{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:H3US5DGHHPLUAKNBFOUUSEIEWB","short_pith_number":"pith:H3US5DGH","schema_version":"1.0","canonical_sha256":"3ee92e8cc73bd74029a12ba9491104b04ff05e68e378f9b54f092bc83267703e","source":{"kind":"arxiv","id":"1809.00889","version":3},"attestation_state":"computed","paper":{"title":"The spectrum and automorphism group of the set-inclusion graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jianfeng Wang, Qiongxiang Huang, Xueyi Huang","submitted_at":"2018-09-04T11:02:39Z","abstract_excerpt":"Let $n$, $k$ and $l$ be integers with $1\\leq k<l\\leq n-1$. The set-inclusion graph $G(n,k,l)$ is the graph whose vertex set consists of all $k$- and $l$-subsets of $[n]=\\{1,2,\\ldots,n\\}$, where two distinct vertices are adjacent if one of them is contained in another. In this paper, we determine the spectrum and automorphism group of $G(n,k,l)$, respectively."},"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":"1809.00889","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-04T11:02:39Z","cross_cats_sorted":[],"title_canon_sha256":"4c445516ad6be07f78ca189c55ef10b8d8c72aca79d137d198894abc9256548d","abstract_canon_sha256":"ebc824826bcafca337fba9a7ddbd6e852bc5fc0e923511f5773fd188e10b91dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:55.178289Z","signature_b64":"+qJgIR0rkiZP/EeVi7CQKcOjKy8XxNk+3V1H2XTt0GX/aEMfcVDqEVet7aggj/EIHDmcShp1N6NbVKQGSFbHAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ee92e8cc73bd74029a12ba9491104b04ff05e68e378f9b54f092bc83267703e","last_reissued_at":"2026-05-17T23:46:55.177746Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:55.177746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The spectrum and automorphism group of the set-inclusion graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jianfeng Wang, Qiongxiang Huang, Xueyi Huang","submitted_at":"2018-09-04T11:02:39Z","abstract_excerpt":"Let $n$, $k$ and $l$ be integers with $1\\leq k<l\\leq n-1$. The set-inclusion graph $G(n,k,l)$ is the graph whose vertex set consists of all $k$- and $l$-subsets of $[n]=\\{1,2,\\ldots,n\\}$, where two distinct vertices are adjacent if one of them is contained in another. In this paper, we determine the spectrum and automorphism group of $G(n,k,l)$, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00889","kind":"arxiv","version":3},"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":"1809.00889","created_at":"2026-05-17T23:46:55.177831+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.00889v3","created_at":"2026-05-17T23:46:55.177831+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00889","created_at":"2026-05-17T23:46:55.177831+00:00"},{"alias_kind":"pith_short_12","alias_value":"H3US5DGHHPLU","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"H3US5DGHHPLUAKNB","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"H3US5DGH","created_at":"2026-05-18T12:32:28.185984+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/H3US5DGHHPLUAKNBFOUUSEIEWB","json":"https://pith.science/pith/H3US5DGHHPLUAKNBFOUUSEIEWB.json","graph_json":"https://pith.science/api/pith-number/H3US5DGHHPLUAKNBFOUUSEIEWB/graph.json","events_json":"https://pith.science/api/pith-number/H3US5DGHHPLUAKNBFOUUSEIEWB/events.json","paper":"https://pith.science/paper/H3US5DGH"},"agent_actions":{"view_html":"https://pith.science/pith/H3US5DGHHPLUAKNBFOUUSEIEWB","download_json":"https://pith.science/pith/H3US5DGHHPLUAKNBFOUUSEIEWB.json","view_paper":"https://pith.science/paper/H3US5DGH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.00889&json=true","fetch_graph":"https://pith.science/api/pith-number/H3US5DGHHPLUAKNBFOUUSEIEWB/graph.json","fetch_events":"https://pith.science/api/pith-number/H3US5DGHHPLUAKNBFOUUSEIEWB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H3US5DGHHPLUAKNBFOUUSEIEWB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H3US5DGHHPLUAKNBFOUUSEIEWB/action/storage_attestation","attest_author":"https://pith.science/pith/H3US5DGHHPLUAKNBFOUUSEIEWB/action/author_attestation","sign_citation":"https://pith.science/pith/H3US5DGHHPLUAKNBFOUUSEIEWB/action/citation_signature","submit_replication":"https://pith.science/pith/H3US5DGHHPLUAKNBFOUUSEIEWB/action/replication_record"}},"created_at":"2026-05-17T23:46:55.177831+00:00","updated_at":"2026-05-17T23:46:55.177831+00:00"}