Science
Six AI-led science findings worth watching
Two independent proofs of Feige’s conjecture, a Werner-state result, a formally checked queueing argument, an optimization counterexample, AI-generated quantum compilers, and a sharp entropy bound.
Published
28 lipca 2026
Observed by
Maciej Czypek
Founder of aeoh
Six findings remained after deduplication in this observation window. Each has a public manuscript and an explicit statement from the authors about substantial AI involvement in the proof, discovery, or implementation.
These are early signals, not settled scientific facts. Most are same-day or recent preprints without peer review. We separate what the manuscript claims, what role the authors assign to AI, and what independent or formal verification is currently visible.
Observation
Six findings after deduplication
Observation window
01:17–07:17 CEST on July 28, 2026
Evidence standard
Primary manuscripts, explicit AI attribution, and separate verification status.
Editorial note
“Found” means observed in this scan. It does not mean peer reviewed, independently reproduced, or formally proved unless the entry says so.
01
Two independent teams report proofs of Feige’s conjecture
Feige’s conjecture concerns independent, nonnegative random variables with expectation one. It states that the probability their sum is below n + 1 is at least (n / (n + 1))ⁿ, which is no smaller than 1/e.
Weibo Fu, Yanjun Han, Guanyang Wang, Jun Yan, Peng Zhang, and Zhengqing Zhou report a sharper small-deviation inequality. For δ ≥ 1, their bound is sharp and implies Feige’s conjecture. Separately, Zipei Nie and Jiaye Wei present a short proof of the standard conjecture. Both approaches build on the recent resolution of Gaffke’s conjecture, but they are separate manuscripts by separate author groups.
AI contribution
The first team states that the proof was found by ChatGPT 5.6 Pro. Nie and Wei state that their proof was obtained with the assistance of GPT-5.6 Sol.
Verification status
This is the strongest finding in the scan on replication grounds: two independent preprints reached the result at nearly the same time. Neither manuscript reports peer review or machine formalization.
Primary sources
Weibo Fu, Yanjun Han, Guanyang Wang, Jun Yan, Peng Zhang, and Zhengqing Zhou.
Zipei Nie and Jiaye Wei.
02
A negative answer to the two-copy Werner-state problem
Thomas C. Fraser, Felix Huber, Balázs Pozsgay, and István Vona answer Problem 5 from Five Open Problems in Quantum Information Theory. They report that the specified two-ququart Werner state is not two-copy distillable.
The manuscript proves a stronger partial-trace inequality and characterizes the full region in which Werner states are two-copy undistillable. In the authors’ result, the one-copy and two-copy distillability regions coincide.
AI contribution
The manuscript says the results were found and written up with GPT Sol 5.6, Claude Fable, and Claude Opus.
Verification status
A complete 13-page preprint is public. We found no independent review or machine formalization attached to this manuscript at the time of observation.
Primary sources
Thomas C. Fraser, Felix Huber, Balázs Pozsgay, and István Vona.
03
A threshold policy for the first nontrivial three-server case
Weina Wang, Taha Ameen, Yudong Chen, Yige Hong, Josh Nichols, and Matthew Zurek study a queue with one fast server and two identical slow servers. They prove that an optimal policy has a threshold structure.
The result resolves the first nontrivial case beyond the two-server problem introduced by Lin and Kumar in 1984. It covers discounted cost and, under the stated stability condition, average cost.
AI contribution
The authors say GPT-5.5 Pro generated the core technical ideas. They verified the proofs and rewrote the manuscript for rigor, clarity, and exposition.
Verification status
Three key lemmas have also been verified in Lean 4, with public code. That materially strengthens confidence in the central machinery, although the full paper has not yet passed peer review.
Primary sources
Author-hosted manuscript.
Formal verification for three key lemmas.
04
The SS–RS inequality fails, while RS–GD survives under a restriction
Binghui Peng addresses a COLT 2021 open question about single-shuffle SGD, random-reshuffle SGD, and gradient descent on quadratic finite sums.
The paper gives explicit positive semidefinite matrices, with condition number arbitrarily close to one, for which the proposed SS–RS inequality fails. It also proves the RS–GD inequality under a stated condition-number restriction.
AI contribution
The author states that the proof was found through extended prompting of GPT-5.5 Pro.
Verification status
The public preprint contains an explicit counterexample and a proof of the positive result. We found no independent review or formal verification linked from the manuscript.
Primary sources
Binghui Peng.
05
Frontier models generate competitive trapped-ion compilers
Fabian Kreppel, Reza Salkhordeh, Ferdinand Schmidt-Kaler, and André Brinkmann asked Claude Opus 4.7 to generate and iteratively refine complete Python shuttling compilers for trapped-ion quantum computers.
Against hand-crafted baselines, the generated compilers reduced shuttling timesteps by up to 76% for linear segmented traps and up to 39% for junction architectures. Repeating the complete process with Claude Fable 5 produced similar findings and surpassed hand-crafted compilers more often on the largest circuits.
AI contribution
The authors describe an unmodified frontier model producing the full compiler code without additional manual algorithmic engineering.
Verification status
This is a benchmarked engineering result with a from-scratch repeat using a second model. The replication was performed by the same research team, and the work remains a preprint.
Primary sources
Fabian Kreppel, Reza Salkhordeh, Ferdinand Schmidt-Kaler, and André Brinkmann.
06
A sharp continuity bound for quantum conditional entropy
Mario Berta, Pablo Costa Rico, Gereon Kossmann, Ludovico Lami, and Julius A. Zeiss report the optimal dimension-only continuity bound for quantum conditional entropy.
They also show tightness across the full state-distance range when the second system is sufficiently large. The result adapts a tight classical argument to a quantum setting that requires a different construction.
AI contribution
The authors say the key proof idea was developed with the assistance of ChatGPT 5.6 Sol.
Verification status
A complete four-page manuscript with a two-page appendix is public. The AI attribution is narrower than in several other findings: it concerns the central proof idea rather than the entire result or write-up.
Primary sources
Mario Berta, Pablo Costa Rico, Gereon Kossmann, Ludovico Lami, and Julius A. Zeiss.
How findings qualify
- A finding must point to a public manuscript or primary technical artifact.
- The authors must explicitly disclose a substantial AI role; outside speculation does not qualify.
- Near-duplicate claims are merged, while independent work is preserved as evidence of replication.
- Preprint, peer-review, independent-replication, and formal-verification status are reported separately.