{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:4S5GLFZPVYDLGUKHTPPLAY22BD","short_pith_number":"pith:4S5GLFZP","schema_version":"1.0","canonical_sha256":"e4ba65972fae06b351479bdeb0635a08ec2e5fad97813be50809ca104b3c93b4","source":{"kind":"arxiv","id":"0911.1979","version":2},"attestation_state":"computed","paper":{"title":"Transformations of triangle ladder diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alvaro Vergara, Igor Kondrashuk","submitted_at":"2009-11-10T19:46:09Z","abstract_excerpt":"It is shown how dual space diagrammatic representation of momentum integrals corresponding to triangle ladder diagrams with an arbitrary number of rungs can be transformed to half-diamonds. In paper arXiv:0803.3420 [hep-th] the half-diamonds were related by conformal integral substitution to the diamonds which represent the dual space image of four-point ladder integrals in the four-dimensional momentum space. Acting in the way described in the present paper we do not need to use the known result for diamond (four-point) diagrams as an external input in deriving relations of arXiv:0803.3420 [h"},"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":"0911.1979","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-11-10T19:46:09Z","cross_cats_sorted":[],"title_canon_sha256":"a723ee2e23220174312f6e63cbf28eefd1e5171917e75dff68d42c56a7b39d29","abstract_canon_sha256":"dc13a6bb3987b318021fe23d562a9321fd29bd713cba031bfdf0d7f374cb9684"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:24:09.447826Z","signature_b64":"hXHAl8kB44bmBopjaV7f+AWKK2HEDQgMDlguj8Acavcvn0uFxr9ae9SRaB6WyMnqJWxOzFCtEiHFHEZ4Iwi3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4ba65972fae06b351479bdeb0635a08ec2e5fad97813be50809ca104b3c93b4","last_reissued_at":"2026-07-04T17:24:09.447410Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:24:09.447410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transformations of triangle ladder diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alvaro Vergara, Igor Kondrashuk","submitted_at":"2009-11-10T19:46:09Z","abstract_excerpt":"It is shown how dual space diagrammatic representation of momentum integrals corresponding to triangle ladder diagrams with an arbitrary number of rungs can be transformed to half-diamonds. In paper arXiv:0803.3420 [hep-th] the half-diamonds were related by conformal integral substitution to the diamonds which represent the dual space image of four-point ladder integrals in the four-dimensional momentum space. Acting in the way described in the present paper we do not need to use the known result for diamond (four-point) diagrams as an external input in deriving relations of arXiv:0803.3420 [h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1979","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/0911.1979/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":"0911.1979","created_at":"2026-07-04T17:24:09.447477+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.1979v2","created_at":"2026-07-04T17:24:09.447477+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1979","created_at":"2026-07-04T17:24:09.447477+00:00"},{"alias_kind":"pith_short_12","alias_value":"4S5GLFZPVYDL","created_at":"2026-07-04T17:24:09.447477+00:00"},{"alias_kind":"pith_short_16","alias_value":"4S5GLFZPVYDLGUKH","created_at":"2026-07-04T17:24:09.447477+00:00"},{"alias_kind":"pith_short_8","alias_value":"4S5GLFZP","created_at":"2026-07-04T17:24:09.447477+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.07787","citing_title":"Inverse Laplace and Mellin integral transforms modified for use in quantum communications","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4S5GLFZPVYDLGUKHTPPLAY22BD","json":"https://pith.science/pith/4S5GLFZPVYDLGUKHTPPLAY22BD.json","graph_json":"https://pith.science/api/pith-number/4S5GLFZPVYDLGUKHTPPLAY22BD/graph.json","events_json":"https://pith.science/api/pith-number/4S5GLFZPVYDLGUKHTPPLAY22BD/events.json","paper":"https://pith.science/paper/4S5GLFZP"},"agent_actions":{"view_html":"https://pith.science/pith/4S5GLFZPVYDLGUKHTPPLAY22BD","download_json":"https://pith.science/pith/4S5GLFZPVYDLGUKHTPPLAY22BD.json","view_paper":"https://pith.science/paper/4S5GLFZP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.1979&json=true","fetch_graph":"https://pith.science/api/pith-number/4S5GLFZPVYDLGUKHTPPLAY22BD/graph.json","fetch_events":"https://pith.science/api/pith-number/4S5GLFZPVYDLGUKHTPPLAY22BD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4S5GLFZPVYDLGUKHTPPLAY22BD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4S5GLFZPVYDLGUKHTPPLAY22BD/action/storage_attestation","attest_author":"https://pith.science/pith/4S5GLFZPVYDLGUKHTPPLAY22BD/action/author_attestation","sign_citation":"https://pith.science/pith/4S5GLFZPVYDLGUKHTPPLAY22BD/action/citation_signature","submit_replication":"https://pith.science/pith/4S5GLFZPVYDLGUKHTPPLAY22BD/action/replication_record"}},"created_at":"2026-07-04T17:24:09.447477+00:00","updated_at":"2026-07-04T17:24:09.447477+00:00"}