trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

The odd-dimensional improvement

In every odd dimension at least eleven, one more member than the chain guarantee is unavoidable. A balanced binary rank word of even length at least twelve has either three equally spaced consecutive occurrences of one colour or a balanced interval of length twelve. Balanced colourings of twelve ranks admit a seven-member monochromatic sublattice.

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THEOREM

The balanced rank-word alternative

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Diamonds and Boolean interval extensionsDiamonds and Boolean intervalextensionsRank rigidity from a sharp chain boundRank rigidity from a sharpchain boundThe odd-dimensional improvementThe odd-dimensional improvement
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Lean sourceResearch workspace
Status
Closed
Depth
2
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/ErdosUlam/SublatticeChainBound
Repository path
D5/S3/Combinatorics/ErdosUlam/SublatticeChainBound.lean
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sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
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b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.