The Lattice Triangle Problem in the Hard Obtuse Window
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Statement
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.
Context
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.
The lattice triangle classification is a central named problem of Teichmüller dynamics, with a literature from Veech through Mirzakhani-Wright, invisible outside the field.
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"The main engine in this paper (Theorem 6.1) was autoformalized by AxiomProver in Lean (using mathlib)" - a test case for the autonomous system, with the protocol and artifacts documented in their own section.
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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Machine check · not human verification
machine: partially checkedscope Lean formalization of the core argument; statement correspondence not independently audited
The paper's main engine is autoformalized and kernel-checked in Lean by AxiomProver; the surrounding derivations are informal, and no independent review has appeared. Tier: the main engine was autoformalized by AxiomProver itself; the informal-to-formal correspondence is author-audited only.
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