What was already known
The undirected Erdős–Sós theorem did not cover arbitrary orientations. Earlier Eulerian directed-path bounds were weaker than this sharp threshold.
AI involvement
Mubayi and Verstraëte proposed the directed extension and prompted Astra, which they credit with every proof. The authors revised and explained the presentation; Riordan and Scott supplied a later independent proof.
Authors supplied the directed extension and prompts; Astra is credited with all mathematical proofs.
Importance
The theorem gives a sharp embedding threshold for every oriented tree in Eulerian digraphs.
Limitations
Mubayi and Verstraëte checked the directed-path case of Astra’s argument, not its full oriented-tree proof. Riordan and Scott later proved the complete conclusion independently by another argument.
Technical verification
The authors explicitly checked only the path special case. Riordan–Scott later gave a separate full human proof, which corroborates the result but does not audit Astra’s general-tree argument.
Independent checking
author check of the short path proof; §1 AI Declaration; §3
- Checker
- Dhruv Mubayi and Jacques Verstraëte
- Scope
- Theorem 2.2 restricted to directed paths
- Basis
- Reported by the linked checker
Human understanding
The original authors explain the permutation method, and Riordan–Scott give a simpler full human proof of the oriented-tree conclusion.
Correction and publication history
The theorem gives a sharp embedding threshold for every oriented tree in Eulerian digraphs.
Read this published revision