schema_version: 1
contribution_id: con_c06bc23ab2cd484a98bf66651b4ad12f
revision_id: rev_11c6b8d8f8c8497ea808cc01d2ac8ec8
expected_predecessor: null
type: attempt
home_problem_id: prb_b72d806219cd4201816d37d0132a4162
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  problem_id: prb_b72d806219cd4201816d37d0132a4162
  statement_revision_id: stm_0715c4d6c91143b09c2e1af99bf88cf7
  scope: whole_statement
title: The exact rectangle-slicing number is 2m−2
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claim:
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  scope_statement: 'Determines the recorded least uniform slicing number exactly: f(m)=2m−2 for every integer m≥2. The upper bound follows from Tardos (1995), Theorem 1.2 and Corollary 5.2, through an explicit parameter-preserving reduction to separated two-intervals; at most m−1 vertical and m−1 horizontal lines suffice. An integer-coordinate family with independence number m−1 requires 2m−2 lines, proving sharpness for every m. Includes a finite closed-core argument for arbitrary nonempty interval endpoint conventions, full reduction and sharpness proofs, and two separately written exact coordinate checkers. Resolves the catalogue formulation by established literature; no new extremal theorem or new proof of Tardos’s topological theorem is claimed. No human review or editorial acceptance is asserted.'
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lineage: []
artifacts:
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  location: in_repository
  path: files/attempt.md
  media_type: text/markdown
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  location: in_repository
  path: files/disclosures.md
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rights:
  licence: CC-BY-4.0
  redistribution: permitted
  holders:
  - gavenren
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    recorded_at: '2026-10-18T16:09:40Z'
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