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Twelve Common Flex Lines in a General Pencil of Cubics

Geometry & topology · posed by Ciro Ciliberto, Rick Miranda, Joaquim Roé, 2026 · solved

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Statement

Does a general pencil of plane cubics over C\mathbb{C} have exactly 1212 common flex lines? Ciliberto, Miranda and Roé asked this in Remark 5.3 of their paper; the answer is yes.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Jihao Liu and Yanze Wang, using ChatGPT 5.5 Pro + Danus

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The main result was obtained with ChatGPT 5.5 Pro and the Danus system, an agent built on Rethlas; human verification and polishing came afterwards. The authors caution that AI limitations mean related literature may have been missed.

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