{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UQEV4VR5WYFWUHV5LZLU2HKEC2","short_pith_number":"pith:UQEV4VR5","canonical_record":{"source":{"id":"2410.18886","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-10-24T16:22:30Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"9db8e5bb92a96149509c36c3413dc538c753275345e08be952d2e9e0799bd1bc","abstract_canon_sha256":"2ae87f6fb946d125ce2d6ac88a887e49133995d6f38aa92a1c4caf90aa959e42"},"schema_version":"1.0"},"canonical_sha256":"a4095e563db60b6a1ebd5e574d1d44168e1dd9bd342bda17f2a9139ff7c83bcd","source":{"kind":"arxiv","id":"2410.18886","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.18886","created_at":"2026-07-05T09:25:21Z"},{"alias_kind":"arxiv_version","alias_value":"2410.18886v1","created_at":"2026-07-05T09:25:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.18886","created_at":"2026-07-05T09:25:21Z"},{"alias_kind":"pith_short_12","alias_value":"UQEV4VR5WYFW","created_at":"2026-07-05T09:25:21Z"},{"alias_kind":"pith_short_16","alias_value":"UQEV4VR5WYFWUHV5","created_at":"2026-07-05T09:25:21Z"},{"alias_kind":"pith_short_8","alias_value":"UQEV4VR5","created_at":"2026-07-05T09:25:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UQEV4VR5WYFWUHV5LZLU2HKEC2","target":"record","payload":{"canonical_record":{"source":{"id":"2410.18886","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-10-24T16:22:30Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"9db8e5bb92a96149509c36c3413dc538c753275345e08be952d2e9e0799bd1bc","abstract_canon_sha256":"2ae87f6fb946d125ce2d6ac88a887e49133995d6f38aa92a1c4caf90aa959e42"},"schema_version":"1.0"},"canonical_sha256":"a4095e563db60b6a1ebd5e574d1d44168e1dd9bd342bda17f2a9139ff7c83bcd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:25:21.469423Z","signature_b64":"lfFOue/BvOCypnbgIpmZXd4sCrnhaGCSKAtliWjCP8E+Z7/5ynJnAF5JhPSLFJMtyMITln01FN5YMXjDjphNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4095e563db60b6a1ebd5e574d1d44168e1dd9bd342bda17f2a9139ff7c83bcd","last_reissued_at":"2026-07-05T09:25:21.468949Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:25:21.468949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.18886","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":"2026-07-05T09:25:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"897ZBEnFvwtUGgMqmZMgQOAwXB8bIjfciHjdPCiBRTbeoPj+76Ge0SrFzxlw71inb09NL9/WwvNw4Y9u0dtyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:57:26.578447Z"},"content_sha256":"a76faaee978ba5a2eec1c398f6d88b058fef85f1c416706886bf8e6eee42cb38","schema_version":"1.0","event_id":"sha256:a76faaee978ba5a2eec1c398f6d88b058fef85f1c416706886bf8e6eee42cb38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UQEV4VR5WYFWUHV5LZLU2HKEC2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phase-space integrals through Mellin-Barnes representation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Andreas Rapakoulias, Syed Mehedi Hasan, Taushif Ahmed","submitted_at":"2024-10-24T16:22:30Z","abstract_excerpt":"This letter introduces a novel analytical approach to calculating phase-space integrals, crucial for precision in particle physics. We develop a method to compute angular components using multifold Mellin-Barnes integrals, yielding results in terms of Goncharov polylogarithms for integrals involving three denominators. Our results include expressions for massless momenta up to $\\cal{O}(\\epsilon^2)$ and for one massive momentum up to $\\cal{O}(\\epsilon)$. Additionally, we derive recursion relations that reduce integrals with higher powers of denominators to simpler ones. We detail how to combine"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18886","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.18886/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":"2026-07-05T09:25:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kmYkkG0FL73kdZfDjfRo2Dgj6N+JCOutu+6Tedn11hE51YXeL6ISSS72crKG5thg3BIRysNfFcuwbma/SzzTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:57:26.579306Z"},"content_sha256":"d00e29a0133508fa43d8448f3ec3b696be6fdb4afaf3a8637496abaed6b42721","schema_version":"1.0","event_id":"sha256:d00e29a0133508fa43d8448f3ec3b696be6fdb4afaf3a8637496abaed6b42721"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQEV4VR5WYFWUHV5LZLU2HKEC2/bundle.json","state_url":"https