{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FCQZI3AHW4LUSVZX3C52MO7QU2","short_pith_number":"pith:FCQZI3AH","canonical_record":{"source":{"id":"1104.4779","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-04-25T19:49:40Z","cross_cats_sorted":[],"title_canon_sha256":"d3834eca93ccab9f32a81f8814a3409ec266ffdd5eded47c6e75e1d7154cb0ec","abstract_canon_sha256":"39f62dbf32a5613a29f048880b5e787c1d1dbe7b37b6a0f1cc81bebd284bb637"},"schema_version":"1.0"},"canonical_sha256":"28a1946c07b717495737d8bba63bf0a6880d79245262454f21e80d7337faaa1b","source":{"kind":"arxiv","id":"1104.4779","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4779","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4779v3","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4779","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"FCQZI3AHW4LU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FCQZI3AHW4LUSVZX","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FCQZI3AH","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FCQZI3AHW4LUSVZX3C52MO7QU2","target":"record","payload":{"canonical_record":{"source":{"id":"1104.4779","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-04-25T19:49:40Z","cross_cats_sorted":[],"title_canon_sha256":"d3834eca93ccab9f32a81f8814a3409ec266ffdd5eded47c6e75e1d7154cb0ec","abstract_canon_sha256":"39f62dbf32a5613a29f048880b5e787c1d1dbe7b37b6a0f1cc81bebd284bb637"},"schema_version":"1.0"},"canonical_sha256":"28a1946c07b717495737d8bba63bf0a6880d79245262454f21e80d7337faaa1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:09.398123Z","signature_b64":"wFFMAXfL1ZOsapK0tVgAufSPF/igcvsCxJatLxfrp/tZFLsCRQ1ovuC/DiyaOn3Rdl+rZiZgtiwW7/Bu7OqkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28a1946c07b717495737d8bba63bf0a6880d79245262454f21e80d7337faaa1b","last_reissued_at":"2026-05-18T02:39:09.397543Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:09.397543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.4779","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":"2026-05-18T02:39:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7h7gaN1r0WB9IKLmk/Z5PS9l3CP/LxTJrpWko181eedMPM8OZAIRYpbV2KHAEM77L5wYzGTVoL8qNMBxa2csBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:09:22.300305Z"},"content_sha256":"9b963507776462c24a32635bfd9e69b6caf721b1e0b0eb24933920bfcc292029","schema_version":"1.0","event_id":"sha256:9b963507776462c24a32635bfd9e69b6caf721b1e0b0eb24933920bfcc292029"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FCQZI3AHW4LUSVZX3C52MO7QU2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Computational Complexity of Disconnected Cut and 2K2-Partition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Barnaby Martin, Daniel Paulusma","submitted_at":"2011-04-25T19:49:40Z","abstract_excerpt":"For a connected graph G=(V,E), a subset U of V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. We show that the problem to test whether a graph has a disconnected cut is NP-complete. This problem is polynomially equivalent to the following problems: testing if a graph has a 2K2-partition, testing if a graph allows a vertex-surjective homomorphism to the reflexive 4-cycle and testing if a graph has a spanning subgraph that consists of at most two bicliques. Hence, as an immediate consequence, these three decision problems are NP-com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4779","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":"2026-05-18T02:39:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fn5DmWgI8RdNi5cmzULEKsHIHwzZwC2AKj9ZInz358yD+iKEpHTKYXUV8CQ2yVFZ5zHkDfYPaV2s1aZqi0SaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:09:22.300675Z"},"content_sha256":"a111d531fbd2e4b81158759824adb8856de6fbacff0bf9a88dcb4874341518a7","schema_version":"1.0","event_id":"sha256:a111d531fbd2e4b81158759824adb8856de6fbacff0bf9a88dcb4874341518a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FCQZI3AHW4LUSVZX3C52MO7QU2/bundle.json","state_url":"https://pith.science/pith/FCQZI3AHW4LUSVZX3C52MO7QU2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FCQZI3AHW4LUSVZX3C52MO7QU2/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":"2026-06-03T16:09:22Z","links":{"resolver":"https://pith.science/pith/FCQZI3AHW4LUSVZX3C52MO7QU2","bundle":"https://pith.science/pith/FCQZI3AHW4LUSVZX3C52MO7QU2/bundle.json","state":"https://pith.science/pith/FCQZI3AHW4LUSVZX3C52MO7QU2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FCQZI3AHW4LUSVZX3C52MO7QU2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FCQZI3AHW4LUSVZX3C52MO7QU2","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":"39f62dbf32a5613a29f048880b5e787c1d1dbe7b37b6a0f1cc81bebd284bb637","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-04-25T19:49:40Z","title_canon_sha256":"d3834eca93ccab9f32a81f8814a3409ec266ffdd5eded47c6e75e1d7154cb0ec"},"schema_version":"1.0","source":{"id":"1104.4779","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4779","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4779v3","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4779","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"FCQZI3AHW4LU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FCQZI3AHW4LUSVZX","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FCQZI3AH","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:a111d531fbd2e4b81158759824adb8856de6fbacff0bf9a88dcb4874341518a7","target":"graph","created_at":"2026-05-18T02:39:09Z","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":"For a connected graph G=(V,E), a subset U of V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. We show that the problem to test whether a graph has a disconnected cut is NP-complete. This problem is polynomially equivalent to the following problems: testing if a graph has a 2K2-partition, testing if a graph allows a vertex-surjective homomorphism to the reflexive 4-cycle and testing if a graph has a spanning subgraph that consists of at most two bicliques. Hence, as an immediate consequence, these three decision problems are NP-com","authors_text":"Barnaby Martin, Daniel Paulusma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-04-25T19:49:40Z","title":"The Computational Complexity of Disconnected Cut and 2K2-Partition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4779","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":"sha256:9b963507776462c24a32635bfd9e69b6caf721b1e0b0eb24933920bfcc292029","target":"record","created_at":"2026-05-18T02:39:09Z","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":"39f62dbf32a5613a29f048880b5e787c1d1dbe7b37b6a0f1cc81bebd284bb637","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-04-25T19:49:40Z","title_canon_sha256":"d3834eca93ccab9f32a81f8814a3409ec266ffdd5eded47c6e75e1d7154cb0ec"},"schema_version":"1.0","source":{"id":"1104.4779","kind":"arxiv","version":3}},"canonical_sha256":"28a1946c07b717495737d8bba63bf0a6880d79245262454f21e80d7337faaa1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28a1946c07b717495737d8bba63bf0a6880d79245262454f21e80d7337faaa1b","first_computed_at":"2026-05-18T02:39:09.397543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:09.397543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wFFMAXfL1ZOsapK0tVgAufSPF/igcvsCxJatLxfrp/tZFLsCRQ1ovuC/DiyaOn3Rdl+rZiZgtiwW7/Bu7OqkCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:09.398123Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4779","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b963507776462c24a32635bfd9e69b6caf721b1e0b0eb24933920bfcc292029","sha256:a111d531fbd2e4b81158759824adb8856de6fbacff0bf9a88dcb4874341518a7"],"state_sha256":"f38e862e0b334462cb02ff305a1941fd04e7511819d1db9204033040995d9d22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"62Pg07bz4GfuL9tIxCeoTir39VOy0RWGgRbgNb43MWnNnCvOH6vw3UXG7PEaUlAoYx68tkD2MLmgw7oO+ai4Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:09:22.302600Z","bundle_sha256":"002adf4d950dd06e03c4686f6e630bbda305b07722d3b3583535006de0143858"}}