assessed to the best of our knowledge: inaccessible papers most likely to contain equivalent or stronger results are disclosed, not silently ruled out. Completed accepted packages are published to the annual GitHub archive.
Explore the findings on Resultary