{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:RLAOV7KDI34JRVLNT3OMJVWRKD","short_pith_number":"pith:RLAOV7KD","canonical_record":{"source":{"id":"2410.00648","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-01T13:01:17Z","cross_cats_sorted":[],"title_canon_sha256":"b2a367b18efdf8419491109e0512d1972542d4811997656007b13e9f58f36b10","abstract_canon_sha256":"056b762265e742821bb1ff5c9cfeec0e774121ec9561fe07ba8393dcdf971445"},"schema_version":"1.0"},"canonical_sha256":"8ac0eafd4346f898d56d9edcc4d6d150f4000a3db676e3f8b10c33130d807570","source":{"kind":"arxiv","id":"2410.00648","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.00648","created_at":"2026-07-05T11:29:02Z"},{"alias_kind":"arxiv_version","alias_value":"2410.00648v2","created_at":"2026-07-05T11:29:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.00648","created_at":"2026-07-05T11:29:02Z"},{"alias_kind":"pith_short_12","alias_value":"RLAOV7KDI34J","created_at":"2026-07-05T11:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"RLAOV7KDI34JRVLN","created_at":"2026-07-05T11:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"RLAOV7KD","created_at":"2026-07-05T11:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:RLAOV7KDI34JRVLNT3OMJVWRKD","target":"record","payload":{"canonical_record":{"source":{"id":"2410.00648","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-01T13:01:17Z","cross_cats_sorted":[],"title_canon_sha256":"b2a367b18efdf8419491109e0512d1972542d4811997656007b13e9f58f36b10","abstract_canon_sha256":"056b762265e742821bb1ff5c9cfeec0e774121ec9561fe07ba8393dcdf971445"},"schema_version":"1.0"},"canonical_sha256":"8ac0eafd4346f898d56d9edcc4d6d150f4000a3db676e3f8b10c33130d807570","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:29:02.189352Z","signature_b64":"kDRCddH9cVoEh3vpkyAyfIQ5T9wJkDouRqTvOk7Ow4em1FtbjHoFWZIDXTpO4g7fsnbHhOD/83FjekZ8GZ7FCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ac0eafd4346f898d56d9edcc4d6d150f4000a3db676e3f8b10c33130d807570","last_reissued_at":"2026-07-05T11:29:02.188764Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:29:02.188764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.00648","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:29:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lwh7Zf0IGf69jOKolEl9Y1ewpOULK/c5SelLF+GBiSPoz0asEvfX/tIE/v9eIeZtScpGjP0umtEk4elapoACBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T00:25:43.100137Z"},"content_sha256":"7a10855cd72192c65322ce9d17312eca138099983d88565be304007359291b6f","schema_version":"1.0","event_id":"sha256:7a10855cd72192c65322ce9d17312eca138099983d88565be304007359291b6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:RLAOV7KDI34JRVLNT3OMJVWRKD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A strengthening on consecutive odd cycles in graphs of given minimum degree","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guanghui Wang, Hao Lin, Wenling Zhou","submitted_at":"2024-10-01T13:01:17Z","abstract_excerpt":"Liu and Ma [J. Combin. Theory Ser. B, 2018] conjectured that every $2$-connected non-bipartite graph with minimum degree at least $k+1$ contains $\\lceil k/2\\rceil $ cycles with consecutive odd lengths. In particular, they showed that this conjecture holds when $k$ is even. In this paper, we confirm this conjecture for any $k\\in \\mathbb N$. Moreover, we also improve some previous results about cycles of consecutive lengths."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00648","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.00648/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:29:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JO+kUGpL39qZ3NL6j2NIk0l7c3rvK5lmqTO7msJVH4CoADxenaB8EbMsmuDjFMTNb3nkibRjmk8Gl+bBLYcSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T00:25:43.100691Z"},"content_sha256":"7a259acacb87d7efb9d285bab78dbdbfe4fa144210632e31ea8c22720a927a26","schema_version":"1.0","event_id":"sha256:7a259acacb87d7efb9d285bab78dbdbfe4fa144210632e31ea8c22720a927a26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RLAOV7KDI34JRVLNT3OMJVWRKD/bundle.json","state_url":"https://pith.science/pith/RLAOV7KDI34JRVLNT3OMJVWRKD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RLAOV7KDI34JRVLNT3OMJVWRKD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T00:25:43Z","links":{"resolver":"https://pith.science/pith/RLAOV7KDI34JRVLNT3OMJVWRKD","bundle":"https://pith.science/pith/RLAOV7KDI34JRVLNT3OMJVWRKD/bundle.json","state":"https://pith.science/pith/RLAOV7KDI34JRVLNT3OMJVWRKD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RLAOV7KDI34JRVLNT3OMJVWRKD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RLAOV7KDI34JRVLNT3OMJVWRKD","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":"056b762265e742821bb1ff5c9cfeec0e774121ec9561fe07ba8393dcdf971445","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-01T13:01:17Z","title_canon_sha256":"b2a367b18efdf8419491109e0512d1972542d4811997656007b13e9f58f36b10"},"schema_version":"1.0","source":{"id":"2410.00648","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.00648","created_at":"2026-07-05T11:29:02Z"},{"alias_kind":"arxiv_version","alias_value":"2410.00648v2","created_at":"2026-07-05T11:29:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.00648","created_at":"2026-07-05T11:29:02Z"},{"alias_kind":"pith_short_12","alias_value":"RLAOV7KDI34J","created_at":"2026-07-05T11:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"RLAOV7KDI34JRVLN","created_at":"2026-07-05T11:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"RLAOV7KD","created_at":"2026-07-05T11:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:7a259acacb87d7efb9d285bab78dbdbfe4fa144210632e31ea8c22720a927a26","target":"graph","created_at":"2026-07-05T11:29:02Z","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/2410.00648/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Liu and Ma [J. Combin. Theory Ser. B, 2018] conjectured that every $2$-connected non-bipartite graph with minimum degree at least $k+1$ contains $\\lceil k/2\\rceil $ cycles with consecutive odd lengths. In particular, they showed that this conjecture holds when $k$ is even. In this paper, we confirm this conjecture for any $k\\in \\mathbb N$. Moreover, we also improve some previous results about cycles of consecutive lengths.","authors_text":"Guanghui Wang, Hao Lin, Wenling Zhou","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-01T13:01:17Z","title":"A strengthening on consecutive odd cycles in graphs of given minimum degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00648","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":"sha256:7a10855cd72192c65322ce9d17312eca138099983d88565be304007359291b6f","target":"record","created_at":"2026-07-05T11:29:02Z","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":"056b762265e742821bb1ff5c9cfeec0e774121ec9561fe07ba8393dcdf971445","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-01T13:01:17Z","title_canon_sha256":"b2a367b18efdf8419491109e0512d1972542d4811997656007b13e9f58f36b10"},"schema_version":"1.0","source":{"id":"2410.00648","kind":"arxiv","version":2}},"canonical_sha256":"8ac0eafd4346f898d56d9edcc4d6d150f4000a3db676e3f8b10c33130d807570","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ac0eafd4346f898d56d9edcc4d6d150f4000a3db676e3f8b10c33130d807570","first_computed_at":"2026-07-05T11:29:02.188764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:29:02.188764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kDRCddH9cVoEh3vpkyAyfIQ5T9wJkDouRqTvOk7Ow4em1FtbjHoFWZIDXTpO4g7fsnbHhOD/83FjekZ8GZ7FCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:29:02.189352Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.00648","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a10855cd72192c65322ce9d17312eca138099983d88565be304007359291b6f","sha256:7a259acacb87d7efb9d285bab78dbdbfe4fa144210632e31ea8c22720a927a26"],"state_sha256":"a6005027667339c8f46308e403fa6cbc8835f23b4634e2330619c5ac45bd0927"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sKbQIY5uBlpHVvBJ2dZ5t7vjgWNAig+GnRQnySWjmmOoGKnHROz5lkI+7lgHrypH2rpfxFVpI8kOq3oyC4H6Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T00:25:43.105024Z","bundle_sha256":"aab6154aa4c0a211b8ab514bff3904f8b0bbc3ce61ac3d8c35923952c1b88b75"}}