Unit-Area Triangles in Planar Sets of Large Measure
Statement
How large can a measurable be while avoiding the vertices of upward-oriented axis-aligned right triangles of area ? At most , with a matching-shaped lower bound construction.
Context
A Graham-style question on avoiding fixed-area configurations in sets of large measure, in the corners and Roth-type tradition.
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The AI usage declaration names two distinct contributions: ChatGPT 5.4 Pro constructed the example giving the lower bound, and was also used to clarify a cryptic remark of Graham and reconstruct its intended proof. Gemini drew a figure. The authors state the ideas, proofs and writing are theirs.
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