{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZQP2OFQXIFDQOQCCDN76YRKTHG","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":"b91ecea3bce0a7787826f1b1516556eb582b68f5706cf9f2f46f3a402c053092","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-16T11:54:34Z","title_canon_sha256":"66e8b06809b634fddab3a3164398d438f90ae8219e43e863f271ab80d8dcdec6"},"schema_version":"1.0","source":{"id":"1606.05152","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05152","created_at":"2026-05-18T00:44:13Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05152v4","created_at":"2026-05-18T00:44:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05152","created_at":"2026-05-18T00:44:13Z"},{"alias_kind":"pith_short_12","alias_value":"ZQP2OFQXIFDQ","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZQP2OFQXIFDQOQCC","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZQP2OFQX","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:7c2c92b926bb67692318fbee41c9e386852b87ab52958760a18d1d845618539b","target":"graph","created_at":"2026-05-18T00:44:13Z","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":"The balanced hypercube, $BH_n$, is a variant of hypercube $Q_n$. R.X. Hao et al. $(2014)$ \\cite{R.X.Hao} showed that there exists a fault-free Hamiltonian path between any two adjacent vertices in $BH_n$ with $(2n-2)$ faulty edges. D.Q. Cheng et al. $(2015)$ \\cite{Dongqincheng2} proved that $BH_n$ is $6$-edge-bipancyclic after $(2n-3)$ faulty edges occur for all $n\\ge2$. In this paper, we improve these two results by demonstrating that $BH_n$ is $6$-edge-bipancyclic even when there exist $(2n-2)$ faulty edges for all $n\\ge2$. Our result is optimal with respect to the maximum number of tolerate","authors_text":"Min Xu, Pingshan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-16T11:54:34Z","title":"Edge-fault-tolerant edge-bipancyclicity of balanced hypercubes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05152","kind":"arxiv","version":4},"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":"sha256:5bfbdadb81cb9d08a356feb6e58b2190739d955fb3890e329c6e4e54f549c9b9","target":"record","created_at":"2026-05-18T00:44:13Z","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":"b91ecea3bce0a7787826f1b1516556eb582b68f5706cf9f2f46f3a402c053092","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-16T11:54:34Z","title_canon_sha256":"66e8b06809b634fddab3a3164398d438f90ae8219e43e863f271ab80d8dcdec6"},"schema_version":"1.0","source":{"id":"1606.05152","kind":"arxiv","version":4}},"canonical_sha256":"cc1fa7161741470740421b7fec455339a776d9a70a6c5f1790de6456e4a7d8b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc1fa7161741470740421b7fec455339a776d9a70a6c5f1790de6456e4a7d8b3","first_computed_at":"2026-05-18T00:44:13.735769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:13.735769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0eRgfgqOlS3zLXFqwUbeMkOhv+v03jKFSjEjkNGbGuwK5cofselqXnku2V3R/YSxdgvusxTobL/8AJT2EVWACg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:13.736211Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.05152","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bfbdadb81cb9d08a356feb6e58b2190739d955fb3890e329c6e4e54f549c9b9","sha256:7c2c92b926bb67692318fbee41c9e386852b87ab52958760a18d1d845618539b"],"state_sha256":"39551ff69a78e6bc2d3be0a0a8f1694188f6ceea751985b9b29960e85008212e"}