What was already known
EF1 and fractional Pareto optimality were known together without balancedness. Balanced results had weaker guarantees or restricted valuation classes.
AI involvement
Cookson, Shah and Verma supplied research direction, connections and strategies. They credit Codex GPT-5.6 Sol with deriving all proofs and counterexamples, then verified and simplified them.
The authors explicitly credit Codex with all proofs and counterexamples, while crediting themselves with strategy and review.
Importance
Extends the combined existence guarantee to general nonnegative additive valuations.
Limitations
The result proves existence, not a polynomial-time allocation algorithm.
Technical verification
The three human authors explicitly report verifying all mathematical details of this paper, including the main balanced EF1/fPO theorem; this is a reported complete human check.
Formal checking
Mathematical details of the balanced EF1 and fPO existence theorem. author proof verification and simplification
- Checker
- Benjamin Cookson, Nisarg Shah, and Paritosh Verma (authors)
- Scope
- Mathematical details of the balanced EF1 and fPO existence theorem
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The human authors give a technical overview of weighted-welfare faces, price interlacing, KKM selection, and the order-statistic correction, and report simplifying the proofs.
Correction and publication history
Proves a general balanced EF1 and fPO existence theorem.
Read this published revision