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Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
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Problem 509: Why separate component covers lose the radius budget
componentwise_cover_obstruction: Pommerenke lemniscates with many long components rule out summing separate component radius or capacity budgets; a successful cover must share disks across components.
The [[research/erdos_509/componentwise_cover_obstruction|argument on why separate component covers lose the radius budget]] records its exact scope, source premises, and remaining gap toward Problem 509.
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