{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:K7DY247NRNOYEJLZ5JAFTYOG7O","short_pith_number":"pith:K7DY247N","canonical_record":{"source":{"id":"1102.5441","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-02-26T20:07:27Z","cross_cats_sorted":[],"title_canon_sha256":"7402638c42b111e087424a804ae2572f5242e29ba1c3a94315d8c4ad9f1a8f8c","abstract_canon_sha256":"496fbd26f3bf41e162c14ceae39d9167dfe0a699d28494625179e1328acbb617"},"schema_version":"1.0"},"canonical_sha256":"57c78d73ed8b5d822579ea4059e1c6fbae3e14ed7f9f23db8a9096c42b6e5757","source":{"kind":"arxiv","id":"1102.5441","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5441","created_at":"2026-05-18T04:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5441v2","created_at":"2026-05-18T04:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5441","created_at":"2026-05-18T04:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"K7DY247NRNOY","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K7DY247NRNOYEJLZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K7DY247N","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:K7DY247NRNOYEJLZ5JAFTYOG7O","target":"record","payload":{"canonical_record":{"source":{"id":"1102.5441","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-02-26T20:07:27Z","cross_cats_sorted":[],"title_canon_sha256":"7402638c42b111e087424a804ae2572f5242e29ba1c3a94315d8c4ad9f1a8f8c","abstract_canon_sha256":"496fbd26f3bf41e162c14ceae39d9167dfe0a699d28494625179e1328acbb617"},"schema_version":"1.0"},"canonical_sha256":"57c78d73ed8b5d822579ea4059e1c6fbae3e14ed7f9f23db8a9096c42b6e5757","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:17.432588Z","signature_b64":"wjTnyGQYw6bjlqySXBblBnbBd9EbQMRuYHbTUWCOQsseyTHdnPGDFT92cuzwrSyj/NEe1KuQBUsZKCF57HX5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57c78d73ed8b5d822579ea4059e1c6fbae3e14ed7f9f23db8a9096c42b6e5757","last_reissued_at":"2026-05-18T04:27:17.431988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:17.431988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.5441","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":"2026-05-18T04:27:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mqCXtHs2G0Q64ZtPMu41p9XUozMD2gScAoTr0a5G6w9lQA5OdhBinaSnU+hCjbUkzEbx5yxYMDnNHa3M1yqMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:45:07.563443Z"},"content_sha256":"05611dd829e56c8b1210a6831e9d200d23cd62f657275703efca3046dd197cbc","schema_version":"1.0","event_id":"sha256:05611dd829e56c8b1210a6831e9d200d23cd62f657275703efca3046dd197cbc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:K7DY247NRNOYEJLZ5JAFTYOG7O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Obtaining a Bipartite Graph by Contracting Few Edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christophe Paul, Daniel Lokshtanov, Pim van 't Hof, Pinar Heggernes","submitted_at":"2011-02-26T20:07:27Z","abstract_excerpt":"We initiate the study of the Bipartite Contraction problem from the perspective of parameterized complexity. In this problem we are given a graph $G$ and an integer $k$, and the task is to determine whether we can obtain a bipartite graph from $G$ by a sequence of at most $k$ edge contractions. Our main result is an $f(k) n^{O(1)}$ time algorithm for Bipartite Contraction. Despite a strong resemblance between Bipartite Contraction and the classical Odd Cycle Transversal (OCT) problem, the methods developed to tackle OCT do not seem to be directly applicable to Bipartite Contraction. Our algori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5441","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":"2026-05-18T04:27:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sQ6ADpVbCVgCx4kOAsode3CxjzmyKRbBKOJ8iJ18a9tRIDkUHd6l8Q62EUsbsm/4pCajO5a19K0eYM7gmMLfAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:45:07.563994Z"},"content_sha256":"74531ef7b60724d27a1a60c22c9ca39eaff900edbad1dc0af63174fff2ffd1ee","schema_version":"1.0","event_id":"sha256:74531ef7b60724d27a1a60c22c9ca39eaff900edbad1dc0af63174fff2ffd1ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K7DY247NRNOYEJLZ5JAFTYOG7O/bundle.json","state_url":"https://pith.science/pith/