{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JBZM7I2HDRC77PINIZCSJYTCQR","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":"0d20638dfe48706d670e0e537db3f1b838142cfc78d1e7e2f5ce1e3826060b37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-20T08:25:43Z","title_canon_sha256":"55996f8931924a9c7321deb10186a698976eb89821599533b591ca1cb46567a5"},"schema_version":"1.0","source":{"id":"1301.4639","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4639","created_at":"2026-05-18T03:35:56Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4639v1","created_at":"2026-05-18T03:35:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4639","created_at":"2026-05-18T03:35:56Z"},{"alias_kind":"pith_short_12","alias_value":"JBZM7I2HDRC7","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JBZM7I2HDRC77PIN","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JBZM7I2H","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:2b6ddb710368405428d02fc6dd6517680e34186696970c2dccb9d375c9e9d263","target":"graph","created_at":"2026-05-18T03:35:56Z","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":"A subset $F$ of edges in a connected graph $G$ is a $h$-extra edge-cut if $G-F$ is disconnected and every component has more than $h$ vertices. The $h$-extra edge-connectivity $\\la^{(h)}(G)$ of $G$ is defined as the minimum cardinality over all $h$-extra edge-cuts of $G$. A graph $G$, if $\\la^{(h)}(G)$ exists, is super-$\\la^{(h)}$ if every minimum $h$-extra edge-cut of $G$ isolates at least one connected subgraph of order $h+1$. The persistence $\\rho^{(h)}(G)$ of a super-$\\la^{(h)}$ graph $G$ is the maximum integer $m$ for which $G-F$ is still super-$\\la^{(h)}$ for any set $F\\subseteq E(G)$ wi","authors_text":"Jun-Ming Xu, Zhen-Mu Hong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-20T08:25:43Z","title":"Vulnerability of super edge-connected graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4639","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":"sha256:66850e44d76ff17b016a6c8fc50d3de19e5fbedebde90ce1a5acc0cfadf90e6c","target":"record","created_at":"2026-05-18T03:35:56Z","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":"0d20638dfe48706d670e0e537db3f1b838142cfc78d1e7e2f5ce1e3826060b37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-20T08:25:43Z","title_canon_sha256":"55996f8931924a9c7321deb10186a698976eb89821599533b591ca1cb46567a5"},"schema_version":"1.0","source":{"id":"1301.4639","kind":"arxiv","version":1}},"canonical_sha256":"4872cfa3471c45ffbd0d464524e262846be49102b569fd73eeb14af75e62c133","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4872cfa3471c45ffbd0d464524e262846be49102b569fd73eeb14af75e62c133","first_computed_at":"2026-05-18T03:35:56.072739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:56.072739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2bnSdi8M/orDWRPeV22ynDgRZB7hJd9atZ0YD1pKXkeCBfM538YuRn91IrGacl0vKtLRTETaAV+5/qmfHyZVDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:56.073341Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4639","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66850e44d76ff17b016a6c8fc50d3de19e5fbedebde90ce1a5acc0cfadf90e6c","sha256:2b6ddb710368405428d02fc6dd6517680e34186696970c2dccb9d375c9e9d263"],"state_sha256":"601a197c4fcbc14df98ab484939d5d4f8ae7f934232917a0400dfce7462bd404"}