{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:N5563LQX47XZAOKNMB6QWO5TDT","short_pith_number":"pith:N5563LQX","canonical_record":{"source":{"id":"1508.02512","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-08-11T08:12:50Z","cross_cats_sorted":[],"title_canon_sha256":"f05baeb1c80f5e9ab639060bb00c84a8a717f416c191b746f940326638f566b5","abstract_canon_sha256":"3264b59eddd3df8f599929245b9c3aa504bacbc34c653429b9445773affc252a"},"schema_version":"1.0"},"canonical_sha256":"6f7bedae17e7ef90394d607d0b3bb31cc9b6e1a3db8d0099d42194d3e93bd283","source":{"kind":"arxiv","id":"1508.02512","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02512","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02512v2","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02512","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"N5563LQX47XZ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N5563LQX47XZAOKN","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N5563LQX","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:N5563LQX47XZAOKNMB6QWO5TDT","target":"record","payload":{"canonical_record":{"source":{"id":"1508.02512","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-08-11T08:12:50Z","cross_cats_sorted":[],"title_canon_sha256":"f05baeb1c80f5e9ab639060bb00c84a8a717f416c191b746f940326638f566b5","abstract_canon_sha256":"3264b59eddd3df8f599929245b9c3aa504bacbc34c653429b9445773affc252a"},"schema_version":"1.0"},"canonical_sha256":"6f7bedae17e7ef90394d607d0b3bb31cc9b6e1a3db8d0099d42194d3e93bd283","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:08.225365Z","signature_b64":"3x+BwKy+/dKvPzMoU0tCdsxfkQxAp560FXRaqkK80w5vDgW5Cf5R54mHC7/2Hc9bk9RtKXreElSrJzy7clEgBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f7bedae17e7ef90394d607d0b3bb31cc9b6e1a3db8d0099d42194d3e93bd283","last_reissued_at":"2026-05-18T01:23:08.224898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:08.224898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.02512","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":"2026-05-18T01:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QycbIiLNYCuxyR3IiHKyTIGb7ZoH/uJMzPsB5dBLkzS0KsiS8ufjgGo1hciAAmnGs5lATCN5CunrSjig8jphAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:57:04.065328Z"},"content_sha256":"953f4ef87a7b3cf94f6751bdc00a552a78566d21666e72fb463472d6e5b22535","schema_version":"1.0","event_id":"sha256:953f4ef87a7b3cf94f6751bdc00a552a78566d21666e72fb463472d6e5b22535"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:N5563LQX47XZAOKNMB6QWO5TDT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Numerical Evaluation of Feynman Integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Jian Wang, Qi-Shu Yan, Xiaoran Zhao, Zhao Li","submitted_at":"2015-08-11T08:12:50Z","abstract_excerpt":"Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kine"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02512","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":""},"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":"2026-05-18T01:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQ1bqHVzyLGEnZstm2a+sSWc8cknrAOaaxU864wk7S2PX9UA+gDs6Ytdiib1ajT/RBI8DhGHTPeEKKBwW4KsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:57:04.065973Z"},"content_sha256":"05cec27ab2cf9db653f69f5d8c019f4e9859c55bf591c2b753a63e85abe1b2c2","schema_version":"1.0","event_id":"sha256:05cec27ab2cf9db653f69f5d8c019f4e9859c55bf591c2b753a63e85abe1b2c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N5563LQX47XZAOKNMB6QWO5TDT/bundle.json","state_url":"https://pith.science/pith/N5563LQX47XZAOKNMB6QWO5TDT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N5563LQX47XZAOKNMB6QWO5TDT/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":"2026-06-07T02:57:04Z","links":{"resolver":"https://pith.science/pith/N5563LQX47XZAOKNMB6QWO5TDT","bundle":"https://pith.science/pith/N5563LQX47XZAOKNMB6QWO5TDT/bundle.json","state":"https://pith.science/pith/N5563LQX47XZAOKNMB6QWO5TDT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N5563LQX47XZAOKNMB6QWO5TDT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N5563LQX47XZAOKNMB6QWO5TDT","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":"3264b59eddd3df8f599929245b9c3aa504bacbc34c653429b9445773affc252a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-08-11T08:12:50Z","title_canon_sha256":"f05baeb1c80f5e9ab639060bb00c84a8a717f416c191b746f940326638f566b5"},"schema_version":"1.0","source":{"id":"1508.02512","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02512","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02512v2","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02512","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"N5563LQX47XZ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N5563LQX47XZAOKN","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N5563LQX","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:05cec27ab2cf9db653f69f5d8c019f4e9859c55bf591c2b753a63e85abe1b2c2","target":"graph","created_at":"2026-05-18T01:23:08Z","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":"Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kine","authors_text":"Jian Wang, Qi-Shu Yan, Xiaoran Zhao, Zhao Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-08-11T08:12:50Z","title":"Efficient Numerical Evaluation of Feynman Integral"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02512","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":"sha256:953f4ef87a7b3cf94f6751bdc00a552a78566d21666e72fb463472d6e5b22535","target":"record","created_at":"2026-05-18T01:23:08Z","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":"3264b59eddd3df8f599929245b9c3aa504bacbc34c653429b9445773affc252a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-08-11T08:12:50Z","title_canon_sha256":"f05baeb1c80f5e9ab639060bb00c84a8a717f416c191b746f940326638f566b5"},"schema_version":"1.0","source":{"id":"1508.02512","kind":"arxiv","version":2}},"canonical_sha256":"6f7bedae17e7ef90394d607d0b3bb31cc9b6e1a3db8d0099d42194d3e93bd283","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f7bedae17e7ef90394d607d0b3bb31cc9b6e1a3db8d0099d42194d3e93bd283","first_computed_at":"2026-05-18T01:23:08.224898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:08.224898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3x+BwKy+/dKvPzMoU0tCdsxfkQxAp560FXRaqkK80w5vDgW5Cf5R54mHC7/2Hc9bk9RtKXreElSrJzy7clEgBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:08.225365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02512","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:953f4ef87a7b3cf94f6751bdc00a552a78566d21666e72fb463472d6e5b22535","sha256:05cec27ab2cf9db653f69f5d8c019f4e9859c55bf591c2b753a63e85abe1b2c2"],"state_sha256":"20146a4058f41cc4641c8ddaf4879f750be8dba455999730062b5d952971130b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"urFlDa9XYuUqNuGDdPptPa93p+LUxQ/gWNxkSckvUPERPV8BPA7IVWP6XSgBLTB3tc79sNwvbaEwfX+xW+SHDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:57:04.069452Z","bundle_sha256":"076f40dc4f048511b625fbf091e0f5a194cde730efe219d5d2936cd99e7d99cc"}}