The authors report that AlphaEvolve rediscovered many best-known solutions and improved several mathematical constructions across 67 problems.
Reported discoveryMathematicsreviewed 2026-07-16
Mathematical exploration and discovery at scale
Certiv evidence level
Selected check replayedcentral claim independently reproduced?
No.
That answer stays “no” even when a selected check passed.
claim boundary
Three statements that must not be collapsed.
The exact v3 paper was pinned. Selected public verifiers for an Erdős step-function bound and a dimension-11 kissing construction ran successfully in isolation.
The 67-problem campaign, system autonomy, comparative preparation time, novelty, generality, and all unselected constructions were not independently reproduced.
source identity
The paper is versioned bytes.
A mutable title or unversioned link is not enough to reproduce what was reviewed.
- arXiv version
- 2511.02864v3
- Submitted
- 2025-11-03
- Version date
- 2025-12-22
- Size
- 12,141,713 bytes · 81 pages
- PDF SHA-256
- 77b43844077c98c26dfc76ad391cadbbd53d48a1d290ddae575ff4d1bcdef9d2
Observed parser properties
- Recognized as a PDF and not encrypted.
- pdfinfo reported JavaScript: no.
- pdfdetach reported no embedded files.
- pdftotext completed successfully.
These probes reduce ambiguity and obvious PDF attack surface. They are not a comprehensive malware analysis.
Certiv T0 exercise: this exact PDF was hash-pinned without executing its declared command. The unchanged input remained explicitly unverifiable; a one-byte tamper produced a failed input_hash_drift finding.
test record
Checks, failures, and blockers.
Status is always paired with text. A pass applies only to the check and boundary shown in the same row.
Observed
Exact PDF identity
Observed
The downloaded v3 PDF matched the recorded SHA-256, byte count, and page count.
Boundary
This establishes file identity, not mathematical validity.
Passed · bounded
Selected Erdős verifier
Observed
Reviewed notebook cells 77–79 accepted the supplied step function and produced C5 ≤ 0.38092303510845016.
Boundary
One construction was checked; the surrounding theorem, comparative literature, and novelty were not adjudicated.
Passed · bounded
Selected kissing-number verifier
Observed
Reviewed notebook cells 113–114 accepted the supplied construction showing at least 593 spheres in dimension 11.
Boundary
This validates the supplied witness under the notebook's check, not the paper's full campaign.
Not run
Full study reproduction
Observed
No end-to-end replay of all 67 problems was attempted.
Boundary
The dossier must not be read as 67 independent reproductions.
external artifacts
Pinned, not trusted by default.
AlphaEvolve mathematical results repository
Observed revision4226acbf237ff9ad10ba7673a2af127a2d8a5971
Recorded SHA-2562cce2543e48c89aa3e91614272a698a0147dd2548ea11cf92f1292b7435d38ff
SHA-256 is for mathematical_results.ipynb at the observed revision. The Certiv cell-selection runner SHA-256 is 82a2424c064ff5a6e2a75d8291c8d9b65577b9d2243580e4e467934fe5f9f73c.
red-team findings
Where a confident summary can outrun the evidence.
- Two accepted witnesses cannot support a claim that the entire 67-problem study was reproduced.
- The results repository supplies checkable outputs but not the proprietary discovery engine.
- Literature comparison and novelty require domain-expert review outside a computational receipt.
primary sources
Follow the evidence outward.
Dossier certiv-ai-discovery-2026-07-16/mathematical-exploration-at-scale. Certiv produced this test record; the paper authors did not issue or endorse it.