{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:H7P2B7NH55DXTUG2G33WI2GCPS","short_pith_number":"pith:H7P2B7NH","canonical_record":{"source":{"id":"1203.0454","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-03-02T13:31:22Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"4f931c1452d2b38ca58dcfad6cf3ab8462ea83a010472509d5fff3becb96b932","abstract_canon_sha256":"1737334620f8305b65ac03f501772f6b9c12992881c5024b2e03e57f38741390"},"schema_version":"1.0"},"canonical_sha256":"3fdfa0fda7ef4779d0da36f76468c27c8ef37e13cac32d527ef6620bd4963d7a","source":{"kind":"arxiv","id":"1203.0454","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0454","created_at":"2026-05-18T01:58:15Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0454v1","created_at":"2026-05-18T01:58:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0454","created_at":"2026-05-18T01:58:15Z"},{"alias_kind":"pith_short_12","alias_value":"H7P2B7NH55DX","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"H7P2B7NH55DXTUG2","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"H7P2B7NH","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:H7P2B7NH55DXTUG2G33WI2GCPS","target":"record","payload":{"canonical_record":{"source":{"id":"1203.0454","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-03-02T13:31:22Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"4f931c1452d2b38ca58dcfad6cf3ab8462ea83a010472509d5fff3becb96b932","abstract_canon_sha256":"1737334620f8305b65ac03f501772f6b9c12992881c5024b2e03e57f38741390"},"schema_version":"1.0"},"canonical_sha256":"3fdfa0fda7ef4779d0da36f76468c27c8ef37e13cac32d527ef6620bd4963d7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:15.651923Z","signature_b64":"pPxbr+2f4OOirmoNoT1XcT67sv16pHSDwpzgfERA+tYIweQA/ZvJ/EU5eSgYWpxC4HFniw48MhaH7OKIuJEzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fdfa0fda7ef4779d0da36f76468c27c8ef37e13cac32d527ef6620bd4963d7a","last_reissued_at":"2026-05-18T01:58:15.651356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:15.651356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.0454","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:58:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KWNCjgxAxt1lIRanSFfuqyaXQTc/dwfcMicqfk1Mjty9UlACyRjVtJexqtNxf1QgEYaeV6/KxLioSWZspjx9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T14:27:54.444816Z"},"content_sha256":"72f7f3ad2922dac51c2509e0911e56ec33a68869d00111dbfb0e991abc30db90","schema_version":"1.0","event_id":"sha256:72f7f3ad2922dac51c2509e0911e56ec33a68869d00111dbfb0e991abc30db90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:H7P2B7NH55DXTUG2G33WI2GCPS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Claude Duhr","submitted_at":"2012-03-02T13:31:22Z","abstract_excerpt":"We show how the Hopf algebra structure of multiple polylogarithms can be used to simplify complicated expressions for multi-loop amplitudes in perturbative quantum field theory and we argue that, unlike the recently popularized symbol-based approach, the coproduct incorporates information about the zeta values. We illustrate our approach by rewriting the two-loop helicity amplitudes for a Higgs boson plus three gluons in a simplified and compact form involving only classical polylogarithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0454","kind":"arxiv","version":1},"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":"2026-05-18T01:58:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ERV8iQjRLERhD6z8N2yHnh2+JVQte/sTQPENa/CVOsPJ4HADrm8UT77TpyNgJ69mMlNwwP02qd0Bsb6Y1nrhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T14:27:54.445160Z"},"content_sha256":"9529b2379f59e4acd2f40f012214b3a43638396c1a344c157063ecde53f76266","schema_version":"1.0","event_id":"sha256:9529b2379f59e4acd2f40f012214b3a43638396c1a344c157063ecde53f76266"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H7P2B7NH55DXTUG2G33WI2GCPS/bundle.json","state_url":"https://pith.science/pith/H7P2B7NH55DXTUG2G33WI2GCPS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H7P2B7NH55DXTUG2G33WI2GCPS/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":"2026-07-11T14:27:54Z","links":{"resolver":"https://pith.science/pith/H7P2B7NH55DXTUG2G33WI2GCPS","bundle":"https://pith.science/pith/H7P2B7NH55DXTUG2G33WI2GCPS/bundle.json","state":"https://pith.science/pith/H7P2B7NH55DXTUG2G33WI2GCPS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H7P2B7NH55DXTUG2G33WI2GCPS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:H7P2B7NH55DXTUG2G33WI2GCPS","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":"1737334620f8305b65ac03f501772f6b9c12992881c5024b2e03e57f38741390","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-03-02T13:31:22Z","title_canon_sha256":"4f931c1452d2b38ca58dcfad6cf3ab8462ea83a010472509d5fff3becb96b932"},"schema_version":"1.0","source":{"id":"1203.0454","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0454","created_at":"2026-05-18T01:58:15Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0454v1","created_at":"2026-05-18T01:58:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0454","created_at":"2026-05-18T01:58:15Z"},{"alias_kind":"pith_short_12","alias_value":"H7P2B7NH55DX","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"H7P2B7NH55DXTUG2","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"H7P2B7NH","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:9529b2379f59e4acd2f40f012214b3a43638396c1a344c157063ecde53f76266","target":"graph","created_at":"2026-05-18T01:58:15Z","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 show how the Hopf algebra structure of multiple polylogarithms can be used to simplify complicated expressions for multi-loop amplitudes in perturbative quantum field theory and we argue that, unlike the recently popularized symbol-based approach, the coproduct incorporates information about the zeta values. We illustrate our approach by rewriting the two-loop helicity amplitudes for a Higgs boson plus three gluons in a simplified and compact form involving only classical polylogarithms.","authors_text":"Claude Duhr","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-03-02T13:31:22Z","title":"Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0454","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":"sha256:72f7f3ad2922dac51c2509e0911e56ec33a68869d00111dbfb0e991abc30db90","target":"record","created_at":"2026-05-18T01:58:15Z","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":"1737334620f8305b65ac03f501772f6b9c12992881c5024b2e03e57f38741390","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-03-02T13:31:22Z","title_canon_sha256":"4f931c1452d2b38ca58dcfad6cf3ab8462ea83a010472509d5fff3becb96b932"},"schema_version":"1.0","source":{"id":"1203.0454","kind":"arxiv","version":1}},"canonical_sha256":"3fdfa0fda7ef4779d0da36f76468c27c8ef37e13cac32d527ef6620bd4963d7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fdfa0fda7ef4779d0da36f76468c27c8ef37e13cac32d527ef6620bd4963d7a","first_computed_at":"2026-05-18T01:58:15.651356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:15.651356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pPxbr+2f4OOirmoNoT1XcT67sv16pHSDwpzgfERA+tYIweQA/ZvJ/EU5eSgYWpxC4HFniw48MhaH7OKIuJEzDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:15.651923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.0454","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72f7f3ad2922dac51c2509e0911e56ec33a68869d00111dbfb0e991abc30db90","sha256:9529b2379f59e4acd2f40f012214b3a43638396c1a344c157063ecde53f76266"],"state_sha256":"12a3fdfbe6601f44fe01691573aeb089e8bb374db335434478f7715af370aca5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ILggKzoFa08tKtf97mBNDvJJ3+gvxozaepP7NKUFip+4ye+EmICd9R9CLTSSqxu3CrtnKwKsXi8EC/GUvYnPAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-11T14:27:54.447436Z","bundle_sha256":"90e2e5d5b12e205a9d8c25ee47b6996fc5d2e1ec0bddb42438b15d33c8a529df"}}