{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XARZJKSNTL77VOAU2PG3MVFYVE","short_pith_number":"pith:XARZJKSN","canonical_record":{"source":{"id":"1608.05729","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T20:21:07Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"26d7b93898a90e25074d2f230c3fe2ac029454f2dec4a95245a3302f2eebfb73","abstract_canon_sha256":"1387dd2cd364a6b917d879ff399aac7b812ec00a9a0446b75c8578e412473404"},"schema_version":"1.0"},"canonical_sha256":"b82394aa4d9afffab814d3cdb654b8a91c03ff8a0bb2e4f5b7ae480b15a1d0ad","source":{"kind":"arxiv","id":"1608.05729","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05729","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05729v2","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05729","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"pith_short_12","alias_value":"XARZJKSNTL77","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XARZJKSNTL77VOAU","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XARZJKSN","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XARZJKSNTL77VOAU2PG3MVFYVE","target":"record","payload":{"canonical_record":{"source":{"id":"1608.05729","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T20:21:07Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"26d7b93898a90e25074d2f230c3fe2ac029454f2dec4a95245a3302f2eebfb73","abstract_canon_sha256":"1387dd2cd364a6b917d879ff399aac7b812ec00a9a0446b75c8578e412473404"},"schema_version":"1.0"},"canonical_sha256":"b82394aa4d9afffab814d3cdb654b8a91c03ff8a0bb2e4f5b7ae480b15a1d0ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:09.637371Z","signature_b64":"6RQpLAOCtRahLjVojFQ+3oOPar0uZHVrVBgufCI2yKEzXpg5ctAJXRw/qUodhJQ0+cCnGKEXgR18dP3QxDJABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b82394aa4d9afffab814d3cdb654b8a91c03ff8a0bb2e4f5b7ae480b15a1d0ad","last_reissued_at":"2026-05-18T00:36:09.636719Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:09.636719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.05729","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":"2026-05-18T00:36:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e3q9a99Z0FRtdKFV3tu6LzeFNjqq+9aD8nmTppLJ0HSre8/igiGuTyg81F0Fo8bGelJlycEY6XAPgsTpI2guAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:15:13.727407Z"},"content_sha256":"23c4d83869f608af60e2302f1d0fcd455739fed2c60e95a32eb769c9f12908b0","schema_version":"1.0","event_id":"sha256:23c4d83869f608af60e2302f1d0fcd455739fed2c60e95a32eb769c9f12908b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XARZJKSNTL77VOAU2PG3MVFYVE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Supermodularity in Unweighted Graph Opitimization III: Highly-connected Digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andr\\'as Frank, Krist\\'of B\\'erczi","submitted_at":"2016-08-19T20:21:07Z","abstract_excerpt":"By generalizing a recent result of Hong, Liu, and Lai on characterizing the degree-sequences of simple strongly connected directed graphs, a characterization is provided for degree-sequences of simple $k$-node-connected digraphs. More generally, we solve the directed node-connectivity augmentation problem when the augmented digraph is degree-specified and simple. As for edge-connectivity augmentation, we solve the special case when the edge-connectivity is to be increased by one and the augmenting digraph must be simple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05729","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":""},"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":"2026-05-18T00:36:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7H7hFbORFnQJoFfE2P+P1LRIeGawBfjKjHgN/HxfltYJ5P4jzgPQxfaPw8TrMbA0JywsGQ0mKvSZRLoekM25AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:15:13.727757Z"},"content_sha256":"b9d194c31704fef10e5b0b9eea6a90ea81a53fd7a0b83f6c8dd662e68489301e","schema_version":"1.0","event_id":"sha256:b9d194c31704fef10e5b0b9eea6a90ea81a53fd7a0b83f6c8dd662e68489301e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XARZJKSNTL77VOAU2PG3MVFYVE/bundle.json","state_url":"https://pith.science/pith/XARZJKSNTL77VOAU2PG3MVFYVE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XARZJKSNTL77VOAU2PG3MVFYVE/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":"2026-06-27T12:15:13Z","links":{"resolver":"https://pith.science/pith/XARZJKSNTL77VOAU2PG3MVFYVE","bundle":"https://pith.science/pith/XARZJKSNTL77VOAU2PG3MVFYVE/bundle.json","state":"https://pith.science/pith/XARZJKSNTL77VOAU2PG3MVFYVE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XARZJKSNTL77VOAU2PG3MVFYVE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XARZJKSNTL77VOAU2PG3MVFYVE","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":"1387dd2cd364a6b917d879ff399aac7b812ec00a9a0446b75c8578e412473404","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T20:21:07Z","title_canon_sha256":"26d7b93898a90e25074d2f230c3fe2ac029454f2dec4a95245a3302f2eebfb73"},"schema_version":"1.0","source":{"id":"1608.05729","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05729","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05729v2","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05729","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"pith_short_12","alias_value":"XARZJKSNTL77","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XARZJKSNTL77VOAU","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XARZJKSN","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:b9d194c31704fef10e5b0b9eea6a90ea81a53fd7a0b83f6c8dd662e68489301e","target":"graph","created_at":"2026-05-18T00:36:09Z","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":"By generalizing a recent result of Hong, Liu, and Lai on characterizing the degree-sequences of simple strongly connected directed graphs, a characterization is provided for degree-sequences of simple $k$-node-connected digraphs. More generally, we solve the directed node-connectivity augmentation problem when the augmented digraph is degree-specified and simple. As for edge-connectivity augmentation, we solve the special case when the edge-connectivity is to be increased by one and the augmenting digraph must be simple.","authors_text":"Andr\\'as Frank, Krist\\'of B\\'erczi","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T20:21:07Z","title":"Supermodularity in Unweighted Graph Opitimization III: Highly-connected Digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05729","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":"sha256:23c4d83869f608af60e2302f1d0fcd455739fed2c60e95a32eb769c9f12908b0","target":"record","created_at":"2026-05-18T00:36:09Z","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":"1387dd2cd364a6b917d879ff399aac7b812ec00a9a0446b75c8578e412473404","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T20:21:07Z","title_canon_sha256":"26d7b93898a90e25074d2f230c3fe2ac029454f2dec4a95245a3302f2eebfb73"},"schema_version":"1.0","source":{"id":"1608.05729","kind":"arxiv","version":2}},"canonical_sha256":"b82394aa4d9afffab814d3cdb654b8a91c03ff8a0bb2e4f5b7ae480b15a1d0ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b82394aa4d9afffab814d3cdb654b8a91c03ff8a0bb2e4f5b7ae480b15a1d0ad","first_computed_at":"2026-05-18T00:36:09.636719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:09.636719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6RQpLAOCtRahLjVojFQ+3oOPar0uZHVrVBgufCI2yKEzXpg5ctAJXRw/qUodhJQ0+cCnGKEXgR18dP3QxDJABw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:09.637371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05729","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23c4d83869f608af60e2302f1d0fcd455739fed2c60e95a32eb769c9f12908b0","sha256:b9d194c31704fef10e5b0b9eea6a90ea81a53fd7a0b83f6c8dd662e68489301e"],"state_sha256":"3f7aaa42dd078fce097b9eefcfb25acdab2670ee19cf2aa64edddce67dfd2a0e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dJzltFhW1P+vo17Vscowc6AwP5LNIsMmD5Mb3sxq1tcS7+/izbXfunEz+o8ETubWAHFNWJcFcCJJtwFWqFrIAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T12:15:13.729675Z","bundle_sha256":"91c60d8f6f3ee8e99d23121c6df5d2ad8bb9bc4f3d911801f1ecf4c20386229e"}}