{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:THSJB4W7ANUZCVHS7G7ZVV2EEU","short_pith_number":"pith:THSJB4W7","canonical_record":{"source":{"id":"hep-th/9805098","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1998-05-16T19:30:03Z","cross_cats_sorted":[],"title_canon_sha256":"d3d8c41b48310dcea0719f6166546c4abc5db9c691836940b4a2a5ee5602fa13","abstract_canon_sha256":"7d7c52e3967a3110ca9eda71193bfec4065fba005f46afd1e532818d14f1a177"},"schema_version":"1.0"},"canonical_sha256":"99e490f2df03699154f2f9bf9ad744252202700927224804f2352d3a9687587d","source":{"kind":"arxiv","id":"hep-th/9805098","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9805098","created_at":"2026-05-18T04:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9805098v4","created_at":"2026-05-18T04:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9805098","created_at":"2026-05-18T04:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"THSJB4W7ANUZ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"THSJB4W7ANUZCVHS","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"THSJB4W7","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:THSJB4W7ANUZCVHS7G7ZVV2EEU","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9805098","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1998-05-16T19:30:03Z","cross_cats_sorted":[],"title_canon_sha256":"d3d8c41b48310dcea0719f6166546c4abc5db9c691836940b4a2a5ee5602fa13","abstract_canon_sha256":"7d7c52e3967a3110ca9eda71193bfec4065fba005f46afd1e532818d14f1a177"},"schema_version":"1.0"},"canonical_sha256":"99e490f2df03699154f2f9bf9ad744252202700927224804f2352d3a9687587d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:16.704985Z","signature_b64":"qIzu9JXSXGW3K7+DjIHtBgzbjcDwnJ50qCfyw/T1DZFQ5ejhiT1l6RtJ+jW6pZiD9V0SJI/gr3iuEF+mH3dUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99e490f2df03699154f2f9bf9ad744252202700927224804f2352d3a9687587d","last_reissued_at":"2026-05-18T04:13:16.704333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:16.704333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9805098","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oDjpvQucCvJwV4zfQmGWBUogoCFNNzx/X7nAWRdbEO+Ycvu3X193G/WDBs180AItkpOkli1h3qgeHPhJP53FCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T04:59:59.767900Z"},"content_sha256":"0dc2a6e8e2cbba3de00381497b6e1c3e91fb5714816af133d11ebe51dcf804a1","schema_version":"1.0","event_id":"sha256:0dc2a6e8e2cbba3de00381497b6e1c3e91fb5714816af133d11ebe51dcf804a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:THSJB4W7ANUZCVHS7G7ZVV2EEU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Kreimer's Hopf algebra structure of Feynman graphs","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Raimar Wulkenhaar (CPT Luminy), Thomas Krajewski","submitted_at":"1998-05-16T19:30:03Z","abstract_excerpt":"We reinvestigate Kreimer's Hopf algebra structure of perturbative quantum field theories with a special emphasis on overlapping divergences. Kreimer first disentangles overlapping divergences into a linear combination of disjoint and nested ones and then tackles that linear combination by the Hopf algebra operations. We present a formulation where the Hopf algebra operations are directly defined on any type of divergence. We explain the precise relation to Kreimer's Hopf algebra and obtain thereby a characterization of their primitive elements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9805098","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wh4o87HyTRYdKHJh7rUiWc3AESIPMXhgCn+0hS17niRkEcoRDTS6f0448umiOf39ljKoB8aZJAwQqQXjuoVtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T04:59:59.768298Z"},"content_sha256":"442e8bac5591ec445d2e536007dd67dfc3eb484289f40993bf63db4b71f1a220","schema_version":"1.0","event_id":"sha256:442e8bac5591ec445d2e536007dd67dfc3eb484289f40993bf63db4b71f1a220"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/THSJB4W7ANUZCVHS7G7ZVV2EEU/bundle.json","state_url":"https://pith.science/pith/THSJB4W7ANUZCVHS7G7ZVV2EEU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/THSJB4W7ANUZCVHS7G7ZVV2EEU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-02T04:59:59Z","links":{"resolver":"https://pith.science/pith/THSJB4W7ANUZCVHS7G7ZVV2EEU","bundle":"https://pith.science/pith/THSJB4W7ANUZCVHS7G7ZVV2EEU/bundle.json","state":"https://pith.science/pith/THSJB4W7ANUZCVHS7G7ZVV2EEU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/THSJB4W7ANUZCVHS7G7ZVV2EEU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:THSJB4W7ANUZCVHS7G7ZVV2EEU","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":"7d7c52e3967a3110ca9eda71193bfec4065fba005f46afd1e532818d14f1a177","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1998-05-16T19:30:03Z","title_canon_sha256":"d3d8c41b48310dcea0719f6166546c4abc5db9c691836940b4a2a5ee5602fa13"},"schema_version":"1.0","source":{"id":"hep-th/9805098","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9805098","created_at":"2026-05-18T04:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9805098v4","created_at":"2026-05-18T04:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9805098","created_at":"2026-05-18T04:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"THSJB4W7ANUZ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"THSJB4W7ANUZCVHS","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"THSJB4W7","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:442e8bac5591ec445d2e536007dd67dfc3eb484289f40993bf63db4b71f1a220","target":"graph","created_at":"2026-05-18T04:13:16Z","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 reinvestigate Kreimer's Hopf algebra structure of perturbative quantum field theories with a special emphasis on overlapping divergences. Kreimer first disentangles overlapping divergences into a linear combination of disjoint and nested ones and then tackles that linear combination by the Hopf algebra operations. We present a formulation where the Hopf algebra operations are directly defined on any type of divergence. We explain the precise relation to Kreimer's Hopf algebra and obtain thereby a characterization of their primitive elements.","authors_text":"Raimar Wulkenhaar (CPT Luminy), Thomas Krajewski","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1998-05-16T19:30:03Z","title":"On Kreimer's Hopf algebra structure of Feynman graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9805098","kind":"arxiv","version":4},"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":"sha256:0dc2a6e8e2cbba3de00381497b6e1c3e91fb5714816af133d11ebe51dcf804a1","target":"record","created_at":"2026-05-18T04:13:16Z","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":"7d7c52e3967a3110ca9eda71193bfec4065fba005f46afd1e532818d14f1a177","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1998-05-16T19:30:03Z","title_canon_sha256":"d3d8c41b48310dcea0719f6166546c4abc5db9c691836940b4a2a5ee5602fa13"},"schema_version":"1.0","source":{"id":"hep-th/9805098","kind":"arxiv","version":4}},"canonical_sha256":"99e490f2df03699154f2f9bf9ad744252202700927224804f2352d3a9687587d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99e490f2df03699154f2f9bf9ad744252202700927224804f2352d3a9687587d","first_computed_at":"2026-05-18T04:13:16.704333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:16.704333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qIzu9JXSXGW3K7+DjIHtBgzbjcDwnJ50qCfyw/T1DZFQ5ejhiT1l6RtJ+jW6pZiD9V0SJI/gr3iuEF+mH3dUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:16.704985Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9805098","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dc2a6e8e2cbba3de00381497b6e1c3e91fb5714816af133d11ebe51dcf804a1","sha256:442e8bac5591ec445d2e536007dd67dfc3eb484289f40993bf63db4b71f1a220"],"state_sha256":"84a54cf77ba40d58e4284216b04b88dbfcf56c0c42afbd695bb6013948ed191d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wBX6uMWG0ugZvUyELi8fb7eItVtY70TWF9+Nhpppq8pPNEzfRV/4jRGJg6+OyDs4KIXc/MBFyjKkIVagJQo4CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T04:59:59.770248Z","bundle_sha256":"4cbb99ea882c2ac57105f26ef802c16624cac1ab7ae30007c4635750ee8fc761"}}