{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:Q6S2CWVWIKDLGCWE5VFBJPIHZ3","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":"e401e64c7d877fd6a4d5515bc312109831459b58f44f599f68713cb6e0996263","cross_cats_sorted":["hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-06-16T16:31:08Z","title_canon_sha256":"21a87bd879c10ea5aca4dd3300b721c9aeba1d55df0d24d3bb1af4d06d1e5320"},"schema_version":"1.0","source":{"id":"math-ph/0606039","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0606039","created_at":"2026-05-17T23:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0606039v2","created_at":"2026-05-17T23:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0606039","created_at":"2026-05-17T23:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"Q6S2CWVWIKDL","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"Q6S2CWVWIKDLGCWE","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"Q6S2CWVW","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:7671a3e14903d39f8c5b215e5464ce996fff2552e3bcb542fd339de87fee9d0e","target":"graph","created_at":"2026-05-17T23:49:12Z","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 establish Sakakibara's differential equations in a matrix setting for the counter term (respectively renormalized character) in Connes-Kreimer's Birkhoff decomposition in any connected graded Hopf algebra, thus including Feynman rules in perturbative renormalization as a key example.","authors_text":"Dominique Manchon, Kurusch Ebrahimi-Fard","cross_cats":["hep-th","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-06-16T16:31:08Z","title":"On matrix differential equations in the Hopf algebra of renormalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0606039","kind":"arxiv","version":2},"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":"sha256:940a44a5b5faf301b930ad70b3d4b0e83fc14b076b4b7fedf7d0b2f672ac0808","target":"record","created_at":"2026-05-17T23:49:12Z","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":"e401e64c7d877fd6a4d5515bc312109831459b58f44f599f68713cb6e0996263","cross_cats_sorted":["hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-06-16T16:31:08Z","title_canon_sha256":"21a87bd879c10ea5aca4dd3300b721c9aeba1d55df0d24d3bb1af4d06d1e5320"},"schema_version":"1.0","source":{"id":"math-ph/0606039","kind":"arxiv","version":2}},"canonical_sha256":"87a5a15ab64286b30ac4ed4a14bd07cee8e01a1b59c2941e5128269a028d89d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87a5a15ab64286b30ac4ed4a14bd07cee8e01a1b59c2941e5128269a028d89d0","first_computed_at":"2026-05-17T23:49:12.402274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:12.402274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y/yD5AQlMq4y9xHncb18qMDaGpEIo0bUqO5xwavGTBF6jWbP7ukP4Ii+ERm4ktno6LS8+2kG74P/NXKwL0EfCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:12.402927Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0606039","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:940a44a5b5faf301b930ad70b3d4b0e83fc14b076b4b7fedf7d0b2f672ac0808","sha256:7671a3e14903d39f8c5b215e5464ce996fff2552e3bcb542fd339de87fee9d0e"],"state_sha256":"a8a68c8cc6224f8dc92f0665b561751140c49f41d8e0ffe4c27ca8bd09293c15"}