The authors report that AlphaEvolve improved algorithms and mathematical constructions, including a 48-scalar-multiplication construction for 4 × 4 complex matrix multiplication.
Reported discoveryAlgorithms and mathematicsreviewed 2026-07-16
AlphaEvolve: A coding agent for scientific and algorithmic discovery
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 PDF was pinned. Three selected cells from the public results notebook ran in a no-network, read-only sandbox and accepted the 48-rank construction, an Erdős step-function bound, and a dimension-11 kissing construction.
The AlphaEvolve agent, its search process, Google infrastructure results, the full paper, and the novelty or priority of any result 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
- 2506.13131v1
- Submitted
- 2025-06-16
- Version date
- 2025-06-16
- Size
- 3,525,764 bytes · 44 pages
- PDF SHA-256
- f092c8cbd65da89951ee6496374da9a54963f9035758c25ac6e4625f506df9ad
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 v1 PDF matched the recorded SHA-256, byte count, and page count.
Boundary
This establishes file identity, not correctness.
Passed · bounded
Selected matrix verifier
Observed
Reviewed notebook cells 4, 36, and 37 accepted a rank-48 decomposition for the 4 × 4 × 4 matrix multiplication tensor.
Boundary
This checks the supplied construction; it does not reproduce how AlphaEvolve found it or establish novelty.
Passed · bounded
Two selected mathematical verifiers
Observed
Reviewed cells 77–79 produced C5 ≤ 0.38092303510845016, and cells 113–114 accepted a dimension-11 kissing construction of at least 593.
Boundary
These are selected executable checks from the authors' result notebook, not a review of every result.
Blocked
Full notebook portability
Observed
A sequential replay stopped at cell 72 because Python 3.9 lacks sys.set_int_max_str_digits.
Boundary
Environment drift made this run inconclusive; it is not evidence that the mathematical result failed.
external artifacts
Pinned, not trusted by default.
AlphaEvolve 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. The repository publishes results and verifiers, not the AlphaEvolve engine.
red-team findings
Where a confident summary can outrun the evidence.
- The public repository does not expose the discovery engine, so generation claims cannot be replayed from this artifact.
- A verifier accepting an author-supplied construction is stronger than prose but narrower than reproducing the search or establishing priority.
- The notebook has a Python-version portability dependency that was not declared as a locked environment.
primary sources
Follow the evidence outward.
Dossier certiv-ai-discovery-2026-07-16/alphaevolve. Certiv produced this test record; the paper authors did not issue or endorse it.