K7DY247NRNOYEJLZ5JAFTYOG7O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K7DY247NRNOYEJLZ5JAFTYOG7O/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":"2026-06-26T00:45:07Z","links":{"resolver":"https://pith.science/pith/K7DY247NRNOYEJLZ5JAFTYOG7O","bundle":"https://pith.science/pith/K7DY247NRNOYEJLZ5JAFTYOG7O/bundle.json","state":"https://pith.science/pith/K7DY247NRNOYEJLZ5JAFTYOG7O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K7DY247NRNOYEJLZ5JAFTYOG7O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:K7DY247NRNOYEJLZ5JAFTYOG7O","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":"496fbd26f3bf41e162c14ceae39d9167dfe0a699d28494625179e1328acbb617","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-02-26T20:07:27Z","title_canon_sha256":"7402638c42b111e087424a804ae2572f5242e29ba1c3a94315d8c4ad9f1a8f8c"},"schema_version":"1.0","source":{"id":"1102.5441","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5441","created_at":"2026-05-18T04:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5441v2","created_at":"2026-05-18T04:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5441","created_at":"2026-05-18T04:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"K7DY247NRNOY","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K7DY247NRNOYEJLZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K7DY247N","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:74531ef7b60724d27a1a60c22c9ca39eaff900edbad1dc0af63174fff2ffd1ee","target":"graph","created_at":"2026-05-18T04:27:17Z","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":"We initiate the study of the Bipartite Contraction problem from the perspective of parameterized complexity. In this problem we are given a graph $G$ and an integer $k$, and the task is to determine whether we can obtain a bipartite graph from $G$ by a sequence of at most $k$ edge contractions. Our main result is an $f(k) n^{O(1)}$ time algorithm for Bipartite Contraction. Despite a strong resemblance between Bipartite Contraction and the classical Odd Cycle Transversal (OCT) problem, the methods developed to tackle OCT do not seem to be directly applicable to Bipartite Contraction. Our algori","authors_text":"Christophe Paul, Daniel Lokshtanov, Pim van 't Hof, Pinar Heggernes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-02-26T20:07:27Z","title":"Obtaining a Bipartite Graph by Contracting Few Edges"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5441","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":"sha256:05611dd829e56c8b1210a6831e9d200d23cd62f657275703efca3046dd197cbc","target":"record","created_at":"2026-05-18T04:27:17Z","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":"496fbd26f3bf41e162c14ceae39d9167dfe0a699d28494625179e1328acbb617","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-02-26T20:07:27Z","title_canon_sha256":"7402638c42b111e087424a804ae2572f5242e29ba1c3a94315d8c4ad9f1a8f8c"},"schema_version":"1.0","source":{"id":"1102.5441","kind":"arxiv","version":2}},"canonical_sha256":"57c78d73ed8b5d822579ea4059e1c6fbae3e14ed7f9f23db8a9096c42b6e5757","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57c78d73ed8b5d822579ea4059e1c6fbae3e14ed7f9f23db8a9096c42b6e5757","first_computed_at":"2026-05-18T04:27:17.431988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:17.431988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wjTnyGQYw6bjlqySXBblBnbBd9EbQMRuYHbTUWCOQsseyTHdnPGDFT92cuzwrSyj/NEe1KuQBUsZKCF57HX5Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:17.432588Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.5441","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05611dd829e56c8b1210a6831e9d200d23cd62f657275703efca3046dd197cbc","sha256:74531ef7b60724d27a1a60c22c9ca39eaff900edbad1dc0af63174fff2ffd1ee"],"state_sha256":"81031f02ca44f1cb898b39aa0c1db632c5ee560fc92d3b92750f2968749fe2b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AbE6E4/Iy/M8qo+ZN2zw8Q9scRD+xGeDppAhe1yJIxXrBc2XLg3p1sEafR9IgFAr3VC8VNA+2LjByWNnfRoJDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:45:07.566745Z","bundle_sha256":"26964c7aaa891dda8fa70b4849a93f9e5f7a0f7973e7fbe3d6c49798e4738094"}}