{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7JER7ENKAW3Q6YTAY6CYP7FOBN","short_pith_number":"pith:7JER7ENK","canonical_record":{"source":{"id":"1105.2080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-05-11T00:25:13Z","cross_cats_sorted":[],"title_canon_sha256":"29763874ccce93841957bb0e92ba560617d6c77248ac47544b4b210c9267f822","abstract_canon_sha256":"5813e878d8763881d39dde17eef593e7bb847c00a6e9457ecd50011975a8ca63"},"schema_version":"1.0"},"canonical_sha256":"fa491f91aa05b70f6260c78587fcae0b6505e450e92c3ee8347e9e429bc2a4a5","source":{"kind":"arxiv","id":"1105.2080","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2080","created_at":"2026-05-18T04:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2080v1","created_at":"2026-05-18T04:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2080","created_at":"2026-05-18T04:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"7JER7ENKAW3Q","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7JER7ENKAW3Q6YTA","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7JER7ENK","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7JER7ENKAW3Q6YTAY6CYP7FOBN","target":"record","payload":{"canonical_record":{"source":{"id":"1105.2080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-05-11T00:25:13Z","cross_cats_sorted":[],"title_canon_sha256":"29763874ccce93841957bb0e92ba560617d6c77248ac47544b4b210c9267f822","abstract_canon_sha256":"5813e878d8763881d39dde17eef593e7bb847c00a6e9457ecd50011975a8ca63"},"schema_version":"1.0"},"canonical_sha256":"fa491f91aa05b70f6260c78587fcae0b6505e450e92c3ee8347e9e429bc2a4a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:21.558779Z","signature_b64":"TU0s5lj7S1HodYQK0RsTupH7+8L2Lt/JUd+bl5gSvn+tGRX7C4zKsC0Rnzahf5QQPRtu7KPhs8pST3c1YMu2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa491f91aa05b70f6260c78587fcae0b6505e450e92c3ee8347e9e429bc2a4a5","last_reissued_at":"2026-05-18T04:22:21.558351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:21.558351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.2080","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":"2026-05-18T04:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4L5iC+1omzVuBXjcjJi35c8/gP3Z/jqp2/7vLGUHuDugb1DqS1xnZRD6DXuAcEu6Wu4ocZGceJJtjavBx7IuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:08:19.957623Z"},"content_sha256":"919a2a638f4c9a2a431acabe693ac0c6ea05a68bae94514a3d14628b481893f8","schema_version":"1.0","event_id":"sha256:919a2a638f4c9a2a431acabe693ac0c6ea05a68bae94514a3d14628b481893f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7JER7ENKAW3Q6YTAY6CYP7FOBN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical calculation of one-loop integration with hypergeometric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Toshiaki KANEKO","submitted_at":"2011-05-11T00:25:13Z","abstract_excerpt":"One-loop two-, three- and four-point scalar functions are analytically integrated directly such that they are expressed in terms of Lauricella's hypergeometric function $F_D$. For two- and three-point functions, exact expressions are obtained with arbitrary combination of kinematic and mass parameters in arbitrary space-time dimension. Four-point function is expressed in terms of $F_D$ up to the finite part in the expansion around 4-dimensional space-time with arbitrary combination of kinematic and mass parameters. Since the location of the possible singularities of $F_D$ is known, information"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2080","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":"2026-05-18T04:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XQBQrobJio6CPImHRIeomeVzGMgFZfpU87ryr+xn7VeSj6Mk5zmHBtHRDABvTJKmEKYm6qRMLTd45uf6OAf0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:08:19.958097Z"},"content_sha256":"145e82a5d5d917c8b6f2cdd6ac24cabbe2287688c09893cd54d1f0e7335113b0","schema_version":"1.0","event_id":"sha256:145e82a5d5d917c8b6f2cdd6ac24cabbe2287688c09893cd54d1f0e7335113b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7JER7ENKAW3Q6YTAY6CYP7FOBN/bundle.json","state_url":"https://pith.science/pith/7JER7ENKAW