{"id":"palomar/PALOMAR-2026-11-03-000012","url":"https://github.com/jtraverso/physical-typed-absorption/tree/9d36e80d75d81d9eabbfacd370dc4394b54e3d52","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-03-000012-v1.json","repo":"https://github.com/jtraverso/physical-typed-absorption","tags":["math.CO","msc:05C70","msc:05B15","msc:05C35"],"score":0,"title":"Triangle decompositions III: physical typed absorption and prescribed statistics","trust":"high","domain":"math.CO","source":"palomar","authors":["Juan Pablo Traverso Gianini"],"reviews":0,"subject":"math.CO","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-03","reactions":{},"formalized":true,"formalizes":[{"title":"Triangle decompositions III: Physical typed absorption and prescribed statistics","identifier":"doi:10.5281/zenodo.23867836","relationship":"formalizes"}]}