{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4EF7KQC5WKTL5J2C2INSCBYAQM","short_pith_number":"pith:4EF7KQC5","canonical_record":{"source":{"id":"1802.10189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-27T22:22:20Z","cross_cats_sorted":[],"title_canon_sha256":"5e6824b5e93b3cf7adf5de0d6c7566197764e81ffe1c591ae1a2663c9bf23bcb","abstract_canon_sha256":"826477179e7962c4baa4ff4fa5d643926945e45806f2090194dae3c41bc4f4e2"},"schema_version":"1.0"},"canonical_sha256":"e10bf5405db2a6bea742d21b2107008331eaf7b0dca5a4e927e431e74710abcb","source":{"kind":"arxiv","id":"1802.10189","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.10189","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"1802.10189v1","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.10189","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"4EF7KQC5WKTL","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4EF7KQC5WKTL5J2C","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4EF7KQC5","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4EF7KQC5WKTL5J2C2INSCBYAQM","target":"record","payload":{"canonical_record":{"source":{"id":"1802.10189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-27T22:22:20Z","cross_cats_sorted":[],"title_canon_sha256":"5e6824b5e93b3cf7adf5de0d6c7566197764e81ffe1c591ae1a2663c9bf23bcb","abstract_canon_sha256":"826477179e7962c4baa4ff4fa5d643926945e45806f2090194dae3c41bc4f4e2"},"schema_version":"1.0"},"canonical_sha256":"e10bf5405db2a6bea742d21b2107008331eaf7b0dca5a4e927e431e74710abcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:17.856140Z","signature_b64":"MZzCShpEZxeDBaZ2yCbPR4jsR9Z2y7jPAJB8PDdTIrJW0sHkMqtp2qvVk5cf0O4tM4wpStvNNvFtcaL2zv6DBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e10bf5405db2a6bea742d21b2107008331eaf7b0dca5a4e927e431e74710abcb","last_reissued_at":"2026-05-18T00:22:17.855407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:17.855407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.10189","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xaVgyNTEq+8mSa9HHeK1L5HBKh3KnkGRbATG/Amh3+jvAuzq6eqGpWnOO0mIFknH2SKaOnqLOpeYfpe9AMnoBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:12:41.335350Z"},"content_sha256":"05a51aa95ec7055b2a027cf8a6f0a0bdbffe484ad570029757463dc63288a8a8","schema_version":"1.0","event_id":"sha256:05a51aa95ec7055b2a027cf8a6f0a0bdbffe484ad570029757463dc63288a8a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4EF7KQC5WKTL5J2C2INSCBYAQM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Incremental Strong Connectivity and 2-Connectivity in Directed Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Giuseppe F. Italiano, Loukas Georgiadis, Nikos Parotsidis","submitted_at":"2018-02-27T22:22:20Z","abstract_excerpt":"In this paper, we present new incremental algorithms for maintaining data structures that represent all connectivity cuts of size one in directed graphs (digraphs), and the strongly connected components that result by the removal of each of those cuts. We give a conditional lower bound that provides evidence that our algorithms may be tight up to sub-polynomial factors. As an additional result, with our approach we can also maintain dynamically the $2$-vertex-connected components of a digraph during any sequence of edge insertions in a total of $O(mn)$ time. This matches the bounds for the inc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10189","kind":"arxiv","version":1},"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":"2026-05-18T00:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5+8bNY+atNT472nlF4/T/JWNQvEG//2VXf76xOnFd2H+T0FNpg8gjOsarRzXCZyouxmyap2Bg1RlxG5B+ZITDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:12:41.335715Z"},"content_sha256":"6e19b3c83fff6e4eba7b096a6f73d4e85baa948ec6f0577ef0dc500b3d438b95","schema_version":"1.0","event_id":"sha256:6e19b3c83fff6e4eba7b096a6f73d4e85baa948ec6f0577ef0dc500b3d438b95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4EF7KQC5WKTL5J2C2INSCBYAQM/bundle.json","state_url":"https://pith.science/pith/4EF7KQC5WKTL5J2C2