What was already known
Axiotis and Sviridenko obtained O(kκ) support bounds and asked whether the condition-number exponent could be improved. Earlier obstructions applied to particular algorithms, not all randomized polynomial-time methods.
AI involvement
Lin, Mirrokni and Woodruff say a fully automated Gemini-based system first obtained the proof. They verified it, edited the paper and explain the graph-to-regression reduction.
The abstract and acknowledgements explicitly say a fully automated Gemini-based system first obtained the proof; no initial human mathematical step is identified.
Importance
Under the stated hypothesis, extends an algorithm-specific barrier to all randomized polynomial-time sparse least-squares algorithms.
Limitations
The conclusion is conditional on the exact-volume SSE hypothesis and specific to least squares; it is not an unconditional barrier for all sparse convex objectives.
Technical verification
The three named human authors report verifying the complete proof of the conditional theorem before editing the final version. This is a source-reported author check, not one reproduced here; it does not verify the SSE hypothesis itself.
Formal checking
Human verification of the model-origin proof and editing of the final mathematical presentation
- Checker
- Honghao Lin, Vahab Mirrokni and David P. Woodruff, author-reviewers
- Scope
- Theorem 1.1's conditional sparse-least-squares condition-number lower bound
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The named authors present a detailed explanation of the reduction and its exact-volume soundness step in Sections 1.2 and 4, and say they verified and clarified the proof. No specific central step is identified as unexplained.
Correction and publication history
Under the stated hypothesis, extends an algorithm-specific barrier to all randomized polynomial-time sparse least-squares algorithms.
Read this published revision