{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:IPOWOY5ZLGRA4MBN7CMDNQ4YJF","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":"0bf53d50f6ee8f3e75779f065b3513fa8484aaa9ede3967d9f841877bd5ed71f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-03-02T14:38:38Z","title_canon_sha256":"cb7c1e5d018c2d1fe710997ac7de62cb788e83ef0e2e3931d60adfaefd53beed"},"schema_version":"1.0","source":{"id":"2003.00942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.00942","created_at":"2026-07-05T00:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"2003.00942v1","created_at":"2026-07-05T00:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.00942","created_at":"2026-07-05T00:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"IPOWOY5ZLGRA","created_at":"2026-07-05T00:44:59Z"},{"alias_kind":"pith_short_16","alias_value":"IPOWOY5ZLGRA4MBN","created_at":"2026-07-05T00:44:59Z"},{"alias_kind":"pith_short_8","alias_value":"IPOWOY5Z","created_at":"2026-07-05T00:44:59Z"}],"graph_snapshots":[{"event_id":"sha256:b620fe0ba0d54cfd3aff47bf6739492e4c4423be1c82876c3f215bceea3b3f29","target":"graph","created_at":"2026-07-05T00:44:59Z","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/2003.00942/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 1972 Mader proved that every graph with average degree at least $4k$ has a $(k+1)$-connected subgraph with more than $2k$ vertices. We improve this bound by showing that the constant $4$ can be replaced by $3+\\frac{1}{3}$; this bound is sharp.","authors_text":"Johannes Carmesin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-03-02T14:38:38Z","title":"Large highly connected subgraphs in graphs with linear average degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.00942","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":"sha256:00bf03c2b0a70025c2ea443d4e4bf714ae1f592f6bb9e28bd1e52fd10e47e449","target":"record","created_at":"2026-07-05T00:44:59Z","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":"0bf53d50f6ee8f3e75779f065b3513fa8484aaa9ede3967d9f841877bd5ed71f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-03-02T14:38:38Z","title_canon_sha256":"cb7c1e5d018c2d1fe710997ac7de62cb788e83ef0e2e3931d60adfaefd53beed"},"schema_version":"1.0","source":{"id":"2003.00942","kind":"arxiv","version":1}},"canonical_sha256":"43dd6763b959a20e302df89836c3984974331bcdb737f14805dee73671b2cbc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43dd6763b959a20e302df89836c3984974331bcdb737f14805dee73671b2cbc6","first_computed_at":"2026-07-05T00:44:59.641458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:44:59.641458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f0KYT0uMRHEL34IxkGAirqmO6KRE1tQQm29Q3D+KLJfCOEwrmWI8+oTCWAh7xOBFO6pg8O+V49Z6YRfoem3BDw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:44:59.641844Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.00942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00bf03c2b0a70025c2ea443d4e4bf714ae1f592f6bb9e28bd1e52fd10e47e449","sha256:b620fe0ba0d54cfd3aff47bf6739492e4c4423be1c82876c3f215bceea3b3f29"],"state_sha256":"9d3b25e4476c60954cd5fd8c7919f49c8f63017fb005c3b46aad4d975a1b891d"}