://pith.science/pith/UQEV4VR5WYFWUHV5LZLU2HKEC2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQEV4VR5WYFWUHV5LZLU2HKEC2/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":"2026-08-07T10:57:26Z","links":{"resolver":"https://pith.science/pith/UQEV4VR5WYFWUHV5LZLU2HKEC2","bundle":"https://pith.science/pith/UQEV4VR5WYFWUHV5LZLU2HKEC2/bundle.json","state":"https://pith.science/pith/UQEV4VR5WYFWUHV5LZLU2HKEC2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQEV4VR5WYFWUHV5LZLU2HKEC2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UQEV4VR5WYFWUHV5LZLU2HKEC2","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":"2ae87f6fb946d125ce2d6ac88a887e49133995d6f38aa92a1c4caf90aa959e42","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-10-24T16:22:30Z","title_canon_sha256":"9db8e5bb92a96149509c36c3413dc538c753275345e08be952d2e9e0799bd1bc"},"schema_version":"1.0","source":{"id":"2410.18886","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.18886","created_at":"2026-07-05T09:25:21Z"},{"alias_kind":"arxiv_version","alias_value":"2410.18886v1","created_at":"2026-07-05T09:25:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.18886","created_at":"2026-07-05T09:25:21Z"},{"alias_kind":"pith_short_12","alias_value":"UQEV4VR5WYFW","created_at":"2026-07-05T09:25:21Z"},{"alias_kind":"pith_short_16","alias_value":"UQEV4VR5WYFWUHV5","created_at":"2026-07-05T09:25:21Z"},{"alias_kind":"pith_short_8","alias_value":"UQEV4VR5","created_at":"2026-07-05T09:25:21Z"}],"graph_snapshots":[{"event_id":"sha256:d00e29a0133508fa43d8448f3ec3b696be6fdb4afaf3a8637496abaed6b42721","target":"graph","created_at":"2026-07-05T09:25:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.18886/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This letter introduces a novel analytical approach to calculating phase-space integrals, crucial for precision in particle physics. We develop a method to compute angular components using multifold Mellin-Barnes integrals, yielding results in terms of Goncharov polylogarithms for integrals involving three denominators. Our results include expressions for massless momenta up to $\\cal{O}(\\epsilon^2)$ and for one massive momentum up to $\\cal{O}(\\epsilon)$. Additionally, we derive recursion relations that reduce integrals with higher powers of denominators to simpler ones. We detail how to combine","authors_text":"Andreas Rapakoulias, Syed Mehedi Hasan, Taushif Ahmed","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-10-24T16:22:30Z","title":"Phase-space integrals through Mellin-Barnes representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18886","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:a76faaee978ba5a2eec1c398f6d88b058fef85f1c416706886bf8e6eee42cb38","target":"record","created_at":"2026-07-05T09:25:21Z","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":"2ae87f6fb946d125ce2d6ac88a887e49133995d6f38aa92a1c4caf90aa959e42","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-10-24T16:22:30Z","title_canon_sha256":"9db8e5bb92a96149509c36c3413dc538c753275345e08be952d2e9e0799bd1bc"},"schema_version":"1.0","source":{"id":"2410.18886","kind":"arxiv","version":1}},"canonical_sha256":"a4095e563db60b6a1ebd5e574d1d44168e1dd9bd342bda17f2a9139ff7c83bcd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4095e563db60b6a1ebd5e574d1d44168e1dd9bd342bda17f2a9139ff7c83bcd","first_computed_at":"2026-07-05T09:25:21.468949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:25:21.468949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lfFOue/BvOCypnbgIpmZXd4sCrnhaGCSKAtliWjCP8E+Z7/5ynJnAF5JhPSLFJMtyMITln01FN5YMXjDjphNCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:25:21.469423Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.18886","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a76faaee978ba5a2eec1c398f6d88b058fef85f1c416706886bf8e6eee42cb38","sha256:d00e29a0133508fa43d8448f3ec3b696be6fdb4afaf3a8637496abaed6b42721"],"state_sha256":"ac2d9faf77fd0d483a30ca471772f084d7337278294d6d33e42a66f29dfd59e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IkPD1/O8AEC3M7RhLHZn8Xf8c6nihIsIER20dMEMWiLdmPVUxPjN4ObuQqbntck4yHVDiMYTqCg8AO4Ruj6UBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T10:57:26.585785Z","bundle_sha256":"e8b1d538e826cdaf6ee5868106c59207f202388f1ccd38189507b100524850a1"}}