{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:M2XVO56LAI7GNSPQXO7ZFLQAR3","short_pith_number":"pith:M2XVO56L","canonical_record":{"source":{"id":"1808.08337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-25T01:04:32Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"2c03df4add348fa2c1797299b8f014b9e4748c5c8bdf9a9aa3aa135ca74e9aa8","abstract_canon_sha256":"267bdd8e563152664738e6e86141ce8626284465324175ada51c985dd19ff520"},"schema_version":"1.0"},"canonical_sha256":"66af5777cb023e66c9f0bbbf92ae008efc06c89ad98c44bdf7636ef41c8676ad","source":{"kind":"arxiv","id":"1808.08337","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08337","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08337v1","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08337","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"M2XVO56LAI7G","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"M2XVO56LAI7GNSPQ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"M2XVO56L","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:M2XVO56LAI7GNSPQXO7ZFLQAR3","target":"record","payload":{"canonical_record":{"source":{"id":"1808.08337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-25T01:04:32Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"2c03df4add348fa2c1797299b8f014b9e4748c5c8bdf9a9aa3aa135ca74e9aa8","abstract_canon_sha256":"267bdd8e563152664738e6e86141ce8626284465324175ada51c985dd19ff520"},"schema_version":"1.0"},"canonical_sha256":"66af5777cb023e66c9f0bbbf92ae008efc06c89ad98c44bdf7636ef41c8676ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:44.398019Z","signature_b64":"rtziXA0QB5bLZ4MlFHiada2UlRfs8V+qLmJNbScTc/Gqwqzca/MeuB8HoEn4msfXl5KgBGlqupaSPYfde7IzAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66af5777cb023e66c9f0bbbf92ae008efc06c89ad98c44bdf7636ef41c8676ad","last_reissued_at":"2026-05-18T00:02:44.397333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:44.397333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.08337","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":"2026-05-18T00:02:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fw1o6xIhE7oA4GOvDplzHoS3fLLkNnOlIrbiOV1baRuL/R1NomeZ6QhM5Kwz7m9/7A57rqzNzCfFs1u993d1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T13:20:18.301068Z"},"content_sha256":"bc04eb694fffb600863ad1f8985001d8f5dcdbf028603c84c8725e9b0a9cc8b4","schema_version":"1.0","event_id":"sha256:bc04eb694fffb600863ad1f8985001d8f5dcdbf028603c84c8725e9b0a9cc8b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:M2XVO56LAI7GNSPQXO7ZFLQAR3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-fold contour integrals of certain ratios of Euler gamma functions from Feynman diagrams: orthogonality of triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Eduardo A. Notte-Cuello, Igor Kondrashuk, Ivan Gonzalez, Ivan Parra-Ferrada","submitted_at":"2018-08-25T01:04:32Z","abstract_excerpt":"We observe a property of orthogonality of the Mellin-Barnes transformation of the triangle one-loop diagrams, which follows from our previous papers [JHEP {\\bf 0808} (2008) 106, JHEP {\\bf 1003} (2010) 051, JMP {\\bf 51} (2010) 052304]. In those papers it has been established that Usyukina-Davydychev functions are invariant with respect to Fourier transformation. This has been proved at the level of graphs and also via the Mellin-Barnes transformation. We partially apply to one-loop massless scalar diagram the same trick in which the Mellin-Barnes transformation was involved and obtain the prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08337","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nU84+RVqS6QYynyn4bAmiOuBT1VBZ+lt4PSOQOTL86PCSl00AvrheTcbInUYNFEG2j2dNmsW0pyhjQa03QYVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T13:20:18.301433Z"},"content_sha256":"4919eb5f478696ef6f7c76f0f86c4ef8b9f09b734350838c6e63a65e138f5859","schema_version":"1.0","event_id":"sha256:4919eb5f478696ef6f7c76f0f86c4ef8b9f09b734350838c6e63a65e138f5859"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M2XVO56LAI7GNSPQXO7ZFLQAR3/bundle.json","state_url":"https://pith.science/pith/M2XVO56LAI7GNSPQXO7ZFLQAR3