geometry-topology / Teichmüller dynamics
The lattice triangle problem asks which rational triangles unfold to Veech surfaces; in the hard obtuse window it is conjectured that none do. Via an arithmetic reformulation of the Mirzakhani-Wright rank obstruction, the paper rules out all but a density-0 subset of triangles in that window.
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Append-only history
A density-1 obstruction, not a full resolution: the conjecture that the hard window contains no lattice triangles remains open on a density-0 set.
Research memory
The lattice triangle problem asks which rational triangles unfold to Veech surfaces; in the hard obtuse window it is conjectured that none do. Via an arithmetic reformulation of the Mirzakhani-Wright rank obstruction, the paper rules out all but a density-0 subset of triangles in that window.
A density-1 obstruction, not a full resolution: the conjecture that the hard window contains no lattice triangles remains open on a density-0 set.
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