{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:Z75ZRMHGAV7G4IRAWAGYDPD3TH","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":"262d2c5671b5000c65756f8d9335419222a780a4e1dada26adfc25d29066dd3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-20T11:28:08Z","title_canon_sha256":"be8a86b598de05656298f9b2ebe53f5d9f6b0fce50004e16f89e69edecd2e25f"},"schema_version":"1.0","source":{"id":"1905.08001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.08001","created_at":"2026-07-05T02:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1905.08001v1","created_at":"2026-07-05T02:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.08001","created_at":"2026-07-05T02:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"Z75ZRMHGAV7G","created_at":"2026-07-05T02:13:10Z"},{"alias_kind":"pith_short_16","alias_value":"Z75ZRMHGAV7G4IRA","created_at":"2026-07-05T02:13:10Z"},{"alias_kind":"pith_short_8","alias_value":"Z75ZRMHG","created_at":"2026-07-05T02:13:10Z"}],"graph_snapshots":[{"event_id":"sha256:1a975710551a7506ae393295dfcbad80124d3ebdcd78173902e18aba925f71e9","target":"graph","created_at":"2026-07-05T02:13:10Z","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/1905.08001/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a multigraph $F$, the $k$-subdivision of $F$ is the graph obtained by replacing the edges of $F$ with pairwise internally vertex-disjoint paths of length $k+1$. Conlon and Lee conjectured that if $k$ is even, then the $(k-1)$-subdivision of any multigraph has extremal number $O(n^{1+\\frac{1}{k}})$, and moreover, that for any simple graph $F$ there exists $\\varepsilon>0$ such that the $(k-1)$-subdivision of $F$ has extremal number $O(n^{1+\\frac{1}{k}-\\varepsilon})$. In this paper, we prove both conjectures.","authors_text":"Oliver Janzer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-20T11:28:08Z","title":"The extremal number of longer subdivisions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08001","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:ba0c21645b1b7e8ed15a5118435a8effd04564e87dd88b26df23bfec20d1d91f","target":"record","created_at":"2026-07-05T02:13:10Z","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":"262d2c5671b5000c65756f8d9335419222a780a4e1dada26adfc25d29066dd3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-20T11:28:08Z","title_canon_sha256":"be8a86b598de05656298f9b2ebe53f5d9f6b0fce50004e16f89e69edecd2e25f"},"schema_version":"1.0","source":{"id":"1905.08001","kind":"arxiv","version":1}},"canonical_sha256":"cffb98b0e6057e6e2220b00d81bc7b99d44097695af3d98df79842d25eafb2e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cffb98b0e6057e6e2220b00d81bc7b99d44097695af3d98df79842d25eafb2e8","first_computed_at":"2026-07-05T02:13:10.545489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:13:10.545489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xIIbsVp3xQFIViCBdRPYvagI1nZt7C7nVMZ9GC1cldS2NSmStuBRpJ/4JOh2jgcrqU5n8ikBmFcA215StwjVBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:13:10.545918Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.08001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba0c21645b1b7e8ed15a5118435a8effd04564e87dd88b26df23bfec20d1d91f","sha256:1a975710551a7506ae393295dfcbad80124d3ebdcd78173902e18aba925f71e9"],"state_sha256":"4ca99be4c72f71d515cb6c4ead4d43eda335c8a184c570c428d2251e1855a945"}