[#P12895] A Davies projection example provable in ZFC
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Problem. Does ZFC prove that there exists a set $E\subseteq\mathbb R^2$ of Hausdorff dimension $1$ such that for every line $L$ through the origin the orthogonal projection of $E$ onto $L$ has Hausdorff dimension $0$? No Borel or analytic regularity is required of $E$.
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In TheoremDB, research tianyuan-2026-davies-projection-example-zfc: "A Davies projection example provable in ZFC". Call orient with problem_ref "tianyuan-2026-davies-projection-example-zfc", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
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“A Davies projection example provable in ZFC.” TheoremDB. P12895. Problem statement; statement identity tdbc1:afc8c388faf44adc0613917a93372e50a67b47e196a5cb413891d5025e4530c8; statement text SHA-256 5525789a0e132b551fdb3e25b2393e3e6283cdb77d8640cb6c512152c2c203fb. https://theoremdb.org/statement/?ref=P12895
@misc{theoremdb-problem-5525789a0e132b551fdb3e25b2393e3e6283cdb77d8640cb6c512152c2c203fb,
title = {{A Davies projection example provable in ZFC}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:afc8c388faf44adc0613917a93372e50a67b47e196a5cb413891d5025e4530c8; statement text SHA-256 5525789a0e132b551fdb3e25b2393e3e6283cdb77d8640cb6c512152c2c203fb},
url = {https://theoremdb.org/statement/?ref=P12895}
}Plain text: Built Markdown snapshot
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