{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:P76PJCZYH23NFKXZ7GE7INQD3O","short_pith_number":"pith:P76PJCZY","schema_version":"1.0","canonical_sha256":"7ffcf48b383eb6d2aaf9f989f43603dbbf3b1686931ad63348791b8d2a28754b","source":{"kind":"arxiv","id":"2605.30821","version":1},"attestation_state":"computed","paper":{"title":"The spectral inducibility of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Liying Kang, Xizhi Liu, Yongchun Lu","submitted_at":"2026-05-29T04:12:48Z","abstract_excerpt":"We introduce a spectral version of the classical inducibility problem. Given an $\\ell$-vertex graph $F$ and an $n$-vertex graph $G$, let $H_F(G)$ be the $\\ell$-uniform hypergraph whose edges are the $\\ell$-sets inducing a copy of $F$ in $G$. We study the maximum possible $\\alpha$-spectral radius of $H_F(G)$ over all $n$-vertex graphs $G$. For fixed $G$, this spectral parameter tends to $\\ell!$ times the number of induced copies of $F$ in $G$ as $\\alpha\\to\\infty$, and therefore refines the usual induced-copy count.\n  Our main result is a spectral analogue of the Brown--Sidorenko reduction: for "},"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":"2605.30821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-29T04:12:48Z","cross_cats_sorted":[],"title_canon_sha256":"cc6dd97258339d5e0dad9cb8238ad4bb71c32e74c804b3e1f43d92bd9e4b0fb5","abstract_canon_sha256":"241e05a57e5e1f80d9c173ccfcab585c5263fda0943181141afd3843bea44078"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:03:18.952395Z","signature_b64":"BFvJZpxBwf98Ql7U9lsqM/A+NvjtbaCTG66b4SRiC85zOu1ZbsuQzith186ArN2hgxr28HigEaLCJUVDs7CtBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ffcf48b383eb6d2aaf9f989f43603dbbf3b1686931ad63348791b8d2a28754b","last_reissued_at":"2026-06-01T01:03:18.951451Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:03:18.951451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The spectral inducibility of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Liying Kang, Xizhi Liu, Yongchun Lu","submitted_at":"2026-05-29T04:12:48Z","abstract_excerpt":"We introduce a spectral version of the classical inducibility problem. Given an $\\ell$-vertex graph $F$ and an $n$-vertex graph $G$, let $H_F(G)$ be the $\\ell$-uniform hypergraph whose edges are the $\\ell$-sets inducing a copy of $F$ in $G$. We study the maximum possible $\\alpha$-spectral radius of $H_F(G)$ over all $n$-vertex graphs $G$. For fixed $G$, this spectral parameter tends to $\\ell!$ times the number of induced copies of $F$ in $G$ as $\\alpha\\to\\infty$, and therefore refines the usual induced-copy count.\n  Our main result is a spectral analogue of the Brown--Sidorenko reduction: for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30821","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/2605.30821/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":"2605.30821","created_at":"2026-06-01T01:03:18.951591+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.30821v1","created_at":"2026-06-01T01:03:18.951591+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30821","created_at":"2026-06-01T01:03:18.951591+00:00"},{"alias_kind":"pith_short_12","alias_value":"P76PJCZYH23N","created_at":"2026-06-01T01:03:18.951591+00:00"},{"alias_kind":"pith_short_16","alias_value":"P76PJCZYH23NFKXZ","created_at":"2026-06-01T01:03:18.951591+00:00"},{"alias_kind":"pith_short_8","alias_value":"P76PJCZY","created_at":"2026-06-01T01:03:18.951591+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/P76PJCZYH23NFKXZ7GE7INQD3O","json":"https://pith.science/pith/P76PJCZYH23NFKXZ7GE7INQD3O.json","graph_json":"https://pith.science/api/pith-number/P76PJCZYH23NFKXZ7GE7INQD3O/graph.json","events_json":"https://pith.science/api/pith-number/P76PJCZYH23NFKXZ7GE7INQD3O/events.json","paper":"https://pith.science/paper/P76PJCZY"},"agent_actions":{"view_html":"https://pith.science/pith/P76PJCZYH23NFKXZ7GE7INQD3O","download_json":"https://pith.science/pith/P76PJCZYH23NFKXZ7GE7INQD3O.json","view_paper":"https://pith.science/paper/P76PJCZY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.30821&json=true","fetch_graph":"https://pith.science/api/pith-number/P76PJCZYH23NFKXZ7GE7INQD3O/graph.json","fetch_events":"https://pith.science/api/pith-number/P76PJCZYH23NFKXZ7GE7INQD3O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P76PJCZYH23NFKXZ7GE7INQD3O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P76PJCZYH23NFKXZ7GE7INQD3O/action/storage_attestation","attest_author":"https://pith.science/pith/P76PJCZYH23NFKXZ7GE7INQD3O/action/author_attestation","sign_citation":"https://pith.science/pith/P76PJCZYH23NFKXZ7GE7INQD3O/action/citation_signature","submit_replication":"https://pith.science/pith/P76PJCZYH23NFKXZ7GE7INQD3O/action/replication_record"}},"created_at":"2026-06-01T01:03:18.951591+00:00","updated_at":"2026-06-01T01:03:18.951591+00:00"}