{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IU6LRVV7MQPLYGDROWWLBJZFTT","short_pith_number":"pith:IU6LRVV7","canonical_record":{"source":{"id":"1710.01965","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-05T11:12:33Z","cross_cats_sorted":[],"title_canon_sha256":"8293a81c8d96a03fd635a44bba26bfcdc7d6f39d55c01be8e9a303f1113f5f0b","abstract_canon_sha256":"2274e538bf3e485b3e29849f476224999e2007ff173c993b4bb7986be68746e9"},"schema_version":"1.0"},"canonical_sha256":"453cb8d6bf641ebc187175acb0a7259cf5875e8dfa28c257bd5f8b35eb5906f1","source":{"kind":"arxiv","id":"1710.01965","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.01965","created_at":"2026-05-17T23:57:50Z"},{"alias_kind":"arxiv_version","alias_value":"1710.01965v4","created_at":"2026-05-17T23:57:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01965","created_at":"2026-05-17T23:57:50Z"},{"alias_kind":"pith_short_12","alias_value":"IU6LRVV7MQPL","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IU6LRVV7MQPLYGDR","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IU6LRVV7","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IU6LRVV7MQPLYGDROWWLBJZFTT","target":"record","payload":{"canonical_record":{"source":{"id":"1710.01965","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-05T11:12:33Z","cross_cats_sorted":[],"title_canon_sha256":"8293a81c8d96a03fd635a44bba26bfcdc7d6f39d55c01be8e9a303f1113f5f0b","abstract_canon_sha256":"2274e538bf3e485b3e29849f476224999e2007ff173c993b4bb7986be68746e9"},"schema_version":"1.0"},"canonical_sha256":"453cb8d6bf641ebc187175acb0a7259cf5875e8dfa28c257bd5f8b35eb5906f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:50.913045Z","signature_b64":"FcRpyVZxCfDJgnJf7iV+JxbCh4fcA5qEJwQCXOGOM07RCIUh8cqTTsM0HhlvR5w7t651JnLlZ4VNngDmrtAPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"453cb8d6bf641ebc187175acb0a7259cf5875e8dfa28c257bd5f8b35eb5906f1","last_reissued_at":"2026-05-17T23:57:50.912422Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:50.912422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.01965","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OiDqCRhCls7ctHArqm+26V5cS1Eh7q5pkajJh7WBTAhtMdvzhvW7JZ9l7LRGNMSor4XsvXJWuuZn7ufB0IFCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:08:08.721070Z"},"content_sha256":"2ffd4ec0c71614a476dd51b6e77a344e5381bc8c18fd41bbe990917fd1b546e9","schema_version":"1.0","event_id":"sha256:2ffd4ec0c71614a476dd51b6e77a344e5381bc8c18fd41bbe990917fd1b546e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IU6LRVV7MQPLYGDROWWLBJZFTT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Max flow vitality in general and $st$-planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andrea Ribichini, Giorgio Ausiello, Isabella Lari, Paolo Giulio Franciosa","submitted_at":"2017-10-05T11:12:33Z","abstract_excerpt":"The \\emph{vitality} of an arc/node of a graph with respect to the maximum flow between two fixed nodes $s$ and $t$ is defined as the reduction of the maximum flow caused by the removal of that arc/node. In this paper we address the issue of determining the vitality of arcs and/or nodes for the maximum flow problem. We show how to compute the vitality of all arcs in a general undirected graph by solving only $2(n-1)$ max flow instances and, In $st$-planar graphs (directed or undirected) we show how to compute the vitality of all arcs and all nodes in $O(n)$ worst-case time. Moreover, after dete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01965","kind":"arxiv","version":4},"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":"2026-05-17T23:57:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U8+fbJLmThIw1qsuQGk7X1LP/N88Aoua3CRqJ+Lqk7CfiB5jN+zPRFulkZ9BuSvy0mHAqpeJU0lzsXMsVlRWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:08:08.721439Z"},"content_sha256":"fce89da67c6081ec6934fae5ac1ff61371b77f0400cff052ad52a9cfabc1dc79","schema_version":"1.0","event_id":"sha256:fce89da67c6081ec6934fae5ac1ff61371b77f0400cff052ad52a9cfabc1dc79"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IU6LRVV7MQPLYGDROWWLBJZFTT/bundle.json","state_url":"https://pith.science/pith/IU6LRVV7MQPLYGDROWWLBJZFTT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IU6LRVV7MQPLYGDROWWLBJZFTT/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":"2026-06-03T16:08:08Z","links":{"resolver":"https://pith.science/pith/IU6LRVV7MQPLYGDROWWLBJZFTT","bundle":"https://pith.science/pith/IU6LRVV7MQPLYGDROWWLBJZFTT/bundle.json","state":"https://pith.science/pith/IU6LRVV7MQPLYGDROWWLBJZFTT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IU6LRVV7MQPLYGDROWWLBJZFTT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IU6LRVV7MQPLYGDROWWLBJZFTT","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":"2274e538bf3e485b3e29849f476224999e2007ff173c993b4bb7986be68746e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-05T11:12:33Z","title_canon_sha256":"8293a81c8d96a03fd635a44bba26bfcdc7d6f39d55c01be8e9a303f1113f5f0b"},"schema_version":"1.0","source":{"id":"1710.01965","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.01965","created_at":"2026-05-17T23:57:50Z"},{"alias_kind":"arxiv_version","alias_value":"1710.01965v4","created_at":"2026-05-17T23:57:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01965","created_at":"2026-05-17T23:57:50Z"},{"alias_kind":"pith_short_12","alias_value":"IU6LRVV7MQPL","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IU6LRVV7MQPLYGDR","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IU6LRVV7","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:fce89da67c6081ec6934fae5ac1ff61371b77f0400cff052ad52a9cfabc1dc79","target":"graph","created_at":"2026-05-17T23:57:50Z","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 \\emph{vitality} of an arc/node of a graph with respect to the maximum flow between two fixed nodes $s$ and $t$ is defined as the reduction of the maximum flow caused by the removal of that arc/node. In this paper we address the issue of determining the vitality of arcs and/or nodes for the maximum flow problem. We show how to compute the vitality of all arcs in a general undirected graph by solving only $2(n-1)$ max flow instances and, In $st$-planar graphs (directed or undirected) we show how to compute the vitality of all arcs and all nodes in $O(n)$ worst-case time. Moreover, after dete","authors_text":"Andrea Ribichini, Giorgio Ausiello, Isabella Lari, Paolo Giulio Franciosa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-05T11:12:33Z","title":"Max flow vitality in general and $st$-planar graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01965","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":"sha256:2ffd4ec0c71614a476dd51b6e77a344e5381bc8c18fd41bbe990917fd1b546e9","target":"record","created_at":"2026-05-17T23:57:50Z","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":"2274e538bf3e485b3e29849f476224999e2007ff173c993b4bb7986be68746e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-05T11:12:33Z","title_canon_sha256":"8293a81c8d96a03fd635a44bba26bfcdc7d6f39d55c01be8e9a303f1113f5f0b"},"schema_version":"1.0","source":{"id":"1710.01965","kind":"arxiv","version":4}},"canonical_sha256":"453cb8d6bf641ebc187175acb0a7259cf5875e8dfa28c257bd5f8b35eb5906f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"453cb8d6bf641ebc187175acb0a7259cf5875e8dfa28c257bd5f8b35eb5906f1","first_computed_at":"2026-05-17T23:57:50.912422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:50.912422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FcRpyVZxCfDJgnJf7iV+JxbCh4fcA5qEJwQCXOGOM07RCIUh8cqTTsM0HhlvR5w7t651JnLlZ4VNngDmrtAPDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:50.913045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.01965","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ffd4ec0c71614a476dd51b6e77a344e5381bc8c18fd41bbe990917fd1b546e9","sha256:fce89da67c6081ec6934fae5ac1ff61371b77f0400cff052ad52a9cfabc1dc79"],"state_sha256":"8b66c1eff207b207314eeec6e0d038119ebad4bdb0386f7006e5912e727fd2c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ejiqDfzhQG8R89BYnpRrjFVH1q+K9f5oqgEFiUDonR2eLX86o2+Orvpib2FISDVFXda6D3dBBNuCBiQ9fxN4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:08:08.723440Z","bundle_sha256":"3a0130083a2c8661a0002cb964ff016170fae895447709a4b2526529ad598aa7"}}