{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:Z4IDQT5GIV4OYIQLUOHS4JOGSJ","short_pith_number":"pith:Z4IDQT5G","canonical_record":{"source":{"id":"2005.01942","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-05-05T04:31:46Z","cross_cats_sorted":["hep-ex","hep-th","nucl-ex","nucl-th"],"title_canon_sha256":"6bc61dc2ac9b4a048a9f55f8c9f63cd144ba7843bee8f0009e1449fdc8f6b897","abstract_canon_sha256":"a8e7cd4e3d1c52cb2d2b41be19a6a53d40ec03d27c02548439ad7ddcf9e0d6ce"},"schema_version":"1.0"},"canonical_sha256":"cf10384fa64578ec220ba38f2e25c69274bdc46710bf2fce027a525b85e33c47","source":{"kind":"arxiv","id":"2005.01942","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.01942","created_at":"2026-07-05T02:15:10Z"},{"alias_kind":"arxiv_version","alias_value":"2005.01942v3","created_at":"2026-07-05T02:15:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.01942","created_at":"2026-07-05T02:15:10Z"},{"alias_kind":"pith_short_12","alias_value":"Z4IDQT5GIV4O","created_at":"2026-07-05T02:15:10Z"},{"alias_kind":"pith_short_16","alias_value":"Z4IDQT5GIV4OYIQL","created_at":"2026-07-05T02:15:10Z"},{"alias_kind":"pith_short_8","alias_value":"Z4IDQT5G","created_at":"2026-07-05T02:15:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:Z4IDQT5GIV4OYIQLUOHS4JOGSJ","target":"record","payload":{"canonical_record":{"source":{"id":"2005.01942","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-05-05T04:31:46Z","cross_cats_sorted":["hep-ex","hep-th","nucl-ex","nucl-th"],"title_canon_sha256":"6bc61dc2ac9b4a048a9f55f8c9f63cd144ba7843bee8f0009e1449fdc8f6b897","abstract_canon_sha256":"a8e7cd4e3d1c52cb2d2b41be19a6a53d40ec03d27c02548439ad7ddcf9e0d6ce"},"schema_version":"1.0"},"canonical_sha256":"cf10384fa64578ec220ba38f2e25c69274bdc46710bf2fce027a525b85e33c47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:15:10.251071Z","signature_b64":"cdoX+lSsSRvCWDTtkS268fm469CfwpGWbcx3TOYidehbOpwb1AXsgkUx29S3vmPcEsY9K6qg5D542G8MJWpTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf10384fa64578ec220ba38f2e25c69274bdc46710bf2fce027a525b85e33c47","last_reissued_at":"2026-07-05T02:15:10.250543Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:15:10.250543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2005.01942","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:15:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pEgrx6OPQSBEVeqCzXSybjXWx7MLpO6iZ+eLNnf9gPYgTqmwfjUR6xsrb1n41rqtVNoBUJlqLsHya4bpd2VBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T07:08:54.791345Z"},"content_sha256":"b3e1b512505daf843ea8f27718c68afec163a21e5cec11d1c946a94e4fc0f035","schema_version":"1.0","event_id":"sha256:b3e1b512505daf843ea8f27718c68afec163a21e5cec11d1c946a94e4fc0f035"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:Z4IDQT5GIV4OYIQLUOHS4JOGSJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graphic Method for Arbitrary $n$-body Phase Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ex","hep-th","nucl-ex","nucl-th"],"primary_cat":"hep-ph","authors_text":"Chao-wei Shen, Feng-Kun Guo, Hao-Jie Jing","submitted_at":"2020-05-05T04:31:46Z","abstract_excerpt":"In quantum field theory, the phase space integration is an essential part in all theoretical calculations of cross sections and decay widths. It is also needed for computing the imaginary part of a physical amplitude. A key problem is to get the phase space formula expressed in terms of any chosen invariant masses in an $n$-body system. We propose a graphic method to quickly get the phase space formula of any given invariant masses intuitively for an arbitrary $n$-body system in general $D$-dimensional spacetime, with the involved momenta in any reference frame. The method also greatly simplif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.01942","kind":"arxiv","version":3},"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/2005.01942/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":"2026-07-05T02:15:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d2PWJspvHAdkYd/gUja8eeJHrzMP0XbM42JfO+8yo3xISRBFxfPclHfkJTvOSPT6uH/AT8hbuZSi6XoOijOYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T07:08:54.792159Z"},"content_sha256":"387e896e77482372ee00f47deac9326f303fbd09c855c2b324350780968b9cb6","schema_version":"1.0","event_id":"sha256:387e896e77482372ee00f47deac9326f303fbd09c855c2b324350780968b9cb6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z4IDQT5GIV4OYIQLUOHS4JOGSJ/bundle.json","state_url":"https://pith.science/pith/Z4IDQT5GIV4OYIQLUOHS4JOGSJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z4IDQT5GIV4OYIQLUOHS4JOGSJ/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":"2026-08-05T07:08:54Z","links":{"resolver":"https://pith.science/pith/Z4IDQT5GIV4OYIQLUOHS4JOGSJ","bundle":"https://pith.science/pith/Z4IDQT5GIV4OYIQLUOHS4JOGSJ/bundle.json","state":"https://pith.science/pith/Z4IDQT5GIV4OYIQLUOHS4JOGSJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z4IDQT5GIV4OYIQLUOHS4JOGSJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:Z4IDQT5GIV4OYIQLUOHS4JOGSJ","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":"a8e7cd4e3d1c52cb2d2b41be19a6a53d40ec03d27c02548439ad7ddcf9e0d6ce","cross_cats_sorted":["hep-ex","hep-th","nucl-ex","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-05-05T04:31:46Z","title_canon_sha256":"6bc61dc2ac9b4a048a9f55f8c9f63cd144ba7843bee8f0009e1449fdc8f6b897"},"schema_version":"1.0","source":{"id":"2005.01942","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.01942","created_at":"2026-07-05T02:15:10Z"},{"alias_kind":"arxiv_version","alias_value":"2005.01942v3","created_at":"2026-07-05T02:15:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.01942","created_at":"2026-07-05T02:15:10Z"},{"alias_kind":"pith_short_12","alias_value":"Z4IDQT5GIV4O","created_at":"2026-07-05T02:15:10Z"},{"alias_kind":"pith_short_16","alias_value":"Z4IDQT5GIV4OYIQL","created_at":"2026-07-05T02:15:10Z"},{"alias_kind":"pith_short_8","alias_value":"Z4IDQT5G","created_at":"2026-07-05T02:15:10Z"}],"graph_snapshots":[{"event_id":"sha256:387e896e77482372ee00f47deac9326f303fbd09c855c2b324350780968b9cb6","target":"graph","created_at":"2026-07-05T02:15:10Z","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/2005.01942/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In quantum field theory, the phase space integration is an essential part in all theoretical calculations of cross sections and decay widths. It is also needed for computing the imaginary part of a physical amplitude. A key problem is to get the phase space formula expressed in terms of any chosen invariant masses in an $n$-body system. We propose a graphic method to quickly get the phase space formula of any given invariant masses intuitively for an arbitrary $n$-body system in general $D$-dimensional spacetime, with the involved momenta in any reference frame. The method also greatly simplif","authors_text":"Chao-wei Shen, Feng-Kun Guo, Hao-Jie Jing","cross_cats":["hep-ex","hep-th","nucl-ex","nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-05-05T04:31:46Z","title":"Graphic Method for Arbitrary $n$-body Phase Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.01942","kind":"arxiv","version":3},"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:b3e1b512505daf843ea8f27718c68afec163a21e5cec11d1c946a94e4fc0f035","target":"record","created_at":"2026-07-05T02:15:10Z","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":"a8e7cd4e3d1c52cb2d2b41be19a6a53d40ec03d27c02548439ad7ddcf9e0d6ce","cross_cats_sorted":["hep-ex","hep-th","nucl-ex","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-05-05T04:31:46Z","title_canon_sha256":"6bc61dc2ac9b4a048a9f55f8c9f63cd144ba7843bee8f0009e1449fdc8f6b897"},"schema_version":"1.0","source":{"id":"2005.01942","kind":"arxiv","version":3}},"canonical_sha256":"cf10384fa64578ec220ba38f2e25c69274bdc46710bf2fce027a525b85e33c47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf10384fa64578ec220ba38f2e25c69274bdc46710bf2fce027a525b85e33c47","first_computed_at":"2026-07-05T02:15:10.250543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:15:10.250543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cdoX+lSsSRvCWDTtkS268fm469CfwpGWbcx3TOYidehbOpwb1AXsgkUx29S3vmPcEsY9K6qg5D542G8MJWpTBA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:15:10.251071Z","signed_message":"canonical_sha256_bytes"},"source_id":"2005.01942","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3e1b512505daf843ea8f27718c68afec163a21e5cec11d1c946a94e4fc0f035","sha256:387e896e77482372ee00f47deac9326f303fbd09c855c2b324350780968b9cb6"],"state_sha256":"d9bbee0f4d34d528ec0e1ae7f60bd0ee737be63dbccb236d18da224db5780640"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y9IpcLU68IIADd2PKfzzXRGSNuzvNPVmtJNQVQEpOQOH0U+dC/KVIWL7atWlk9SuHLRzPTn5boNNF7MqRVYdCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T07:08:54.799510Z","bundle_sha256":"82b2d24ff59d62ff821de17181803f090f05264f725fb4c950c5cb21572c4f08"}}