INSCBYAQM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4EF7KQC5WKTL5J2C2INSCBYAQM/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":"2026-06-23T15:12:41Z","links":{"resolver":"https://pith.science/pith/4EF7KQC5WKTL5J2C2INSCBYAQM","bundle":"https://pith.science/pith/4EF7KQC5WKTL5J2C2INSCBYAQM/bundle.json","state":"https://pith.science/pith/4EF7KQC5WKTL5J2C2INSCBYAQM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4EF7KQC5WKTL5J2C2INSCBYAQM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4EF7KQC5WKTL5J2C2INSCBYAQM","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":"826477179e7962c4baa4ff4fa5d643926945e45806f2090194dae3c41bc4f4e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-27T22:22:20Z","title_canon_sha256":"5e6824b5e93b3cf7adf5de0d6c7566197764e81ffe1c591ae1a2663c9bf23bcb"},"schema_version":"1.0","source":{"id":"1802.10189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.10189","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"1802.10189v1","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.10189","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"4EF7KQC5WKTL","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4EF7KQC5WKTL5J2C","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4EF7KQC5","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:6e19b3c83fff6e4eba7b096a6f73d4e85baa948ec6f0577ef0dc500b3d438b95","target":"graph","created_at":"2026-05-18T00:22:17Z","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":"In this paper, we present new incremental algorithms for maintaining data structures that represent all connectivity cuts of size one in directed graphs (digraphs), and the strongly connected components that result by the removal of each of those cuts. We give a conditional lower bound that provides evidence that our algorithms may be tight up to sub-polynomial factors. As an additional result, with our approach we can also maintain dynamically the $2$-vertex-connected components of a digraph during any sequence of edge insertions in a total of $O(mn)$ time. This matches the bounds for the inc","authors_text":"Giuseppe F. Italiano, Loukas Georgiadis, Nikos Parotsidis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-27T22:22:20Z","title":"Incremental Strong Connectivity and 2-Connectivity in Directed Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10189","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":"sha256:05a51aa95ec7055b2a027cf8a6f0a0bdbffe484ad570029757463dc63288a8a8","target":"record","created_at":"2026-05-18T00:22:17Z","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":"826477179e7962c4baa4ff4fa5d643926945e45806f2090194dae3c41bc4f4e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-27T22:22:20Z","title_canon_sha256":"5e6824b5e93b3cf7adf5de0d6c7566197764e81ffe1c591ae1a2663c9bf23bcb"},"schema_version":"1.0","source":{"id":"1802.10189","kind":"arxiv","version":1}},"canonical_sha256":"e10bf5405db2a6bea742d21b2107008331eaf7b0dca5a4e927e431e74710abcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e10bf5405db2a6bea742d21b2107008331eaf7b0dca5a4e927e431e74710abcb","first_computed_at":"2026-05-18T00:22:17.855407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:17.855407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MZzCShpEZxeDBaZ2yCbPR4jsR9Z2y7jPAJB8PDdTIrJW0sHkMqtp2qvVk5cf0O4tM4wpStvNNvFtcaL2zv6DBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:17.856140Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.10189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05a51aa95ec7055b2a027cf8a6f0a0bdbffe484ad570029757463dc63288a8a8","sha256:6e19b3c83fff6e4eba7b096a6f73d4e85baa948ec6f0577ef0dc500b3d438b95"],"state_sha256":"fc8d1de6b6e02b8c080c062f8bf08608e6c636591f0aadb78f09131603e7eef6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H525mQdKYAu5ZdAxSUd4xsQwTXtdWv+er1gskPUMmo112ELOtc2ziRNGKbp28SkAlmnttXHASiEQX91DBjInCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:12:41.337787Z","bundle_sha256":"bba134e9f67482dc1d5e655c2a2c10fc7281dd75240dcce3f41052ebab49451d"}}