{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:7YKPARCJKWFIAKG2DUAIDC7IXF","short_pith_number":"pith:7YKPARCJ","schema_version":"1.0","canonical_sha256":"fe14f04449558a8028da1d00818be8b9671607cf38de6b19f37b033156ccec4e","source":{"kind":"arxiv","id":"2507.02650","version":1},"attestation_state":"computed","paper":{"title":"The ordering of hypertrees and unicyclic hypergraphs by the traces of $\\mathcal{A}_{\\alpha}$-tensor","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Changjiang Bu, Jueru Liu, Lizhu Sun","submitted_at":"2025-07-03T14:16:57Z","abstract_excerpt":"For a real number $\\alpha\\in[0,1]$ and a $k$-uniform hypergraph $\\mathcal{H}$, $\\mathcal{A}_{\\alpha}(\\mathcal{H})=\\alpha\\mathcal{D}(\\mathcal{H})+(1-\\alpha)\\mathcal{A}(\\mathcal{H})$ is called the $\\mathcal{A}_{\\alpha}$-tensor of $\\mathcal{H}$, where $\\mathcal{D}(\\mathcal{H})$ and $\\mathcal{A}(\\mathcal{H})$ are the degree tensor and adjacency tensor of $\\mathcal{H}$, respectively. The sum of the $d$-th powers of all eigenvalues of $\\mathcal{A}_{\\alpha}(\\mathcal{H})$ is called the $d$-th order $\\mathcal{A}_{\\alpha}$-spectral moment of $\\mathcal{H}$, which is equal to the $d$-th order trace of $\\m"},"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":"2507.02650","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-03T14:16:57Z","cross_cats_sorted":[],"title_canon_sha256":"8656d532f812d38f59a383784f656aa798e625abd8f9f5efb91715ca7069d120","abstract_canon_sha256":"b88397ff5adcf9eb8c0fccc92c856963fec286f119b6a67423371ff4a01d5a1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:31:32.371868Z","signature_b64":"i5bOVLVFCSyuT2j2Gx8T5OEQ8QOKr/feOhCBaZkAN+g5Flrdbf1PuFe9eOfW/A/cXiT9OR/Y3dVT/R3O77gUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe14f04449558a8028da1d00818be8b9671607cf38de6b19f37b033156ccec4e","last_reissued_at":"2026-07-05T11:31:32.371472Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:31:32.371472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The ordering of hypertrees and unicyclic hypergraphs by the traces of $\\mathcal{A}_{\\alpha}$-tensor","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Changjiang Bu, Jueru Liu, Lizhu Sun","submitted_at":"2025-07-03T14:16:57Z","abstract_excerpt":"For a real number $\\alpha\\in[0,1]$ and a $k$-uniform hypergraph $\\mathcal{H}$, $\\mathcal{A}_{\\alpha}(\\mathcal{H})=\\alpha\\mathcal{D}(\\mathcal{H})+(1-\\alpha)\\mathcal{A}(\\mathcal{H})$ is called the $\\mathcal{A}_{\\alpha}$-tensor of $\\mathcal{H}$, where $\\mathcal{D}(\\mathcal{H})$ and $\\mathcal{A}(\\mathcal{H})$ are the degree tensor and adjacency tensor of $\\mathcal{H}$, respectively. The sum of the $d$-th powers of all eigenvalues of $\\mathcal{A}_{\\alpha}(\\mathcal{H})$ is called the $d$-th order $\\mathcal{A}_{\\alpha}$-spectral moment of $\\mathcal{H}$, which is equal to the $d$-th order trace of $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.02650","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.02650/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":"2507.02650","created_at":"2026-07-05T11:31:32.371528+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.02650v1","created_at":"2026-07-05T11:31:32.371528+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.02650","created_at":"2026-07-05T11:31:32.371528+00:00"},{"alias_kind":"pith_short_12","alias_value":"7YKPARCJKWFI","created_at":"2026-07-05T11:31:32.371528+00:00"},{"alias_kind":"pith_short_16","alias_value":"7YKPARCJKWFIAKG2","created_at":"2026-07-05T11:31:32.371528+00:00"},{"alias_kind":"pith_short_8","alias_value":"7YKPARCJ","created_at":"2026-07-05T11:31:32.371528+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/7YKPARCJKWFIAKG2DUAIDC7IXF","json":"https://pith.science/pith/7YKPARCJKWFIAKG2DUAIDC7IXF.json","graph_json":"https://pith.science/api/pith-number/7YKPARCJKWFIAKG2DUAIDC7IXF/graph.json","events_json":"https://pith.science/api/pith-number/7YKPARCJKWFIAKG2DUAIDC7IXF/events.json","paper":"https://pith.science/paper/7YKPARCJ"},"agent_actions":{"view_html":"https://pith.science/pith/7YKPARCJKWFIAKG2DUAIDC7IXF","download_json":"https://pith.science/pith/7YKPARCJKWFIAKG2DUAIDC7IXF.json","view_paper":"https://pith.science/paper/7YKPARCJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.02650&json=true","fetch_graph":"https://pith.science/api/pith-number/7YKPARCJKWFIAKG2DUAIDC7IXF/graph.json","fetch_events":"https://pith.science/api/pith-number/7YKPARCJKWFIAKG2DUAIDC7IXF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7YKPARCJKWFIAKG2DUAIDC7IXF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7YKPARCJKWFIAKG2DUAIDC7IXF/action/storage_attestation","attest_author":"https://pith.science/pith/7YKPARCJKWFIAKG2DUAIDC7IXF/action/author_attestation","sign_citation":"https://pith.science/pith/7YKPARCJKWFIAKG2DUAIDC7IXF/action/citation_signature","submit_replication":"https://pith.science/pith/7YKPARCJKWFIAKG2DUAIDC7IXF/action/replication_record"}},"created_at":"2026-07-05T11:31:32.371528+00:00","updated_at":"2026-07-05T11:31:32.371528+00:00"}