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graph-theory
graph-isomorphism
color-refinement
weisfeiler-lehman
structural-invariants
graph-kernels
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c401981 76fecdf c401981 76fecdf 7412168 76fecdf | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | cff-version: 1.2.0
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title: "GraphKind — Universes v2: T4 and the universe arc (multilayer, hypergraphs, arity dual)"
abstract: >-
We classify the operators under which the color refinement (1-WL)
profile of a graph is invariant, inside parametric observation
universes (f, iota). T4 (complement-invariance) was proposed and
verified by the engine (the conjecture mechanism was human-built),
checked on 2,131,019 exhaustive graphs and proved in writing. The data selected the count law f(1) != f(2) and further
probing produced the characterization S_n.K, with the forward
direction proved and the converse verified. Changing the type of the
invariant (partition -> orbit -> distribution -> observer) T4 dies in
a deterministic Z3 universe, dies under process randomness, survives
under object randomness, and is inherited by the k-FWL hierarchy (equivalent to (k+1)-WL).
authors:
- family-names: "Argaña Silguero"
given-names: "Josué"
alias: "cripto-bot"
orcid: "https://orcid.org/0009-0009-1983-4711"
website: "https://github.com/cripto-bot"
date-released: "2026-09-14"
version: "2.0.0"
doi: 10.5281/zenodo.22747350
url: "https://doi.org/10.5281/zenodo.22747350"
license: CC-BY-4.0
repository-code: "https://github.com/cripto-bot/graphkind-universos-v2"
keywords:
- color refinement
- Weisfeiler-Leman
- graph invariants
- complement
- emergent laws
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