{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WEGANRETTMBXADMLZ7T55JKRV7","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":"1cc57aaea296be53cb10c30faaaa4bd104c56a6484c868921140e1e049723508","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-09-29T01:52:41Z","title_canon_sha256":"be011e4328c098d3e040a32aad01e7c5f7a07460ed4912165c8fc77c699eaf49"},"schema_version":"1.0","source":{"id":"2309.16925","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.16925","created_at":"2026-07-05T06:55:29Z"},{"alias_kind":"arxiv_version","alias_value":"2309.16925v1","created_at":"2026-07-05T06:55:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.16925","created_at":"2026-07-05T06:55:29Z"},{"alias_kind":"pith_short_12","alias_value":"WEGANRETTMBX","created_at":"2026-07-05T06:55:29Z"},{"alias_kind":"pith_short_16","alias_value":"WEGANRETTMBXADML","created_at":"2026-07-05T06:55:29Z"},{"alias_kind":"pith_short_8","alias_value":"WEGANRET","created_at":"2026-07-05T06:55:29Z"}],"graph_snapshots":[{"event_id":"sha256:235dc6bb4e7a2ebd61a2f0fe4ff7ceb7fbc85d9e01210096d02514fc04f77662","target":"graph","created_at":"2026-07-05T06:55:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.16925/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The lexicographical ordering of hypergraphs via spectral moments is called the $S$-order of hypergraphs.In this paper, the $S$-order of hypergraphs is investigated.We characterize the first and last hypergraphs in an $S$-order of all uniform hypertrees and all linear unicyclic uniformhypergraphs with given girth, respectively. And we give the last hypergraph in an $S$-order of all linear unicyclic uniform hypergraphs.","authors_text":"Changjiang Bu, Hong Zhou","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-09-29T01:52:41Z","title":"Lexicographical ordering of hypergraphs via spectral moment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.16925","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":"sha256:1a3ac97698603e7ed68d9cc0acd12898d909cb811ebc9d4db5eb0cef6edadd90","target":"record","created_at":"2026-07-05T06:55:29Z","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":"1cc57aaea296be53cb10c30faaaa4bd104c56a6484c868921140e1e049723508","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-09-29T01:52:41Z","title_canon_sha256":"be011e4328c098d3e040a32aad01e7c5f7a07460ed4912165c8fc77c699eaf49"},"schema_version":"1.0","source":{"id":"2309.16925","kind":"arxiv","version":1}},"canonical_sha256":"b10c06c4939b03700d8bcfe7dea551afed4be68edcd6e4484df18277fa6d4b14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b10c06c4939b03700d8bcfe7dea551afed4be68edcd6e4484df18277fa6d4b14","first_computed_at":"2026-07-05T06:55:29.821152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:55:29.821152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2mI2+zfKyvj9v8RHAN+1adVffmyGlut7+6WM3ueS3CU8D0JpveJkpnrkNQ1lroD6wSi88FRokuvphDB9Zx9bCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:55:29.821581Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.16925","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a3ac97698603e7ed68d9cc0acd12898d909cb811ebc9d4db5eb0cef6edadd90","sha256:235dc6bb4e7a2ebd61a2f0fe4ff7ceb7fbc85d9e01210096d02514fc04f77662"],"state_sha256":"1e7eddfce4aeac9ba529bf2a0fbbb52e459f0e12970c4733c72749bbbd696ee6"}