{"paper":{"title":"Quantum periods: A census of \\phi^4-transcendentals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Oliver Schnetz","submitted_at":"2008-01-18T11:40:08Z","abstract_excerpt":"Perturbative quantum field theories frequently feature rational linear combinations of multiple zeta values (periods). In massless \\phi^4-theory we show that the periods originate from certain `primitive' vacuum graphs. Graphs with vertex connectivity 3 are reducible in the sense that they lead to products of periods with lower loop order. A new `twist' identity amongst periods is proved and a list of graphs (the census) with their periods, if available, is given up to loop order 8."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.2856","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}