{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:72DIUY3FRNM3HFW4NJPGC3L244","short_pith_number":"pith:72DIUY3F","schema_version":"1.0","canonical_sha256":"fe868a63658b59b396dc6a5e616d7ae720c91f8b75fc05a9a2e9df683a2c43da","source":{"kind":"arxiv","id":"2606.06202","version":1},"attestation_state":"computed","paper":{"title":"Exact extremal constructions for the inducibility of blowup graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Wanfang Chen, Xizhi Liu","submitted_at":"2026-06-04T14:07:23Z","abstract_excerpt":"For a finite graph $H$ and a positive integer $h$, the $h$-blowup $H^{(h)}$ of $H$ is the graph obtained by replacing each vertex of $H$ by a set of size $h$ and each edge by a complete bipartite graph between the corresponding sets. We prove that, for every $H$, there exists a constant $h_*(H)$ such that whenever $h\\ge h_*(H)$ and $n$ is sufficiently large, every $n$-vertex graph maximizing the number of induced copies of $H^{(h)}$ is a blowup of $H$. This refines the asymptotic result of Hatami, Hirst and Norine and settles the question posed by Bollob\\'as, Egawa, Harris and Jin in 1995."},"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":"2606.06202","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-04T14:07:23Z","cross_cats_sorted":[],"title_canon_sha256":"84b33802371aced773f51c16dd48833029fe103f8a6a6227ddd2e3a2763a70b9","abstract_canon_sha256":"25d0dfa2ff5f8f5eba99dd7bcea285134cf7103e5f07e5e94ad79d1a72a14eca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:37.150598Z","signature_b64":"EHwBypoORlTAfd7XrmMaFUaQdXIEu4t4OT9fJ1GYFSEXY0hkpTooWyrgAm3Fo0Yu7NLDErlGyxY1iUtQTXKBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe868a63658b59b396dc6a5e616d7ae720c91f8b75fc05a9a2e9df683a2c43da","last_reissued_at":"2026-06-05T01:15:37.150075Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:37.150075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact extremal constructions for the inducibility of blowup graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Wanfang Chen, Xizhi Liu","submitted_at":"2026-06-04T14:07:23Z","abstract_excerpt":"For a finite graph $H$ and a positive integer $h$, the $h$-blowup $H^{(h)}$ of $H$ is the graph obtained by replacing each vertex of $H$ by a set of size $h$ and each edge by a complete bipartite graph between the corresponding sets. We prove that, for every $H$, there exists a constant $h_*(H)$ such that whenever $h\\ge h_*(H)$ and $n$ is sufficiently large, every $n$-vertex graph maximizing the number of induced copies of $H^{(h)}$ is a blowup of $H$. This refines the asymptotic result of Hatami, Hirst and Norine and settles the question posed by Bollob\\'as, Egawa, Harris and Jin in 1995."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06202","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/2606.06202/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":"2606.06202","created_at":"2026-06-05T01:15:37.150153+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.06202v1","created_at":"2026-06-05T01:15:37.150153+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06202","created_at":"2026-06-05T01:15:37.150153+00:00"},{"alias_kind":"pith_short_12","alias_value":"72DIUY3FRNM3","created_at":"2026-06-05T01:15:37.150153+00:00"},{"alias_kind":"pith_short_16","alias_value":"72DIUY3FRNM3HFW4","created_at":"2026-06-05T01:15:37.150153+00:00"},{"alias_kind":"pith_short_8","alias_value":"72DIUY3F","created_at":"2026-06-05T01:15:37.150153+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/72DIUY3FRNM3HFW4NJPGC3L244","json":"https://pith.science/pith/72DIUY3FRNM3HFW4NJPGC3L244.json","graph_json":"https://pith.science/api/pith-number/72DIUY3FRNM3HFW4NJPGC3L244/graph.json","events_json":"https://pith.science/api/pith-number/72DIUY3FRNM3HFW4NJPGC3L244/events.json","paper":"https://pith.science/paper/72DIUY3F"},"agent_actions":{"view_html":"https://pith.science/pith/72DIUY3FRNM3HFW4NJPGC3L244","download_json":"https://pith.science/pith/72DIUY3FRNM3HFW4NJPGC3L244.json","view_paper":"https://pith.science/paper/72DIUY3F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.06202&json=true","fetch_graph":"https://pith.science/api/pith-number/72DIUY3FRNM3HFW4NJPGC3L244/graph.json","fetch_events":"https://pith.science/api/pith-number/72DIUY3FRNM3HFW4NJPGC3L244/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/72DIUY3FRNM3HFW4NJPGC3L244/action/timestamp_anchor","attest_storage":"https://pith.science/pith/72DIUY3FRNM3HFW4NJPGC3L244/action/storage_attestation","attest_author":"https://pith.science/pith/72DIUY3FRNM3HFW4NJPGC3L244/action/author_attestation","sign_citation":"https://pith.science/pith/72DIUY3FRNM3HFW4NJPGC3L244/action/citation_signature","submit_replication":"https://pith.science/pith/72DIUY3FRNM3HFW4NJPGC3L244/action/replication_record"}},"created_at":"2026-06-05T01:15:37.150153+00:00","updated_at":"2026-06-05T01:15:37.150153+00:00"}