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Density Thresholds for Large Dilates of Point Configurations

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density-large-dilatesAnalysisposer not recordedrecorded: partial

1 attempt · no person has looked

Statement

Near-optimal density thresholds forcing a measurable set in Rd\mathbb{R}^d to contain all sufficiently large similar copies of every nn-point configuration, answering a question from the Euclidean density theorem literature up to logarithmic factors.

Context

Near-optimal rather than optimal: the bounds match up to logarithmic-type factors.

A stated question in the Euclidean density-theorem line (Bourgain, Graham tradition), specialist but documented.

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1 attempt

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  • #1

    Attempt 1

    proof attemptChatGPT 5.4 Pro with Vjekoslav Kovač, Adian Anibal Santos Sepčić ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    ChatGPT 5.4 Pro
    people
    Vjekoslav Kovač, Adian Anibal Santos Sepčić

    ChatGPT 5.4 Pro "was used to suggest and draft approaches to Proposition 5"; in particular the random pattern thinning argument, "somewhat novel in this context," was suggested by the model. Main ideas and final proofs are the authors'.

    Near-optimal rather than optimal: the bounds match up to logarithmic-type factors.

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