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The Lattice Triangle Problem in the Hard Obtuse Window

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lattice-triangles-hard-windowGeometry & topologyposer not recordedrecorded: partial

1 attempt · 1 machine check · no person has looked

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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  • #1

    Attempt 1

    proof attemptAxiomProver with David Kurniadi Angdinata, Evan Chen, Ken Ono, Jiaxin Zhang, Jujian Zhang ·
    AI involvement
    ai assisted
    a person led the work and used a model along the way.
    models
    AxiomProver
    people
    David Kurniadi Angdinata, Evan Chen, Ken Ono, Jiaxin Zhang, Jujian Zhang

    "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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    0 human reviews · 1 machine check

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    • Machine check · not human verification

      machine: partially checked

      Recorded from Lean ·

      scope 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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