{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:HASTOVWGV2D5IQQVDVUTYHGD7V","short_pith_number":"pith:HASTOVWG","schema_version":"1.0","canonical_sha256":"38253756c6ae87d442151d693c1cc3fd4e29ef76232b81dffcf3aa3559241d15","source":{"kind":"arxiv","id":"2001.09460","version":2},"attestation_state":"computed","paper":{"title":"A self-consistent framework of topological amplitude and its $SU(N)$ decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Cai-Ping Jia, Di Wang, Fu-Sheng Yu","submitted_at":"2020-01-26T14:25:21Z","abstract_excerpt":"We propose a systematic theoretical framework for the topological amplitudes of the heavy meson decays and their $SU(N)$ decomposition. In the framework, the topological amplitudes are expressed in invariant tensors and classified into tree- and penguin-operator-induced diagrams according to which four-quark operators, tree or penguin, being inserted into their effective weak vertexes. By decomposing the four-quark operators into irreducible representations of $SU(N)$ group, one can derive the $SU(N)$ irreducible amplitudes from the tensor form of the topology. Taking the $D\\to PP$ decay ($P$ "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2001.09460","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-01-26T14:25:21Z","cross_cats_sorted":[],"title_canon_sha256":"7229534c613955794b5caa2ee33e537b8b7db0e98dc99339da45151fe11082cc","abstract_canon_sha256":"9792590c820f397b216fbf469557ab83f1c20073cf78f7c6cb04389ff9403a2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:16:59.931391Z","signature_b64":"tZH5OxK3O9UGz1DwMMHgaiLC4AenVqT253iaYYUWxj9MpT6uPy74pw/D8rIHdE95ymAGJdJraVU7nWtbh1+CCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38253756c6ae87d442151d693c1cc3fd4e29ef76232b81dffcf3aa3559241d15","last_reissued_at":"2026-07-05T03:16:59.930994Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:16:59.930994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A self-consistent framework of topological amplitude and its $SU(N)$ decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Cai-Ping Jia, Di Wang, Fu-Sheng Yu","submitted_at":"2020-01-26T14:25:21Z","abstract_excerpt":"We propose a systematic theoretical framework for the topological amplitudes of the heavy meson decays and their $SU(N)$ decomposition. In the framework, the topological amplitudes are expressed in invariant tensors and classified into tree- and penguin-operator-induced diagrams according to which four-quark operators, tree or penguin, being inserted into their effective weak vertexes. By decomposing the four-quark operators into irreducible representations of $SU(N)$ group, one can derive the $SU(N)$ irreducible amplitudes from the tensor form of the topology. Taking the $D\\to PP$ decay ($P$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.09460","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/2001.09460/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2001.09460","created_at":"2026-07-05T03:16:59.931047+00:00"},{"alias_kind":"arxiv_version","alias_value":"2001.09460v2","created_at":"2026-07-05T03:16:59.931047+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.09460","created_at":"2026-07-05T03:16:59.931047+00:00"},{"alias_kind":"pith_short_12","alias_value":"HASTOVWGV2D5","created_at":"2026-07-05T03:16:59.931047+00:00"},{"alias_kind":"pith_short_16","alias_value":"HASTOVWGV2D5IQQV","created_at":"2026-07-05T03:16:59.931047+00:00"},{"alias_kind":"pith_short_8","alias_value":"HASTOVWG","created_at":"2026-07-05T03:16:59.931047+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.19612","citing_title":"QCD-factorization amplitudes from flavour symmetries: beyond the $SU(3)$ symmetric case","ref_index":27,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HASTOVWGV2D5IQQVDVUTYHGD7V","json":"https://pith.science/pith/HASTOVWGV2D5IQQVDVUTYHGD7V.json","graph_json":"https://pith.science/api/pith-number/HASTOVWGV2D5IQQVDVUTYHGD7V/graph.json","events_json":"https://pith.science/api/pith-number/HASTOVWGV2D5IQQVDVUTYHGD7V/events.json","paper":"https://pith.science/paper/HASTOVWG"},"agent_actions":{"view_html":"https://pith.science/pith/HASTOVWGV2D5IQQVDVUTYHGD7V","download_json":"https://pith.science/pith/HASTOVWGV2D5IQQVDVUTYHGD7V.json","view_paper":"https://pith.science/paper/HASTOVWG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2001.09460&json=true","fetch_graph":"https://pith.science/api/pith-number/HASTOVWGV2D5IQQVDVUTYHGD7V/graph.json","fetch_events":"https://pith.science/api/pith-number/HASTOVWGV2D5IQQVDVUTYHGD7V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HASTOVWGV2D5IQQVDVUTYHGD7V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HASTOVWGV2D5IQQVDVUTYHGD7V/action/storage_attestation","attest_author":"https://pith.science/pith/HASTOVWGV2D5IQQVDVUTYHGD7V/action/author_attestation","sign_citation":"https://pith.science/pith/HASTOVWGV2D5IQQVDVUTYHGD7V/action/citation_signature","submit_replication":"https://pith.science/pith/HASTOVWGV2D5IQQVDVUTYHGD7V/action/replication_record"}},"created_at":"2026-07-05T03:16:59.931047+00:00","updated_at":"2026-07-05T03:16:59.931047+00:00"}