{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:SBBD3KLHUH42VEORUONGDYVL5N","short_pith_number":"pith:SBBD3KLH","schema_version":"1.0","canonical_sha256":"90423da967a1f9aa91d1a39a61e2abeb6921f48bdd858517a0e20f18a847a14f","source":{"kind":"arxiv","id":"1901.09547","version":1},"attestation_state":"computed","paper":{"title":"Pairs of a tree and a nontree graph with the same status sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Pu Qiao, Xingzhi Zhan","submitted_at":"2019-01-28T08:29:24Z","abstract_excerpt":"The status of a vertex $x$ in a graph is the sum of the distances between $x$ and all other vertices. Let $G$ be a connected graph. The status sequence of $G$ is the list of the statuses of all vertices arranged in nondecreasing order. $G$ is called status injective if all the statuses of its vertices are distinct. Let $G$ be a member of a family of graphs $\\mathscr{F}$ and let the status sequence of $G$ be $s.$ $G$ is said to be status unique in $\\mathscr{F}$ if $G$ is the unique graph in $\\mathscr{F}$ whose status sequence is $s.$ In 2011, J.L. Shang and C. Lin posed the following two conjec"},"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":"1901.09547","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-28T08:29:24Z","cross_cats_sorted":[],"title_canon_sha256":"5a8957f4d79bb22b217394dd81ae228df6690a6d8ba9accb84232ba13f52b477","abstract_canon_sha256":"ae66400717bf23365bdb2a76f5786f51a8a280e2f5e8b548317c900fa3a0f2bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:24.535829Z","signature_b64":"9GIPSIm3SuTVHgMYfh2R0L2PmiOipg0J6s/3YcUIfdEAb6Fuuf7eZ702aAN600bXLnwsY3nC2HsoThAm1Z2bBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90423da967a1f9aa91d1a39a61e2abeb6921f48bdd858517a0e20f18a847a14f","last_reissued_at":"2026-05-17T23:55:24.535341Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:24.535341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pairs of a tree and a nontree graph with the same status sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Pu Qiao, Xingzhi Zhan","submitted_at":"2019-01-28T08:29:24Z","abstract_excerpt":"The status of a vertex $x$ in a graph is the sum of the distances between $x$ and all other vertices. Let $G$ be a connected graph. The status sequence of $G$ is the list of the statuses of all vertices arranged in nondecreasing order. $G$ is called status injective if all the statuses of its vertices are distinct. Let $G$ be a member of a family of graphs $\\mathscr{F}$ and let the status sequence of $G$ be $s.$ $G$ is said to be status unique in $\\mathscr{F}$ if $G$ is the unique graph in $\\mathscr{F}$ whose status sequence is $s.$ In 2011, J.L. Shang and C. Lin posed the following two conjec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09547","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":"1901.09547","created_at":"2026-05-17T23:55:24.535437+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.09547v1","created_at":"2026-05-17T23:55:24.535437+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09547","created_at":"2026-05-17T23:55:24.535437+00:00"},{"alias_kind":"pith_short_12","alias_value":"SBBD3KLHUH42","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"SBBD3KLHUH42VEOR","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"SBBD3KLH","created_at":"2026-05-18T12:33:27.125529+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/SBBD3KLHUH42VEORUONGDYVL5N","json":"https://pith.science/pith/SBBD3KLHUH42VEORUONGDYVL5N.json","graph_json":"https://pith.science/api/pith-number/SBBD3KLHUH42VEORUONGDYVL5N/graph.json","events_json":"https://pith.science/api/pith-number/SBBD3KLHUH42VEORUONGDYVL5N/events.json","paper":"https://pith.science/paper/SBBD3KLH"},"agent_actions":{"view_html":"https://pith.science/pith/SBBD3KLHUH42VEORUONGDYVL5N","download_json":"https://pith.science/pith/SBBD3KLHUH42VEORUONGDYVL5N.json","view_paper":"https://pith.science/paper/SBBD3KLH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.09547&json=true","fetch_graph":"https://pith.science/api/pith-number/SBBD3KLHUH42VEORUONGDYVL5N/graph.json","fetch_events":"https://pith.science/api/pith-number/SBBD3KLHUH42VEORUONGDYVL5N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SBBD3KLHUH42VEORUONGDYVL5N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SBBD3KLHUH42VEORUONGDYVL5N/action/storage_attestation","attest_author":"https://pith.science/pith/SBBD3KLHUH42VEORUONGDYVL5N/action/author_attestation","sign_citation":"https://pith.science/pith/SBBD3KLHUH42VEORUONGDYVL5N/action/citation_signature","submit_replication":"https://pith.science/pith/SBBD3KLHUH42VEORUONGDYVL5N/action/replication_record"}},"created_at":"2026-05-17T23:55:24.535437+00:00","updated_at":"2026-05-17T23:55:24.535437+00:00"}