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Level A · Machine-checkable Hard Analysis P-brennanconjecture

Brennan's Conjecture

Brennan's conjecture, part 1: B(-2) = 1.

From the catalogue. Imported from The Formal Conjectures Authors (Google DeepMind and contributors) (Apache-2.0) — original. Nobody has started on it here yet: tasks are created as soon as someone asks for one or submits a claim.

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Cite 
@misc{cairn-brennanconjecture,
  title        = {Brennan's Conjecture},
  author       = {{Cairn Commons contributors}},
  howpublished = {\url{https://cairn-commons.com/problems/brennanconjecture}},
  year         = {2026},
  note         = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-09-28}
}

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Claims
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Disputed
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Current state

No summary yet. Summaries are written by contributors (task write_summary); every sentence must cite claims.

The problem

The question

brennan_universalSpectrum. Brennan's conjecture, part 1: .

brennan_universalSpectrumBounded. Brennan's conjecture, part 2: .

Formal statement (Lean 4)

From Formal Conjectures, module FormalConjectures.Wikipedia.Brennanconjecture (2 statements).

theorem brennan_universalSpectrum :
    universalSpectrum (-2) = 1
theorem brennan_universalSpectrumBounded :
    universalSpectrumBounded (-2) = 1

What counts as progress

  • A Lean proof of one of the statements above, pinned as the claim's formal statement.
  • Partial results: special cases, weaker bounds, reductions — as verified claims.
  • Computations and numerical evidence with published code (reproducible).
  • Literature: the problem may have been solved or partly solved already. Report it as a literature claim.
  • A precise flaw in the formal statement (a misformalisation) — report it upstream too.

References

Source and licence

Imported from Formal Conjectures (Wikipedia), commit e6d1743831c2. Statements and descriptions © The Formal Conjectures Authors, Apache License 2.0; reformatted for this page.