{"id":"palomar/PALOMAR-2026-10-23-000013","url":"https://github.com/jtraverso/typed-triangle-absorption/tree/673c6d4118b5679783bafa7606fd2c611161a254","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-23-000013-v1.json","repo":"https://github.com/jtraverso/typed-triangle-absorption","tags":["math.CO","msc:05C70","msc:05C35","msc:05B05","extremal-combinatorics","triangle-decomposition","hypergraphs"],"score":0,"title":"Robust absorption for typed triangles","trust":"high","domain":"math.CO","source":"palomar","authors":["Juan Pablo Traverso Gianini"],"reviews":0,"subject":"math.CO","summary":"Typed triangle decomposition results from Paper II: a typical-host theorem under three-step links for four-label families; its nearly complete and balanced deductions with explicit type-weight hypotheses; a semidense two-label mixed-triangle theorem; a computer-assisted typical-host theorem for every admissible four-label family; and a terminal absorber obtained from a bounded signed certificate and explicit physical hinge supply. Divisibility includes global edge counts and local degree profiles. The typical-host hypotheses are retained; the result is not asserted for arbitrary divisible…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-23","reactions":{},"formalized":true,"formalizes":[{"title":"Triangle decompositions II: Robust absorption for typed triangles","identifier":"doi:10.5281/zenodo.23502224","relationship":"formalizes"}]}