3Q6YTAY6CYP7FOBN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7JER7ENKAW3Q6YTAY6CYP7FOBN/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":"2026-06-24T06:08:19Z","links":{"resolver":"https://pith.science/pith/7JER7ENKAW3Q6YTAY6CYP7FOBN","bundle":"https://pith.science/pith/7JER7ENKAW3Q6YTAY6CYP7FOBN/bundle.json","state":"https://pith.science/pith/7JER7ENKAW3Q6YTAY6CYP7FOBN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7JER7ENKAW3Q6YTAY6CYP7FOBN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7JER7ENKAW3Q6YTAY6CYP7FOBN","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":"5813e878d8763881d39dde17eef593e7bb847c00a6e9457ecd50011975a8ca63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-05-11T00:25:13Z","title_canon_sha256":"29763874ccce93841957bb0e92ba560617d6c77248ac47544b4b210c9267f822"},"schema_version":"1.0","source":{"id":"1105.2080","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2080","created_at":"2026-05-18T04:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2080v1","created_at":"2026-05-18T04:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2080","created_at":"2026-05-18T04:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"7JER7ENKAW3Q","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7JER7ENKAW3Q6YTA","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7JER7ENK","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:145e82a5d5d917c8b6f2cdd6ac24cabbe2287688c09893cd54d1f0e7335113b0","target":"graph","created_at":"2026-05-18T04:22:21Z","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":"One-loop two-, three- and four-point scalar functions are analytically integrated directly such that they are expressed in terms of Lauricella's hypergeometric function $F_D$. For two- and three-point functions, exact expressions are obtained with arbitrary combination of kinematic and mass parameters in arbitrary space-time dimension. Four-point function is expressed in terms of $F_D$ up to the finite part in the expansion around 4-dimensional space-time with arbitrary combination of kinematic and mass parameters. Since the location of the possible singularities of $F_D$ is known, information","authors_text":"Toshiaki KANEKO","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-05-11T00:25:13Z","title":"Numerical calculation of one-loop integration with hypergeometric functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2080","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":"sha256:919a2a638f4c9a2a431acabe693ac0c6ea05a68bae94514a3d14628b481893f8","target":"record","created_at":"2026-05-18T04:22:21Z","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":"5813e878d8763881d39dde17eef593e7bb847c00a6e9457ecd50011975a8ca63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-05-11T00:25:13Z","title_canon_sha256":"29763874ccce93841957bb0e92ba560617d6c77248ac47544b4b210c9267f822"},"schema_version":"1.0","source":{"id":"1105.2080","kind":"arxiv","version":1}},"canonical_sha256":"fa491f91aa05b70f6260c78587fcae0b6505e450e92c3ee8347e9e429bc2a4a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa491f91aa05b70f6260c78587fcae0b6505e450e92c3ee8347e9e429bc2a4a5","first_computed_at":"2026-05-18T04:22:21.558351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:21.558351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TU0s5lj7S1HodYQK0RsTupH7+8L2Lt/JUd+bl5gSvn+tGRX7C4zKsC0Rnzahf5QQPRtu7KPhs8pST3c1YMu2CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:21.558779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2080","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:919a2a638f4c9a2a431acabe693ac0c6ea05a68bae94514a3d14628b481893f8","sha256:145e82a5d5d917c8b6f2cdd6ac24cabbe2287688c09893cd54d1f0e7335113b0"],"state_sha256":"962b4074ce298f1e7e5875d187af6d380250f8f83ebfe2bad30c078a34dfd4eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b2/buOevmvMkhoeqxA72ZNlzg1KnI7i9cG8KkLD2j9cL0IzPHvrLrAj9Hb17D32q4ACH4W3WI6Ho49jYwbqHBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:08:19.960715Z","bundle_sha256":"13e6c4a912fd3649db926d180ffa3345e47d01933ddf28e45acb0800999f7f3e"}}