{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:CLKRVWHUWW2IBVFGCFIDRKJZY2","short_pith_number":"pith:CLKRVWHU","schema_version":"1.0","canonical_sha256":"12d51ad8f4b5b480d4a6115038a939c680347bec58003d763cc01e3d437951d4","source":{"kind":"arxiv","id":"1611.10259","version":7},"attestation_state":"computed","paper":{"title":"Oriented Bipartite Graphs and the Goldbach Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.NT"],"primary_cat":"math.CO","authors_text":"Prantar Ghosh, Sagnik Sen, Sandip Das, Shamik Ghosh","submitted_at":"2016-11-30T16:44:03Z","abstract_excerpt":"In this paper, we study oriented bipartite graphs. In particular, we introduce \"bitransitive\" graphs. Several characterizations of bitransitive bitournaments are obtained. We show that bitransitive bitounaments are equivalent to acyclic bitournaments. As applications, we characterize acyclic bitournaments with Hamiltonian paths, determine number of non-isomorphic acyclic bitournaments of a given order, and solve the graph-isomorphism problem in linear time for acyclic bitournaments. Next, we prove the well-known Caccetta-H$\\ddot{\\textrm{a}}$ggkvist Conjecture for oriented bipartite graphs for "},"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":"1611.10259","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-30T16:44:03Z","cross_cats_sorted":["cs.DM","math.NT"],"title_canon_sha256":"917b62946947066c2c4ed07cdf99da04bf90f720720052102eac019ff6353967","abstract_canon_sha256":"3849e0d2e5e8f96caf5a94f2634b9547789c13d5dfbf4387c44a2cb7aa0f1289"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:22:32.519004Z","signature_b64":"3SVWziXxiXjzhwBuoPq8K3c9jY6fzq+EQcE590K0/Yw7S7ipWu68e99ovHpVe4ylO6TH12KtZtqbJwDkHB6RCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12d51ad8f4b5b480d4a6115038a939c680347bec58003d763cc01e3d437951d4","last_reissued_at":"2026-07-05T02:22:32.518508Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:22:32.518508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Oriented Bipartite Graphs and the Goldbach Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.NT"],"primary_cat":"math.CO","authors_text":"Prantar Ghosh, Sagnik Sen, Sandip Das, Shamik Ghosh","submitted_at":"2016-11-30T16:44:03Z","abstract_excerpt":"In this paper, we study oriented bipartite graphs. In particular, we introduce \"bitransitive\" graphs. Several characterizations of bitransitive bitournaments are obtained. We show that bitransitive bitounaments are equivalent to acyclic bitournaments. As applications, we characterize acyclic bitournaments with Hamiltonian paths, determine number of non-isomorphic acyclic bitournaments of a given order, and solve the graph-isomorphism problem in linear time for acyclic bitournaments. Next, we prove the well-known Caccetta-H$\\ddot{\\textrm{a}}$ggkvist Conjecture for oriented bipartite graphs for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10259","kind":"arxiv","version":7},"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/1611.10259/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":"1611.10259","created_at":"2026-07-05T02:22:32.518578+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.10259v7","created_at":"2026-07-05T02:22:32.518578+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.10259","created_at":"2026-07-05T02:22:32.518578+00:00"},{"alias_kind":"pith_short_12","alias_value":"CLKRVWHUWW2I","created_at":"2026-07-05T02:22:32.518578+00:00"},{"alias_kind":"pith_short_16","alias_value":"CLKRVWHUWW2IBVFG","created_at":"2026-07-05T02:22:32.518578+00:00"},{"alias_kind":"pith_short_8","alias_value":"CLKRVWHU","created_at":"2026-07-05T02:22:32.518578+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/CLKRVWHUWW2IBVFGCFIDRKJZY2","json":"https://pith.science/pith/CLKRVWHUWW2IBVFGCFIDRKJZY2.json","graph_json":"https://pith.science/api/pith-number/CLKRVWHUWW2IBVFGCFIDRKJZY2/graph.json","events_json":"https://pith.science/api/pith-number/CLKRVWHUWW2IBVFGCFIDRKJZY2/events.json","paper":"https://pith.science/paper/CLKRVWHU"},"agent_actions":{"view_html":"https://pith.science/pith/CLKRVWHUWW2IBVFGCFIDRKJZY2","download_json":"https://pith.science/pith/CLKRVWHUWW2IBVFGCFIDRKJZY2.json","view_paper":"https://pith.science/paper/CLKRVWHU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.10259&json=true","fetch_graph":"https://pith.science/api/pith-number/CLKRVWHUWW2IBVFGCFIDRKJZY2/graph.json","fetch_events":"https://pith.science/api/pith-number/CLKRVWHUWW2IBVFGCFIDRKJZY2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CLKRVWHUWW2IBVFGCFIDRKJZY2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CLKRVWHUWW2IBVFGCFIDRKJZY2/action/storage_attestation","attest_author":"https://pith.science/pith/CLKRVWHUWW2IBVFGCFIDRKJZY2/action/author_attestation","sign_citation":"https://pith.science/pith/CLKRVWHUWW2IBVFGCFIDRKJZY2/action/citation_signature","submit_replication":"https://pith.science/pith/CLKRVWHUWW2IBVFGCFIDRKJZY2/action/replication_record"}},"created_at":"2026-07-05T02:22:32.518578+00:00","updated_at":"2026-07-05T02:22:32.518578+00:00"}