{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BYWZR2Y4QEVBWBNMVLMVZEBL2I","short_pith_number":"pith:BYWZR2Y4","canonical_record":{"source":{"id":"1305.1089","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-06T05:32:01Z","cross_cats_sorted":[],"title_canon_sha256":"90ef44d14a9f7a6cafba791494854b5f64aea450fce147589b0c413822f10faf","abstract_canon_sha256":"892f59f3a5bb28aeb27aab8d88ef24f64506a561156494b63e5a3fd64ef19758"},"schema_version":"1.0"},"canonical_sha256":"0e2d98eb1c812a1b05acaad95c902bd20ef6b7c6a0cd9945d303d0c2fdc8cf19","source":{"kind":"arxiv","id":"1305.1089","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1089","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1089v3","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1089","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"BYWZR2Y4QEVB","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BYWZR2Y4QEVBWBNM","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BYWZR2Y4","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BYWZR2Y4QEVBWBNMVLMVZEBL2I","target":"record","payload":{"canonical_record":{"source":{"id":"1305.1089","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-06T05:32:01Z","cross_cats_sorted":[],"title_canon_sha256":"90ef44d14a9f7a6cafba791494854b5f64aea450fce147589b0c413822f10faf","abstract_canon_sha256":"892f59f3a5bb28aeb27aab8d88ef24f64506a561156494b63e5a3fd64ef19758"},"schema_version":"1.0"},"canonical_sha256":"0e2d98eb1c812a1b05acaad95c902bd20ef6b7c6a0cd9945d303d0c2fdc8cf19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:36.043747Z","signature_b64":"bEy/Jffd9Iv4n1IE5or47TnLV2FU4TCjq2Xsj2oC90DS9TwgY22CQDoP6INFHbG09CV7yedwndcNxmc5h2cTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e2d98eb1c812a1b05acaad95c902bd20ef6b7c6a0cd9945d303d0c2fdc8cf19","last_reissued_at":"2026-05-18T01:34:36.043076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:36.043076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.1089","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"brkARy/b4HaMp88r5Alx9jsn2cQ4qJVjv0vlBJ5FfMWRz5mXjSU6mYge042hFT6S7SMuyMUV9MSQxfQpSBhpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:31:16.069446Z"},"content_sha256":"1d398e6f7a85b961161cdfc774e278d7d1d36826140bf73a3569e974a64dd23c","schema_version":"1.0","event_id":"sha256:1d398e6f7a85b961161cdfc774e278d7d1d36826140bf73a3569e974a64dd23c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BYWZR2Y4QEVBWBNMVLMVZEBL2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graphs with large generalized (edge-)connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xueliang Li, Yaping Mao","submitted_at":"2013-05-06T05:32:01Z","abstract_excerpt":"The generalized $k$-connectivity $\\kappa_k(G)$ of a graph $G$, introduced by Hager in 1985, is a nice generalization of the classical connectivity. Recently, as a natural counterpart, we proposed the concept of generalized $k$-edge-connectivity $\\lambda_k(G)$. In this paper, graphs of order $n$ such that $\\kappa_k(G)=n-\\frac{k}{2}-1$ and $\\lambda_k(G)=n-\\frac{k}{2}-1$ for even $k$ are characterized."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1089","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:34:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y81JONyc5QbtOwwUf0KxrlrJl9N5loJfXXfMbur/Ug+6U24nlpcuArGFzVu6zAN/GffVLwC0cPxPxexSSO+mDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:31:16.069789Z"},"content_sha256":"8e009fa3c2c7e73e5abc3b446e4b51db2468e74225bb63a7650eda95c8f745b8","schema_version":"1.0","event_id":"sha256:8e009fa3c2c7e73e5abc3b446e4b51db2468e74225bb63a7650eda95c8f745b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BYWZR2Y4QEVBWBNMVLMVZEBL2I/bundle.json","state_url":"https://pith.science/pith/BYWZR2Y4QEVBWBNMVLMVZEBL2