{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PMQ7TPPD5QQLLCZ5CF2N7ETJPY","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":"8fe504685cdb9d133865025989c241c398a50b5c3a17f4546e34978f26ba1605","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-12-23T18:14:10Z","title_canon_sha256":"92d83643e098284e59d9f9e031fc6e3a0f3f014efe292c24b577d0d9e59242ec"},"schema_version":"1.0","source":{"id":"1912.11011","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.11011","created_at":"2026-07-05T01:08:26Z"},{"alias_kind":"arxiv_version","alias_value":"1912.11011v2","created_at":"2026-07-05T01:08:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.11011","created_at":"2026-07-05T01:08:26Z"},{"alias_kind":"pith_short_12","alias_value":"PMQ7TPPD5QQL","created_at":"2026-07-05T01:08:26Z"},{"alias_kind":"pith_short_16","alias_value":"PMQ7TPPD5QQLLCZ5","created_at":"2026-07-05T01:08:26Z"},{"alias_kind":"pith_short_8","alias_value":"PMQ7TPPD","created_at":"2026-07-05T01:08:26Z"}],"graph_snapshots":[{"event_id":"sha256:60fc6b50675294afd01e9d548cd1afcb17e52818e875d005d85bcf01bebe8ea1","target":"graph","created_at":"2026-07-05T01:08:26Z","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/1912.11011/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a positive constant $\\alpha$ a graph $G$ on $n$ vertices is called an $\\alpha$-expander if every vertex set $U$ of size at most $n/2$ has an external neighborhood whose size is at least $\\alpha\\left|U\\right|$. We study cycle lengths in expanding graphs. We first prove that cycle lengths in $\\alpha$-expanders are well distributed. Specifically, we show that for every $0<\\alpha\\leq1$ there exist positive constants $n_{0}$, $C$ and $A=O(1/\\alpha)$ such that for every $\\alpha$-expander $G$ on $n\\geq n_{0}$ vertices and every integer $\\ell\\in\\left[C\\log n,\\frac{n}{C}\\right]$, $G$ contains a cyc","authors_text":"Limor Friedman, Michael Krivelevich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-12-23T18:14:10Z","title":"Cycle lengths in expanding graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.11011","kind":"arxiv","version":2},"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:baa1655a4f5ada80339bbcad5914a33da0298a4bbf368e894b2e5678c33d7b1c","target":"record","created_at":"2026-07-05T01:08:26Z","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":"8fe504685cdb9d133865025989c241c398a50b5c3a17f4546e34978f26ba1605","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-12-23T18:14:10Z","title_canon_sha256":"92d83643e098284e59d9f9e031fc6e3a0f3f014efe292c24b577d0d9e59242ec"},"schema_version":"1.0","source":{"id":"1912.11011","kind":"arxiv","version":2}},"canonical_sha256":"7b21f9bde3ec20b58b3d1174df92697e246e909ce84e8db7b9cf38ada66f9752","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b21f9bde3ec20b58b3d1174df92697e246e909ce84e8db7b9cf38ada66f9752","first_computed_at":"2026-07-05T01:08:26.207845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:08:26.207845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2czOiXPFxRN9iiaSM0r/dFPSC2TU3bibZR7X8dwuBrmIPyMPbT7Ft1DnfsbDJysTsUzawC3ugiLUHFj22SJVCw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:08:26.208205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.11011","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baa1655a4f5ada80339bbcad5914a33da0298a4bbf368e894b2e5678c33d7b1c","sha256:60fc6b50675294afd01e9d548cd1afcb17e52818e875d005d85bcf01bebe8ea1"],"state_sha256":"0d6b74012ebef6a0c83cfa7bf7ae17481274141f4f31cba1ff74b096d2a09ce4"}