{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:7LHVEQUR3S2E55DDMM36UHAFDX","short_pith_number":"pith:7LHVEQUR","schema_version":"1.0","canonical_sha256":"facf524291dcb44ef4636337ea1c051dcbf60b0892b282a85f6443b80d5ea508","source":{"kind":"arxiv","id":"2506.05803","version":2},"attestation_state":"computed","paper":{"title":"Finite $s$-geodesic transitive graphs under certain girths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jun-Jie Huang","submitted_at":"2025-06-06T07:00:34Z","abstract_excerpt":"For an integer $s\\geq1$ and a graph $\\Gamma$, a path $(u_0, u_1, \\ldots, u_{s})$ of vertices of $\\Gamma$ is called an {\\em $s$-geodesic} if it is a shortest path from $u_0$ to $u_{s}$. We say that $\\Gamma$ is {\\em $s$-geodesic transitive} if, for each $i\\leq s$, $\\Gamma$ has at least one $i$-geodesic, and its automorphism group is transitive on the set of $i$-geodesics. In 2021, Jin and Praeger [J. Combin. Theory Ser. A 178 (2021) 105349] have studied $3$-geodesic transitive graphs of girth $5$ or $6$, and they also proposed to the problem that to classify $s$-geodesic transitive graphs of gir"},"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":"2506.05803","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-06T07:00:34Z","cross_cats_sorted":[],"title_canon_sha256":"86be00ed4bbd66c5fa7663bd6076c8e61b45f5eb7148714d57f6ce731b79bc7d","abstract_canon_sha256":"28d6a09077dc3c5c5e0c6409a7b06492d0d3f13d47ac1c7d7d301ff32fbf0beb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:55:40.617357Z","signature_b64":"9uXJQgVbZGD36fzy9HSIMhFPD0/wi949w+p5RD95Lax14wfbIXuofpbg5vg/43I2mdPHJLEU2+Pol1r/8t3nDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"facf524291dcb44ef4636337ea1c051dcbf60b0892b282a85f6443b80d5ea508","last_reissued_at":"2026-07-05T11:55:40.616918Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:55:40.616918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite $s$-geodesic transitive graphs under certain girths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jun-Jie Huang","submitted_at":"2025-06-06T07:00:34Z","abstract_excerpt":"For an integer $s\\geq1$ and a graph $\\Gamma$, a path $(u_0, u_1, \\ldots, u_{s})$ of vertices of $\\Gamma$ is called an {\\em $s$-geodesic} if it is a shortest path from $u_0$ to $u_{s}$. We say that $\\Gamma$ is {\\em $s$-geodesic transitive} if, for each $i\\leq s$, $\\Gamma$ has at least one $i$-geodesic, and its automorphism group is transitive on the set of $i$-geodesics. In 2021, Jin and Praeger [J. Combin. Theory Ser. A 178 (2021) 105349] have studied $3$-geodesic transitive graphs of girth $5$ or $6$, and they also proposed to the problem that to classify $s$-geodesic transitive graphs of gir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05803","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/2506.05803/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":"2506.05803","created_at":"2026-07-05T11:55:40.616976+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.05803v2","created_at":"2026-07-05T11:55:40.616976+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05803","created_at":"2026-07-05T11:55:40.616976+00:00"},{"alias_kind":"pith_short_12","alias_value":"7LHVEQUR3S2E","created_at":"2026-07-05T11:55:40.616976+00:00"},{"alias_kind":"pith_short_16","alias_value":"7LHVEQUR3S2E55DD","created_at":"2026-07-05T11:55:40.616976+00:00"},{"alias_kind":"pith_short_8","alias_value":"7LHVEQUR","created_at":"2026-07-05T11:55:40.616976+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/7LHVEQUR3S2E55DDMM36UHAFDX","json":"https://pith.science/pith/7LHVEQUR3S2E55DDMM36UHAFDX.json","graph_json":"https://pith.science/api/pith-number/7LHVEQUR3S2E55DDMM36UHAFDX/graph.json","events_json":"https://pith.science/api/pith-number/7LHVEQUR3S2E55DDMM36UHAFDX/events.json","paper":"https://pith.science/paper/7LHVEQUR"},"agent_actions":{"view_html":"https://pith.science/pith/7LHVEQUR3S2E55DDMM36UHAFDX","download_json":"https://pith.science/pith/7LHVEQUR3S2E55DDMM36UHAFDX.json","view_paper":"https://pith.science/paper/7LHVEQUR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.05803&json=true","fetch_graph":"https://pith.science/api/pith-number/7LHVEQUR3S2E55DDMM36UHAFDX/graph.json","fetch_events":"https://pith.science/api/pith-number/7LHVEQUR3S2E55DDMM36UHAFDX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7LHVEQUR3S2E55DDMM36UHAFDX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7LHVEQUR3S2E55DDMM36UHAFDX/action/storage_attestation","attest_author":"https://pith.science/pith/7LHVEQUR3S2E55DDMM36UHAFDX/action/author_attestation","sign_citation":"https://pith.science/pith/7LHVEQUR3S2E55DDMM36UHAFDX/action/citation_signature","submit_replication":"https://pith.science/pith/7LHVEQUR3S2E55DDMM36UHAFDX/action/replication_record"}},"created_at":"2026-07-05T11:55:40.616976+00:00","updated_at":"2026-07-05T11:55:40.616976+00:00"}