{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:URVZG5IQE47MBOV4YV36PVZZ35","short_pith_number":"pith:URVZG5IQ","canonical_record":{"source":{"id":"2102.08943","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2021-02-17T18:56:46Z","cross_cats_sorted":[],"title_canon_sha256":"cf826600965c22254fbd613e79c37861f6ad6da38f413f1e3c87c017d583914b","abstract_canon_sha256":"495e382bc3e42ac8fb23937b8a8d006beda8335922a104e1040f4f1b2add8ce3"},"schema_version":"1.0"},"canonical_sha256":"a46b937510273ec0babcc577e7d739df49e1cd614469fe6a30f33b238c3d84cf","source":{"kind":"arxiv","id":"2102.08943","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.08943","created_at":"2026-07-05T02:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"2102.08943v2","created_at":"2026-07-05T02:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.08943","created_at":"2026-07-05T02:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"URVZG5IQE47M","created_at":"2026-07-05T02:47:59Z"},{"alias_kind":"pith_short_16","alias_value":"URVZG5IQE47MBOV4","created_at":"2026-07-05T02:47:59Z"},{"alias_kind":"pith_short_8","alias_value":"URVZG5IQ","created_at":"2026-07-05T02:47:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:URVZG5IQE47MBOV4YV36PVZZ35","target":"record","payload":{"canonical_record":{"source":{"id":"2102.08943","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2021-02-17T18:56:46Z","cross_cats_sorted":[],"title_canon_sha256":"cf826600965c22254fbd613e79c37861f6ad6da38f413f1e3c87c017d583914b","abstract_canon_sha256":"495e382bc3e42ac8fb23937b8a8d006beda8335922a104e1040f4f1b2add8ce3"},"schema_version":"1.0"},"canonical_sha256":"a46b937510273ec0babcc577e7d739df49e1cd614469fe6a30f33b238c3d84cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:47:59.158995Z","signature_b64":"TltsdNltUoa+vwSZFM/OC9J/eHmF6XZOI7DnhCVmuGm1mW67bgEORmweIw2dqbB7dG1zXGPOnSZFXLaw9o4iDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a46b937510273ec0babcc577e7d739df49e1cd614469fe6a30f33b238c3d84cf","last_reissued_at":"2026-07-05T02:47:59.158459Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:47:59.158459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.08943","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H+r2w9IE5AT6X+79qQpWFdkUzxSuRsyKVMU6Fp6HD0pMlFqfUtd4UmGuG0CRBpilI4sSXt+VVDI0ln0LhQn8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T08:21:28.386297Z"},"content_sha256":"635e3e7be1c84b2644b6072416f94f3ba0893b83c52a99129709c40be707b213","schema_version":"1.0","event_id":"sha256:635e3e7be1c84b2644b6072416f94f3ba0893b83c52a99129709c40be707b213"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:URVZG5IQE47MBOV4YV36PVZZ35","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New ideas for handling of loop and angular integrals in D-dimensions in QCD","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Alexey S. Zhevlakov, Fabian Wunder, Valery E. Lyubovitskij","submitted_at":"2021-02-17T18:56:46Z","abstract_excerpt":"We discuss new ideas for consideration of loop diagrams and angular integrals in $D$-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of linear combinations of external momenta. It gives a very simple presentation for the final results and is more convenient for calculations on computer algebra systems. In case of angular integrals we demonstrate how to simplify the integration of differential cross sections over polar angles. Also we derive the recursion relations, which allow to reduce all occur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.08943","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.08943/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j46iysmMwXDfD+VyRzPnC4PhbKaB7/NNYlEMAragjlDvQ0+ht7qIak1/woHZMEiRiTrCiVVmIny8GJct1mnwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T08:21:28.387206Z"},"content_sha256":"31415abff7cefa920fcffc20c77f9a99a5794e7b9f1f36740ae09ee98720e053","schema_version":"1.0","event_id":"sha256:31415abff7cefa920fcffc20c77f9a99a5794e7b9f1f36740ae09ee98720e053"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/URVZG5IQE47MBOV4YV36PVZZ35/bundle.json","state_url":"https://pith.science/pith/URVZG5IQE47MBOV4YV36PVZZ35/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/URVZG5IQE47MBOV4YV36PVZZ35/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":"2026-08-09T08:21:28Z","links":{"resolver":"https://pith.science/pith/URVZG5IQE47MBOV4YV36PVZZ35","bundle":"https://pith.science/pith/URVZG5IQE47MBOV4YV36PVZZ35/bundle.json","state":"https://pith.science/pith/URVZG5IQE47MBOV4YV36PVZZ35/state.json","well_known_bundle":"https://pith.science/.well-known/pith/URVZG5IQE47MBOV4YV36PVZZ35/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:URVZG5IQE47MBOV4YV36PVZZ35","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":"495e382bc3e42ac8fb23937b8a8d006beda8335922a104e1040f4f1b2add8ce3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2021-02-17T18:56:46Z","title_canon_sha256":"cf826600965c22254fbd613e79c37861f6ad6da38f413f1e3c87c017d583914b"},"schema_version":"1.0","source":{"id":"2102.08943","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.08943","created_at":"2026-07-05T02:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"2102.08943v2","created_at":"2026-07-05T02:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.08943","created_at":"2026-07-05T02:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"URVZG5IQE47M","created_at":"2026-07-05T02:47:59Z"},{"alias_kind":"pith_short_16","alias_value":"URVZG5IQE47MBOV4","created_at":"2026-07-05T02:47:59Z"},{"alias_kind":"pith_short_8","alias_value":"URVZG5IQ","created_at":"2026-07-05T02:47:59Z"}],"graph_snapshots":[{"event_id":"sha256:31415abff7cefa920fcffc20c77f9a99a5794e7b9f1f36740ae09ee98720e053","target":"graph","created_at":"2026-07-05T02:47:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.08943/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss new ideas for consideration of loop diagrams and angular integrals in $D$-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of linear combinations of external momenta. It gives a very simple presentation for the final results and is more convenient for calculations on computer algebra systems. In case of angular integrals we demonstrate how to simplify the integration of differential cross sections over polar angles. Also we derive the recursion relations, which allow to reduce all occur","authors_text":"Alexey S. Zhevlakov, Fabian Wunder, Valery E. Lyubovitskij","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2021-02-17T18:56:46Z","title":"New ideas for handling of loop and angular integrals in D-dimensions in QCD"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.08943","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":"sha256:635e3e7be1c84b2644b6072416f94f3ba0893b83c52a99129709c40be707b213","target":"record","created_at":"2026-07-05T02:47:59Z","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":"495e382bc3e42ac8fb23937b8a8d006beda8335922a104e1040f4f1b2add8ce3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2021-02-17T18:56:46Z","title_canon_sha256":"cf826600965c22254fbd613e79c37861f6ad6da38f413f1e3c87c017d583914b"},"schema_version":"1.0","source":{"id":"2102.08943","kind":"arxiv","version":2}},"canonical_sha256":"a46b937510273ec0babcc577e7d739df49e1cd614469fe6a30f33b238c3d84cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a46b937510273ec0babcc577e7d739df49e1cd614469fe6a30f33b238c3d84cf","first_computed_at":"2026-07-05T02:47:59.158459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:47:59.158459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TltsdNltUoa+vwSZFM/OC9J/eHmF6XZOI7DnhCVmuGm1mW67bgEORmweIw2dqbB7dG1zXGPOnSZFXLaw9o4iDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:47:59.158995Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.08943","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:635e3e7be1c84b2644b6072416f94f3ba0893b83c52a99129709c40be707b213","sha256:31415abff7cefa920fcffc20c77f9a99a5794e7b9f1f36740ae09ee98720e053"],"state_sha256":"c785973119d459c4e599178d4b796e3847e88a063c62cd0256ba95c9604816a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XdoS8zk8e0JW88cPNFBeMIvJBwwlG8O4TGwp3UxqMLpzxGFNqJqcpCWKI5G1lR0CKxNukqgtk3jGa4nu3QkxAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T08:21:28.393120Z","bundle_sha256":"2158b2865c9878e289a4ec47a3587b31c9e199c6195d411d1d9e49ce3b90bc0e"}}