{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:BVDA23Q6W7KWXF6HAC53NBH46M","short_pith_number":"pith:BVDA23Q6","schema_version":"1.0","canonical_sha256":"0d460d6e1eb7d56b97c700bbb684fcf32be6eb6326e654221cfefd7f08c9170c","source":{"kind":"arxiv","id":"1011.0585","version":1},"attestation_state":"computed","paper":{"title":"Feynman's Tree Theorem and Loop-Tree Dualities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"German Rodrigo, Isabella Bierenbaum, Petros Draggiotis, Stefano Catani","submitted_at":"2010-11-02T11:50:25Z","abstract_excerpt":"We discuss the duality theorem, which provides a relation between loop integrals and phase space integrals. We rederive the duality relation for the one-loop case and extend it to two and higher-order loops. We explicitly show its application to two- and three-loop scalar master integrals and discuss the structure of the occurring cuts."},"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":"1011.0585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-11-02T11:50:25Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"aa73655104144e2930e4c2d3cc9321d735268d5b45cb706c25134a9d2ae8ea45","abstract_canon_sha256":"952d83fb0a752cf0e6eeaafecf1633f7bdf72ef237185984d0b2088d59abdd6b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:21.303678Z","signature_b64":"ztRnZq40nluvovayjg3iphMJsnNI5KMQi5UwHCs+zI/CGEw6tpqi+IkNyrnuY2LBvNewgFYwoup7coL8aOTRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d460d6e1eb7d56b97c700bbb684fcf32be6eb6326e654221cfefd7f08c9170c","last_reissued_at":"2026-05-18T04:37:21.303302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:21.303302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Feynman's Tree Theorem and Loop-Tree Dualities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"German Rodrigo, Isabella Bierenbaum, Petros Draggiotis, Stefano Catani","submitted_at":"2010-11-02T11:50:25Z","abstract_excerpt":"We discuss the duality theorem, which provides a relation between loop integrals and phase space integrals. We rederive the duality relation for the one-loop case and extend it to two and higher-order loops. We explicitly show its application to two- and three-loop scalar master integrals and discuss the structure of the occurring cuts."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0585","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1011.0585","created_at":"2026-05-18T04:37:21.303361+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.0585v1","created_at":"2026-05-18T04:37:21.303361+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0585","created_at":"2026-05-18T04:37:21.303361+00:00"},{"alias_kind":"pith_short_12","alias_value":"BVDA23Q6W7KW","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BVDA23Q6W7KWXF6H","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BVDA23Q6","created_at":"2026-05-18T12:26:05.355336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BVDA23Q6W7KWXF6HAC53NBH46M","json":"https://pith.science/pith/BVDA23Q6W7KWXF6HAC53NBH46M.json","graph_json":"https://pith.science/api/pith-number/BVDA23Q6W7KWXF6HAC53NBH46M/graph.json","events_json":"https://pith.science/api/pith-number/BVDA23Q6W7KWXF6HAC53NBH46M/events.json","paper":"https://pith.science/paper/BVDA23Q6"},"agent_actions":{"view_html":"https://pith.science/pith/BVDA23Q6W7KWXF6HAC53NBH46M","download_json":"https://pith.science/pith/BVDA23Q6W7KWXF6HAC53NBH46M.json","view_paper":"https://pith.science/paper/BVDA23Q6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.0585&json=true","fetch_graph":"https://pith.science/api/pith-number/BVDA23Q6W7KWXF6HAC53NBH46M/graph.json","fetch_events":"https://pith.science/api/pith-number/BVDA23Q6W7KWXF6HAC53NBH46M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BVDA23Q6W7KWXF6HAC53NBH46M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BVDA23Q6W7KWXF6HAC53NBH46M/action/storage_attestation","attest_author":"https://pith.science/pith/BVDA23Q6W7KWXF6HAC53NBH46M/action/author_attestation","sign_citation":"https://pith.science/pith/BVDA23Q6W7KWXF6HAC53NBH46M/action/citation_signature","submit_replication":"https://pith.science/pith/BVDA23Q6W7KWXF6HAC53NBH46M/action/replication_record"}},"created_at":"2026-05-18T04:37:21.303361+00:00","updated_at":"2026-05-18T04:37:21.303361+00:00"}