{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UY3DKMS62PSTBFTTL7ZWEYO5EJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"146a8a9be39c86a05cfa6634715a6eea198a798e5426f600bf9793aa5ab352a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-07-19T06:16:01Z","title_canon_sha256":"3a69cfc712f9df5fb87afcfd7963ad4f1dc527f500faeeebcf83162c13b6e66d"},"schema_version":"1.0","source":{"id":"1407.5150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5150","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5150v1","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5150","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"pith_short_12","alias_value":"UY3DKMS62PST","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UY3DKMS62PSTBFTT","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UY3DKMS6","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:131e6f303c790fdfbb3608b3080ab1974009cced7b01c402c4b60a75fcc16a57","target":"graph","created_at":"2026-05-18T02:47:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We discuss structural similarities between Knizhnik--Zamolodchikov equations (in fact, their simplest version needed to introduce the Drinfeld associator) and Dyson--Schwinger equations. We emphasize that the latter allow for a filtration by co-radical degree using quasi-shuffle products and the lower central series filtration of the Lie algebra of Feynman graphs. This clarifies how they are a generalization of the KZ equations. This is a starting point for a algebraic organization of the next-to...-to leading log expansion which has been worked out in collaboration with Olaf Krueger and which","authors_text":"Dirk Kreimer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-07-19T06:16:01Z","title":"What can we learn from Knizhnik--Zamolodchikov Equations?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5150","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:45b82d79263eda37a9206162cc10f45e52bd1312d0ab041a81825cbdcc38c946","target":"record","created_at":"2026-05-18T02:47:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"146a8a9be39c86a05cfa6634715a6eea198a798e5426f600bf9793aa5ab352a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-07-19T06:16:01Z","title_canon_sha256":"3a69cfc712f9df5fb87afcfd7963ad4f1dc527f500faeeebcf83162c13b6e66d"},"schema_version":"1.0","source":{"id":"1407.5150","kind":"arxiv","version":1}},"canonical_sha256":"a63635325ed3e53096735ff36261dd2263bebbc06e582c81a73afa2f2d27152e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a63635325ed3e53096735ff36261dd2263bebbc06e582c81a73afa2f2d27152e","first_computed_at":"2026-05-18T02:47:14.832661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:14.832661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DbbxhLPQX2vHWmNyriLtT3c/FDk3C7VlixF4OswLSMG1n2QKTqEY9q9741hJLQyA6S+z9jUKv9qeUugpVq2MAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:14.833138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45b82d79263eda37a9206162cc10f45e52bd1312d0ab041a81825cbdcc38c946","sha256:131e6f303c790fdfbb3608b3080ab1974009cced7b01c402c4b60a75fcc16a57"],"state_sha256":"afdf24c2735fb3d009804a5c17da79c9c10c6bffbe783fbd5ccd97767a698685"}