Triangle decompositions III: physical typed absorption and prescribed statistics
Source: github.com/jtraverso/physical-typed-absorption/tree/9d36e80…
The Lean source supplement of Paper III of the Nash-Williams series (preprint 1.0), packaged with a Mathlib-only Challenge. Theorem T: for fixed labels I, allowed label multisets F and constants alpha > 0, C >= 1, h >= 6, every labelled graph of order at least n0 that has an exact diffuse fractional triangle seed of constant C (H1), whose edge indicator lies in the integer lattice spanned by its allowed triangles (H2), with at least alpha n common neighbours labelled k for every pair of distinct vertices and every label k completing an allowed type (H3), and at least alpha n^(i-4) physical…
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