Ariel Elboim

A Compressed Presentation of OpenAI's Proof of the Unique Games Theorem

We reconstruct the main argument of OpenAI's preprint "The Unique Games Theorem" (23 September 2026). Three earlier theorems are stated as inputs: Håstad's parity gap, the Khot–Minzer–Safra Grassmann expansion theorem, and Dinur–Steurer projection-game repetition. The remaining a...

The Unique Games Theorem: A Short Self-Contained Proof

We give a short proof of the theorem of OpenAI's preprint "The Unique Games Theorem" (23 September 2026). It is self-contained apart from three earlier theorems, which are stated as inputs: Håstad's parity gap, the Khot–Minzer–Safra Grassmann expansion theorem, and Dinur–Steurer...

Why This Language? Historical Symmetry Breaking through Cultural Transmission

Version 2.0 (5 September 2026) corrects Version 1.0 after an independent data verification: a shared adjusted-Rand-index implementation replaces local copies that scored identical singleton partitions as 0 (this changes several second-architecture partition verdicts, in both dire...