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M2XVO56LAI7GNSPQXO7ZFLQAR3/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":"2026-06-20T13:20:18Z","links":{"resolver":"https://pith.science/pith/M2XVO56LAI7GNSPQXO7ZFLQAR3","bundle":"https://pith.science/pith/M2XVO56LAI7GNSPQXO7ZFLQAR3/bundle.json","state":"https://pith.science/pith/M2XVO56LAI7GNSPQXO7ZFLQAR3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M2XVO56LAI7GNSPQXO7ZFLQAR3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:M2XVO56LAI7GNSPQXO7ZFLQAR3","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":"267bdd8e563152664738e6e86141ce8626284465324175ada51c985dd19ff520","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-25T01:04:32Z","title_canon_sha256":"2c03df4add348fa2c1797299b8f014b9e4748c5c8bdf9a9aa3aa135ca74e9aa8"},"schema_version":"1.0","source":{"id":"1808.08337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08337","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08337v1","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08337","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"M2XVO56LAI7G","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"M2XVO56LAI7GNSPQ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"M2XVO56L","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:4919eb5f478696ef6f7c76f0f86c4ef8b9f09b734350838c6e63a65e138f5859","target":"graph","created_at":"2026-05-18T00:02:44Z","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"},"paper":{"abstract_excerpt":"We observe a property of orthogonality of the Mellin-Barnes transformation of the triangle one-loop diagrams, which follows from our previous papers [JHEP {\\bf 0808} (2008) 106, JHEP {\\bf 1003} (2010) 051, JMP {\\bf 51} (2010) 052304]. In those papers it has been established that Usyukina-Davydychev functions are invariant with respect to Fourier transformation. This has been proved at the level of graphs and also via the Mellin-Barnes transformation. We partially apply to one-loop massless scalar diagram the same trick in which the Mellin-Barnes transformation was involved and obtain the prope","authors_text":"Eduardo A. Notte-Cuello, Igor Kondrashuk, Ivan Gonzalez, Ivan Parra-Ferrada","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-25T01:04:32Z","title":"Multi-fold contour integrals of certain ratios of Euler gamma functions from Feynman diagrams: orthogonality of triangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08337","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:bc04eb694fffb600863ad1f8985001d8f5dcdbf028603c84c8725e9b0a9cc8b4","target":"record","created_at":"2026-05-18T00:02:44Z","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":"267bdd8e563152664738e6e86141ce8626284465324175ada51c985dd19ff520","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-25T01:04:32Z","title_canon_sha256":"2c03df4add348fa2c1797299b8f014b9e4748c5c8bdf9a9aa3aa135ca74e9aa8"},"schema_version":"1.0","source":{"id":"1808.08337","kind":"arxiv","version":1}},"canonical_sha256":"66af5777cb023e66c9f0bbbf92ae008efc06c89ad98c44bdf7636ef41c8676ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66af5777cb023e66c9f0bbbf92ae008efc06c89ad98c44bdf7636ef41c8676ad","first_computed_at":"2026-05-18T00:02:44.397333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:44.397333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rtziXA0QB5bLZ4MlFHiada2UlRfs8V+qLmJNbScTc/Gqwqzca/MeuB8HoEn4msfXl5KgBGlqupaSPYfde7IzAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:44.398019Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.08337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc04eb694fffb600863ad1f8985001d8f5dcdbf028603c84c8725e9b0a9cc8b4","sha256:4919eb5f478696ef6f7c76f0f86c4ef8b9f09b734350838c6e63a65e138f5859"],"state_sha256":"28963e2e8898f5366053780aaf2c4bce0c7523f7b3cc83745ec8633b88b23f83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bvwHtKjql47s3jUN7LLq5nLkzFi81MjbSAplmJ+nA/aHzeforEhS1CLVfEeWX87Vc9EAPLkfu5d4pFOWsAjXDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T13:20:18.303370Z","bundle_sha256":"743c456537e9f3a7c736fed02237354f63da96c942488a98618729ea685940d6"}}