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Erdős problem 670

Erdős asked whether every nn-point set in Euclidean space whose pairwise distances are mutually at least 1 apart must have diameter at least (1+o(1))n2(1+o(1))n^2. Disproved: an explicit high-dimensional construction beats the conjectured constant.

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  1. Prior stateNone retained
  2. WorkNo submitted work retained
  3. VerificationNo check retained
  4. DecisionNo Repository has decided
  5. StandingNothing recorded here
  6. Next gapNot recorded

Result history

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Correction history

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Technical detailsExact roots, source, and retained record identifiers

Exact provenance

Problem row
sha256:d2e2f8d8eb512fa85c8a7784a117dc68fec815d85247e56a14e13e65d1118085
Metadata
sha256:79a014565f4c33a3edd5c2d1a34a5cedeae0ae5db5f5c3acbba4061ef3d2f760
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:c20d3dcdb49b124ccbdd3f5bb763532ccba17ef6114bef9128b03f10ee4a3f5e
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb