{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:YBLM3CH632MTM4DADO2RHFNHAO","short_pith_number":"pith:YBLM3CH6","canonical_record":{"source":{"id":"2205.03000","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2022-05-06T03:51:20Z","cross_cats_sorted":[],"title_canon_sha256":"27d10cc3078cd73ab402962f48ea8ee7af4a5d9959cd288956da2ce17cc45788","abstract_canon_sha256":"db0051d56cc9dadb7c54dd8d1ec20138d27381a4751603175c7de58997be113c"},"schema_version":"1.0"},"canonical_sha256":"c056cd88fede993670601bb51395a70387f064b58d9b2add7e1f82181b93bbd1","source":{"kind":"arxiv","id":"2205.03000","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.03000","created_at":"2026-07-05T04:50:56Z"},{"alias_kind":"arxiv_version","alias_value":"2205.03000v2","created_at":"2026-07-05T04:50:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.03000","created_at":"2026-07-05T04:50:56Z"},{"alias_kind":"pith_short_12","alias_value":"YBLM3CH632MT","created_at":"2026-07-05T04:50:56Z"},{"alias_kind":"pith_short_16","alias_value":"YBLM3CH632MTM4DA","created_at":"2026-07-05T04:50:56Z"},{"alias_kind":"pith_short_8","alias_value":"YBLM3CH6","created_at":"2026-07-05T04:50:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:YBLM3CH632MTM4DADO2RHFNHAO","target":"record","payload":{"canonical_record":{"source":{"id":"2205.03000","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2022-05-06T03:51:20Z","cross_cats_sorted":[],"title_canon_sha256":"27d10cc3078cd73ab402962f48ea8ee7af4a5d9959cd288956da2ce17cc45788","abstract_canon_sha256":"db0051d56cc9dadb7c54dd8d1ec20138d27381a4751603175c7de58997be113c"},"schema_version":"1.0"},"canonical_sha256":"c056cd88fede993670601bb51395a70387f064b58d9b2add7e1f82181b93bbd1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:50:56.717154Z","signature_b64":"DqX58kDVb11tK7h8V2WrHuSBlGO37Opvd7wI/iPcZKWJMZ+LcqFhVT6UeCVfqd/alJtA/CUVlKU9aL1h6RRvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c056cd88fede993670601bb51395a70387f064b58d9b2add7e1f82181b93bbd1","last_reissued_at":"2026-07-05T04:50:56.716686Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:50:56.716686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.03000","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":"2026-07-05T04:50:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IYyHFFbt3I27o6V62g6Bc2Tu+Bk9MY1MHL0+oCVjK8DCfXEB4oN6zz3ckDIGHAmhmSqtwhuRp24g//W8Dh4cBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T05:09:22.980639Z"},"content_sha256":"901ab482c241dd6e07ec4304d01f340767adaa86197de4ea53884e624481859d","schema_version":"1.0","event_id":"sha256:901ab482c241dd6e07ec4304d01f340767adaa86197de4ea53884e624481859d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:YBLM3CH632MTM4DADO2RHFNHAO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reduction with Degenerate Gram matrix for One-loop Integrals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Bo Feng, Chang Hu, Tingfei Li, Yuekai Song","submitted_at":"2022-05-06T03:51:20Z","abstract_excerpt":"An improved PV-reduction method for one-loop integrals with auxiliary vector $R$ has been proposed in \\cite{Feng:2021enk,Hu:2021nia}. It has also been shown that the new method is a self-completed method in \\cite{Feng:2022uqp}. Analytic reduction coefficients can be easily produced by recursion relations in this method, where the Gram determinant appears in denominators. The singularity caused by Gram determinant is a well-known fact and it is important to address these divergences in a given frame. In this paper, we propose a systematical algorithm to deal with this problem in our method. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.03000","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/2205.03000/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":"2026-07-05T04:50:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N41yl+1PhhhNqB8C4bG2Nv2xBv3nfNpbhMQR03dZNqNnqo7TA7zs5JQ9ougrNjU41Z4iQGlcS7fBfRv8d0rHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T05:09:22.982076Z"},"content_sha256":"d1948bc366e7b29e03c9fb8b0d5b40fc31b0ab71eac1b2a76b58fe223d7b4ded","schema_version":"1.0","event_id":"sha256:d1948bc366e7b29e03c9fb8b0d5b40fc31b0ab71eac1b2a76b58fe223d7b4ded"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YBLM3CH632MTM4DADO2RHFNHAO/bundle.json","state_url":"https://pith.science/pith/YBLM3CH632MTM4DADO2RHFNHAO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YBLM3CH632MTM4DADO2RHFNHAO/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":"2026-08-11T05:09:22Z","links":{"resolver":"https://pith.science/pith/YBLM3CH632MTM4DADO2RHFNHAO","bundle":"https://pith.science/pith/YBLM3CH632MTM4DADO2RHFNHAO/bundle.json","state":"https://pith.science/pith/YBLM3CH632MTM4DADO2RHFNHAO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YBLM3CH632MTM4DADO2RHFNHAO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YBLM3CH632MTM4DADO2RHFNHAO","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":"db0051d56cc9dadb7c54dd8d1ec20138d27381a4751603175c7de58997be113c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2022-05-06T03:51:20Z","title_canon_sha256":"27d10cc3078cd73ab402962f48ea8ee7af4a5d9959cd288956da2ce17cc45788"},"schema_version":"1.0","source":{"id":"2205.03000","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.03000","created_at":"2026-07-05T04:50:56Z"},{"alias_kind":"arxiv_version","alias_value":"2205.03000v2","created_at":"2026-07-05T04:50:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.03000","created_at":"2026-07-05T04:50:56Z"},{"alias_kind":"pith_short_12","alias_value":"YBLM3CH632MT","created_at":"2026-07-05T04:50:56Z"},{"alias_kind":"pith_short_16","alias_value":"YBLM3CH632MTM4DA","created_at":"2026-07-05T04:50:56Z"},{"alias_kind":"pith_short_8","alias_value":"YBLM3CH6","created_at":"2026-07-05T04:50:56Z"}],"graph_snapshots":[{"event_id":"sha256:d1948bc366e7b29e03c9fb8b0d5b40fc31b0ab71eac1b2a76b58fe223d7b4ded","target":"graph","created_at":"2026-07-05T04:50:56Z","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/2205.03000/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An improved PV-reduction method for one-loop integrals with auxiliary vector $R$ has been proposed in \\cite{Feng:2021enk,Hu:2021nia}. It has also been shown that the new method is a self-completed method in \\cite{Feng:2022uqp}. Analytic reduction coefficients can be easily produced by recursion relations in this method, where the Gram determinant appears in denominators. The singularity caused by Gram determinant is a well-known fact and it is important to address these divergences in a given frame. In this paper, we propose a systematical algorithm to deal with this problem in our method. The","authors_text":"Bo Feng, Chang Hu, Tingfei Li, Yuekai Song","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2022-05-06T03:51:20Z","title":"Reduction with Degenerate Gram matrix for One-loop Integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.03000","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":"sha256:901ab482c241dd6e07ec4304d01f340767adaa86197de4ea53884e624481859d","target":"record","created_at":"2026-07-05T04:50:56Z","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":"db0051d56cc9dadb7c54dd8d1ec20138d27381a4751603175c7de58997be113c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2022-05-06T03:51:20Z","title_canon_sha256":"27d10cc3078cd73ab402962f48ea8ee7af4a5d9959cd288956da2ce17cc45788"},"schema_version":"1.0","source":{"id":"2205.03000","kind":"arxiv","version":2}},"canonical_sha256":"c056cd88fede993670601bb51395a70387f064b58d9b2add7e1f82181b93bbd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c056cd88fede993670601bb51395a70387f064b58d9b2add7e1f82181b93bbd1","first_computed_at":"2026-07-05T04:50:56.716686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:50:56.716686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DqX58kDVb11tK7h8V2WrHuSBlGO37Opvd7wI/iPcZKWJMZ+LcqFhVT6UeCVfqd/alJtA/CUVlKU9aL1h6RRvCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:50:56.717154Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.03000","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:901ab482c241dd6e07ec4304d01f340767adaa86197de4ea53884e624481859d","sha256:d1948bc366e7b29e03c9fb8b0d5b40fc31b0ab71eac1b2a76b58fe223d7b4ded"],"state_sha256":"6a1d4d37d029e606ef8ba23f8298c532bc5036dac29d7e0d20dc8274a5e2f83f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VpsMitl7p06iypoJs35l9O+xnTG12H9gmscqrgbyfki5ZTnFM0H16BmaKQQqiGnAg4Nt9o06Ot0/gzsK94/SAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T05:09:22.987766Z","bundle_sha256":"af162751878d6c2cde27800bd29a02d5fa68a2687236f57ee196e8f3c250f097"}}