{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:L3BMP2QXELKWWNR62H6VZACSFB","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":"57d2728ea0b7a531395bc1fc6018f4f7a342f78a7b3ac7d130d38a54dedb1707","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-06T03:16:43Z","title_canon_sha256":"351fecfbb315a87af7b04b6baa1b2ae7ef3cbc29ce2b106e71f437bf06cc30c0"},"schema_version":"1.0","source":{"id":"1110.1144","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1144","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1144v3","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1144","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"L3BMP2QXELKW","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"L3BMP2QXELKWWNR6","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"L3BMP2QX","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:beb2d9780da0e152a596f5481aa9e2f7b111d17aef3ec7f3938b5fd1990ae274","target":"graph","created_at":"2026-05-18T02:29:53Z","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":"Hajos' conjecture that every simple even graph on $n$ vertices can be decomposed into at most $(n-1)/2$ cycles (see L. Lovasz, On covering of graphs, in: P. Erdos, G.O.H. Katona (Eds.), Theory of Graphs, Academic Press, New York, 1968, pp. 231 - 236). Let $f(n)$ be the maximum number of edges in a graph on $n$ vertices in which no two cycles have the same length. P. Erdos raised the problem of determining $f(n)$ (see J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, New York, 1976), p.247, Problem 11).\n  Given a graph $H$, what is the maximum number of edges of a graph wi","authors_text":"Chunhui Lai, Mingjing Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-06T03:16:43Z","title":"Some unsolved problems on cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1144","kind":"arxiv","version":3},"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":"sha256:288ecee32ae2bd1a5f2fa7079b4ec4d4a221fd02cb249e7e0edaaaf76e60d929","target":"record","created_at":"2026-05-18T02:29:53Z","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":"57d2728ea0b7a531395bc1fc6018f4f7a342f78a7b3ac7d130d38a54dedb1707","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-06T03:16:43Z","title_canon_sha256":"351fecfbb315a87af7b04b6baa1b2ae7ef3cbc29ce2b106e71f437bf06cc30c0"},"schema_version":"1.0","source":{"id":"1110.1144","kind":"arxiv","version":3}},"canonical_sha256":"5ec2c7ea1722d56b363ed1fd5c8052285f492a6956646b6c0dde72f262ad7a6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ec2c7ea1722d56b363ed1fd5c8052285f492a6956646b6c0dde72f262ad7a6d","first_computed_at":"2026-05-18T02:29:53.472578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:53.472578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tPkjYR0LLPJuzAYOVZ4to3d56KpciF1wWzb0dwzITyuAhHCrapH2BARaLFkx5l3r+JZ728V8nKFZV8bnLeR0DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:53.473105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1144","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:288ecee32ae2bd1a5f2fa7079b4ec4d4a221fd02cb249e7e0edaaaf76e60d929","sha256:beb2d9780da0e152a596f5481aa9e2f7b111d17aef3ec7f3938b5fd1990ae274"],"state_sha256":"08b6da5e5b791a09a245e4ad357b21655e374af49271074f56d7f40a58a5a057"}