{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5SCATVMVLTWWLAQNORSP4H2QO4","short_pith_number":"pith:5SCATVMV","canonical_record":{"source":{"id":"1502.07659","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-26T18:10:43Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"3da2244dfe79d8346d13c7aa30b1a369481580c9f63072a356c7da28a15f1c26","abstract_canon_sha256":"4b5784ddb6cd4496f113ef6d017de0589ebb2b665dfcfab77671fb3d5f46e577"},"schema_version":"1.0"},"canonical_sha256":"ec8409d5955ced65820d7464fe1f507733553d967e110fb9ecb5441b9e7256e8","source":{"kind":"arxiv","id":"1502.07659","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07659","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07659v2","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07659","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"5SCATVMVLTWW","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5SCATVMVLTWWLAQN","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5SCATVMV","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5SCATVMVLTWWLAQNORSP4H2QO4","target":"record","payload":{"canonical_record":{"source":{"id":"1502.07659","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-26T18:10:43Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"3da2244dfe79d8346d13c7aa30b1a369481580c9f63072a356c7da28a15f1c26","abstract_canon_sha256":"4b5784ddb6cd4496f113ef6d017de0589ebb2b665dfcfab77671fb3d5f46e577"},"schema_version":"1.0"},"canonical_sha256":"ec8409d5955ced65820d7464fe1f507733553d967e110fb9ecb5441b9e7256e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:30.316626Z","signature_b64":"xrr6zdaZFSoIrfRB0PRVIMOYSC/QAr/Sr1Chv2Fi+mqr/xdDFBApUwIII0DXzGDJrNyZEcuoDd2pZJWHgWhWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec8409d5955ced65820d7464fe1f507733553d967e110fb9ecb5441b9e7256e8","last_reissued_at":"2026-05-18T01:04:30.315978Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:30.315978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.07659","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":"2026-05-18T01:04:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XC9/EliDPR0NiPoUkVZRtkEzuxZMVGIrfop5sBy9VhU+U/4CCUmoRFAAUATIA/n4oP6r3zS1S8FBkUqV5yFkCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:35:49.267808Z"},"content_sha256":"2c9b039eca5052428cf829dc3fd2f91f32fb741e98f720894551ad513eb68a7b","schema_version":"1.0","event_id":"sha256:2c9b039eca5052428cf829dc3fd2f91f32fb741e98f720894551ad513eb68a7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5SCATVMVLTWWLAQNORSP4H2QO4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the complexity of computing the $k$-restricted edge-connectivity of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Ignasi Sau, Luis Pedro Montejano","submitted_at":"2015-02-26T18:10:43Z","abstract_excerpt":"The \\emph{$k$-restricted edge-connectivity} of a graph $G$, denoted by $\\lambda_k(G)$, is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least $k$ vertices. This graph invariant, which can be seen as a generalization of a minimum edge-cut, has been extensively studied from a combinatorial point of view. However, very little is known about the complexity of computing $\\lambda_k(G)$. Very recently, in the parameterized complexity community the notion of \\emph{good edge separation} of a graph has been defined, which happens to b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07659","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":"2026-05-18T01:04:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z64MQVeWsdqEw+m/cs45meN+6i/VWboirIodIc44Z6FJzCT3LspRNoOE8JB79MV+ned2YxbxhtEzFrCgiN67BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:35:49.268163Z"},"content_sha256":"acb7ddb4653c21715fe3ea67c85fe2431002eb4307c73ff5a9bc306bc302054a","schema_version":"1.0","event_id":"sha256:acb7ddb4653c21715fe3ea67c85fe2431002eb4307c73ff5a9bc306bc302054a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5SCATVMVLTWWLAQNORSP4H2QO4/bundle.json","state_url":"https://pith.science/pith/5SCATVMVLTWWLAQNORSP4H2QO4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5SCATVMVLTWWLAQNORSP4H2QO4/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":"2026-05-31T08:35:49Z","links":{"resolver":"https://pith.science/pith/5SCATVMVLTWWLAQNORSP4H2QO4","bundle":"https://pith.science/pith/5SCATVMVLTWWLAQNORSP4H2QO4/bundle.json","state":"https://pith.science/pith/5SCATVMVLTWWLAQNORSP4H2QO4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5SCATVMVLTWWLAQNORSP4H2QO4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5SCATVMVLTWWLAQNORSP4H2QO4","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":"4b5784ddb6cd4496f113ef6d017de0589ebb2b665dfcfab77671fb3d5f46e577","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-26T18:10:43Z","title_canon_sha256":"3da2244dfe79d8346d13c7aa30b1a369481580c9f63072a356c7da28a15f1c26"},"schema_version":"1.0","source":{"id":"1502.07659","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07659","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07659v2","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07659","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"5SCATVMVLTWW","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5SCATVMVLTWWLAQN","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5SCATVMV","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:acb7ddb4653c21715fe3ea67c85fe2431002eb4307c73ff5a9bc306bc302054a","target":"graph","created_at":"2026-05-18T01:04:30Z","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{$k$-restricted edge-connectivity} of a graph $G$, denoted by $\\lambda_k(G)$, is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least $k$ vertices. This graph invariant, which can be seen as a generalization of a minimum edge-cut, has been extensively studied from a combinatorial point of view. However, very little is known about the complexity of computing $\\lambda_k(G)$. Very recently, in the parameterized complexity community the notion of \\emph{good edge separation} of a graph has been defined, which happens to b","authors_text":"Ignasi Sau, Luis Pedro Montejano","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-26T18:10:43Z","title":"On the complexity of computing the $k$-restricted edge-connectivity of a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07659","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":"sha256:2c9b039eca5052428cf829dc3fd2f91f32fb741e98f720894551ad513eb68a7b","target":"record","created_at":"2026-05-18T01:04:30Z","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":"4b5784ddb6cd4496f113ef6d017de0589ebb2b665dfcfab77671fb3d5f46e577","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-26T18:10:43Z","title_canon_sha256":"3da2244dfe79d8346d13c7aa30b1a369481580c9f63072a356c7da28a15f1c26"},"schema_version":"1.0","source":{"id":"1502.07659","kind":"arxiv","version":2}},"canonical_sha256":"ec8409d5955ced65820d7464fe1f507733553d967e110fb9ecb5441b9e7256e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec8409d5955ced65820d7464fe1f507733553d967e110fb9ecb5441b9e7256e8","first_computed_at":"2026-05-18T01:04:30.315978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:30.315978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xrr6zdaZFSoIrfRB0PRVIMOYSC/QAr/Sr1Chv2Fi+mqr/xdDFBApUwIII0DXzGDJrNyZEcuoDd2pZJWHgWhWDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:30.316626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.07659","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c9b039eca5052428cf829dc3fd2f91f32fb741e98f720894551ad513eb68a7b","sha256:acb7ddb4653c21715fe3ea67c85fe2431002eb4307c73ff5a9bc306bc302054a"],"state_sha256":"1d2716967926f023f236e5e9ad279740f5db728f7866d67bb5e9c0cca6865f86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L23E04j7Al3htJ+sTJbWF+JroVhzIzkohPQNXwhh2jwJ8+1stfbfTPA1XeVZmbrRDKPTxDXdhxIRA4r/8OZzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:35:49.270482Z","bundle_sha256":"60b1b62c51626eff6fe0d7c603aed3edd2dcbd1273cffab60459c6cc6c281e73"}}