{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:L3XKXZ6IA3S5F6RCR5QOJBZSDR","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":"5f35ea1bc0addd35eaf9c313f86ed091de30ecde881c7d164a7e7d6dd29bf878","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-05T11:14:58Z","title_canon_sha256":"076ea384aee378acb5d425de6587a1310a4695d156664dc11335d965ae86e253"},"schema_version":"1.0","source":{"id":"1502.01502","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01502","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01502v1","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01502","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"pith_short_12","alias_value":"L3XKXZ6IA3S5","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"L3XKXZ6IA3S5F6RC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"L3XKXZ6I","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:6846ed4afa73341f7510d9161cb8e5b88b18b71ad3514d4f7dbcd842bff29819","target":"graph","created_at":"2026-05-18T02:27:51Z","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"},"paper":{"abstract_excerpt":"We show that the norm graph constructed in [J. Koll\\'{a}r, L. R\\'{o}nyai and T. Szab\\'o, Norm-graphs and bipartite Tur\\'{a}n numbers, Combinatorica, 16 (1996) 399--406] with $n$ vertices about $\\frac{1}{2}n^{2-1/t}$ edges, which contains no copy of $K_{t,(t-1)!+1}$, does not contain a copy of $K_{t+1,(t-1)!-1}$.","authors_text":"Simeon Ball, Valentina Pepe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-05T11:14:58Z","title":"Forbidden subgraphs in the norm graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01502","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:dad5b4700679b02413f558248cb247fad27f295b077bf9c000ae95986c755ef1","target":"record","created_at":"2026-05-18T02:27:51Z","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":"5f35ea1bc0addd35eaf9c313f86ed091de30ecde881c7d164a7e7d6dd29bf878","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-05T11:14:58Z","title_canon_sha256":"076ea384aee378acb5d425de6587a1310a4695d156664dc11335d965ae86e253"},"schema_version":"1.0","source":{"id":"1502.01502","kind":"arxiv","version":1}},"canonical_sha256":"5eeeabe7c806e5d2fa228f60e487321c7ae2bf9bdd0b29579f14ec9991e2bccc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5eeeabe7c806e5d2fa228f60e487321c7ae2bf9bdd0b29579f14ec9991e2bccc","first_computed_at":"2026-05-18T02:27:51.907061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:51.907061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XMChTekSlOD2tkatG0mKwmIzn5qjL2oTHIM/5JDBBzZfmo5z2CUpa4hKUUM3zHsfO0IxZTtDpfvB+PxiEA1BCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:51.907517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01502","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dad5b4700679b02413f558248cb247fad27f295b077bf9c000ae95986c755ef1","sha256:6846ed4afa73341f7510d9161cb8e5b88b18b71ad3514d4f7dbcd842bff29819"],"state_sha256":"57ae0d2fa206244d90d0bafd6f845e21620a55b0f292938fde636ab2ecc1cb90"}