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BYWZR2Y4QEVBWBNMVLMVZEBL2I/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":"2026-06-01T15:31:16Z","links":{"resolver":"https://pith.science/pith/BYWZR2Y4QEVBWBNMVLMVZEBL2I","bundle":"https://pith.science/pith/BYWZR2Y4QEVBWBNMVLMVZEBL2I/bundle.json","state":"https://pith.science/pith/BYWZR2Y4QEVBWBNMVLMVZEBL2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BYWZR2Y4QEVBWBNMVLMVZEBL2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BYWZR2Y4QEVBWBNMVLMVZEBL2I","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":"892f59f3a5bb28aeb27aab8d88ef24f64506a561156494b63e5a3fd64ef19758","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-06T05:32:01Z","title_canon_sha256":"90ef44d14a9f7a6cafba791494854b5f64aea450fce147589b0c413822f10faf"},"schema_version":"1.0","source":{"id":"1305.1089","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1089","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1089v3","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1089","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"BYWZR2Y4QEVB","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BYWZR2Y4QEVBWBNM","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BYWZR2Y4","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:8e009fa3c2c7e73e5abc3b446e4b51db2468e74225bb63a7650eda95c8f745b8","target":"graph","created_at":"2026-05-18T01:34:36Z","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 generalized $k$-connectivity $\\kappa_k(G)$ of a graph $G$, introduced by Hager in 1985, is a nice generalization of the classical connectivity. Recently, as a natural counterpart, we proposed the concept of generalized $k$-edge-connectivity $\\lambda_k(G)$. In this paper, graphs of order $n$ such that $\\kappa_k(G)=n-\\frac{k}{2}-1$ and $\\lambda_k(G)=n-\\frac{k}{2}-1$ for even $k$ are characterized.","authors_text":"Xueliang Li, Yaping Mao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-06T05:32:01Z","title":"Graphs with large generalized (edge-)connectivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1089","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":"sha256:1d398e6f7a85b961161cdfc774e278d7d1d36826140bf73a3569e974a64dd23c","target":"record","created_at":"2026-05-18T01:34:36Z","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":"892f59f3a5bb28aeb27aab8d88ef24f64506a561156494b63e5a3fd64ef19758","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-06T05:32:01Z","title_canon_sha256":"90ef44d14a9f7a6cafba791494854b5f64aea450fce147589b0c413822f10faf"},"schema_version":"1.0","source":{"id":"1305.1089","kind":"arxiv","version":3}},"canonical_sha256":"0e2d98eb1c812a1b05acaad95c902bd20ef6b7c6a0cd9945d303d0c2fdc8cf19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e2d98eb1c812a1b05acaad95c902bd20ef6b7c6a0cd9945d303d0c2fdc8cf19","first_computed_at":"2026-05-18T01:34:36.043076Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:36.043076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bEy/Jffd9Iv4n1IE5or47TnLV2FU4TCjq2Xsj2oC90DS9TwgY22CQDoP6INFHbG09CV7yedwndcNxmc5h2cTDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:36.043747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1089","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d398e6f7a85b961161cdfc774e278d7d1d36826140bf73a3569e974a64dd23c","sha256:8e009fa3c2c7e73e5abc3b446e4b51db2468e74225bb63a7650eda95c8f745b8"],"state_sha256":"1a39fabe7f680cf17873d336f5024275bf054d26cf4fd551a98a0ebc1e3e5a81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1p0EQFrEMXSSLSCGzacI2eJXF0Pz5S2aHKfz7EgUZ6Wii0nHRwg9l9r1HwJHjY6EJY2kOF+BD9NRs3p7PEsLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T15:31:16.071703Z","bundle_sha256":"599508fc0277eb78753f675a92987d9c76ab4e6f5c90efaa8de6424edffbbd1c"}}