Jose-dev/graphkind-universos
Español · Page (ES) · Page (EN) · Paper · Proof · Reproduce Abstract We classify the operators under which the color refinement (1-WL) profile of a graph is invariant, inside a parametric family of observation universes (f, ι) — f compresses neighborhood counts and ι is an involution. The engine proposed and verified that the color refinement partition is complement-invariant (call it T4; the conjecture mechanism was human-built), verified it on 2,131… See the full description on the dataset page: https://huggingface.co/datasets/Jose-dev/graphkind-universos.
05k
1cff-version: 1.2.02message: "If you use this work, please cite it as below."3title: "GraphKind — Universes v2: T4 and the universe arc (multilayer, hypergraphs, arity dual)"4abstract: >-5 We classify the operators under which the color refinement (1-WL)6 profile of a graph is invariant, inside parametric observation7 universes (f, iota). T4 (complement-invariance) was proposed and8 verified by the engine (the conjecture mechanism was human-built),9 checked on 2,131,019 exhaustive graphs and proved in writing. The data selected the count law f(1) != f(2) and further10 probing produced the characterization S_n.K, with the forward11 direction proved and the converse verified. Changing the type of the12 invariant (partition -> orbit -> distribution -> observer) T4 dies in13 a deterministic Z3 universe, dies under process randomness, survives14 under object randomness, and is inherited by the k-FWL hierarchy (equivalent to (k+1)-WL).15authors:16 - family-names: "Argaña Silguero"17 given-names: "Josué"18 alias: "cripto-bot"19 orcid: "https://orcid.org/0009-0009-1983-4711"20 website: "https://github.com/cripto-bot"21date-released: "2026-09-14"22version: "2.0.0"23doi: 10.5281/zenodo.2274735024url: "https://doi.org/10.5281/zenodo.22747350"25license: CC-BY-4.026repository-code: "https://github.com/cripto-bot/graphkind-universos-v2"27keywords:28 - color refinement29 - Weisfeiler-Leman30 - graph invariants31 - complement32 - emergent laws33