{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QZZQ27YPSUOWMO5XG4NF76Z36R","short_pith_number":"pith:QZZQ27YP","canonical_record":{"source":{"id":"1203.4067","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-03-19T09:50:43Z","cross_cats_sorted":[],"title_canon_sha256":"adc1f399630f1f2484a95cf9659909ab7f9f895fedb63d40a5328ad4756de602","abstract_canon_sha256":"0b3e7936fa205890330a1663ef8c78c74736d0b7e4176edf53e7d4612281fa3f"},"schema_version":"1.0"},"canonical_sha256":"86730d7f0f951d663bb7371a5ffb3bf44bdc463f2b54beebf43b249b0c051604","source":{"kind":"arxiv","id":"1203.4067","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4067","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4067v1","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4067","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"pith_short_12","alias_value":"QZZQ27YPSUOW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QZZQ27YPSUOWMO5X","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QZZQ27YP","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QZZQ27YPSUOWMO5XG4NF76Z36R","target":"record","payload":{"canonical_record":{"source":{"id":"1203.4067","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-03-19T09:50:43Z","cross_cats_sorted":[],"title_canon_sha256":"adc1f399630f1f2484a95cf9659909ab7f9f895fedb63d40a5328ad4756de602","abstract_canon_sha256":"0b3e7936fa205890330a1663ef8c78c74736d0b7e4176edf53e7d4612281fa3f"},"schema_version":"1.0"},"canonical_sha256":"86730d7f0f951d663bb7371a5ffb3bf44bdc463f2b54beebf43b249b0c051604","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:48.356350Z","signature_b64":"3F1owtlz34lYtC+e52OrgxozaZ5dn8bqcvD9JC/chh94n847xxtJYTJzS/4sW4ftfyZ8HWmOtE8NM2aMeDezAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86730d7f0f951d663bb7371a5ffb3bf44bdc463f2b54beebf43b249b0c051604","last_reissued_at":"2026-05-18T03:59:48.355844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:48.355844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.4067","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":"2026-05-18T03:59:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4U/LHt9Irby/gpASY5yu7JhAv9cHwKxwVy08W+RJf5XcuIXbuZW0ueD+UpdCTtwuWY15a5d7JZfQ4UqsCsPADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:28:31.439825Z"},"content_sha256":"43baf7f0c77fcefdc355ef3599b495d9bea0c92a27f7185f6a5d70b7b459d69b","schema_version":"1.0","event_id":"sha256:43baf7f0c77fcefdc355ef3599b495d9bea0c92a27f7185f6a5d70b7b459d69b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QZZQ27YPSUOWMO5XG4NF76Z36R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A quadratic kernel for computing the hybridization number of multiple trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.PE","authors_text":"Leo van Iersel, Simone Linz","submitted_at":"2012-03-19T09:50:43Z","abstract_excerpt":"It has recently been shown that the NP-hard problem of calculating the minimum number of hybridization events that is needed to explain a set of rooted binary phylogenetic trees by means of a hybridization network is fixed-parameter tractable if an instance of the problem consists of precisely two such trees. In this paper, we show that this problem remains fixed-parameter tractable for an arbitrarily large set of rooted binary phylogenetic trees. In particular, we present a quadratic kernel."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4067","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":"2026-05-18T03:59:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MA/gNlYYyY0coQ9uh7ZT+A3UpD/GRMcXlWF4E6hkhZa8ppGnsIQH9pzvhTVp8xnBlolvtnLwVxz2Pd01Lr+0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:28:31.440159Z"},"content_sha256":"48d274e690e11ccc30281c1816587e623646f8153ff5373085e8e8b9cb7af2b1","schema_version":"1.0","event_id":"sha256:48d274e690e11ccc30281c1816587e623646f8153ff5373085e8e8b9cb7af2b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZZQ27YPSUOWMO5XG4NF76Z36R/bundle.json","state_url":"https://pith.science/pith/QZZQ27YPSUOWMO5XG4NF76Z36R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZZQ27YPSUOWMO5XG4NF76Z36R/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":"2026-06-26T14:28:31Z","links":{"resolver":"https://pith.science/pith/QZZQ27YPSUOWMO5XG4NF76Z36R","bundle":"https://pith.science/pith/QZZQ27YPSUOWMO5XG4NF76Z36R/bundle.json","state":"https://pith.science/pith/QZZQ27YPSUOWMO5XG4NF76Z36R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZZQ27YPSUOWMO5XG4NF76Z36R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QZZQ27YPSUOWMO5XG4NF76Z36R","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":"0b3e7936fa205890330a1663ef8c78c74736d0b7e4176edf53e7d4612281fa3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-03-19T09:50:43Z","title_canon_sha256":"adc1f399630f1f2484a95cf9659909ab7f9f895fedb63d40a5328ad4756de602"},"schema_version":"1.0","source":{"id":"1203.4067","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4067","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4067v1","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4067","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"pith_short_12","alias_value":"QZZQ27YPSUOW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QZZQ27YPSUOWMO5X","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QZZQ27YP","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:48d274e690e11ccc30281c1816587e623646f8153ff5373085e8e8b9cb7af2b1","target":"graph","created_at":"2026-05-18T03:59:48Z","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":"It has recently been shown that the NP-hard problem of calculating the minimum number of hybridization events that is needed to explain a set of rooted binary phylogenetic trees by means of a hybridization network is fixed-parameter tractable if an instance of the problem consists of precisely two such trees. In this paper, we show that this problem remains fixed-parameter tractable for an arbitrarily large set of rooted binary phylogenetic trees. In particular, we present a quadratic kernel.","authors_text":"Leo van Iersel, Simone Linz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-03-19T09:50:43Z","title":"A quadratic kernel for computing the hybridization number of multiple trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4067","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":"sha256:43baf7f0c77fcefdc355ef3599b495d9bea0c92a27f7185f6a5d70b7b459d69b","target":"record","created_at":"2026-05-18T03:59:48Z","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":"0b3e7936fa205890330a1663ef8c78c74736d0b7e4176edf53e7d4612281fa3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-03-19T09:50:43Z","title_canon_sha256":"adc1f399630f1f2484a95cf9659909ab7f9f895fedb63d40a5328ad4756de602"},"schema_version":"1.0","source":{"id":"1203.4067","kind":"arxiv","version":1}},"canonical_sha256":"86730d7f0f951d663bb7371a5ffb3bf44bdc463f2b54beebf43b249b0c051604","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86730d7f0f951d663bb7371a5ffb3bf44bdc463f2b54beebf43b249b0c051604","first_computed_at":"2026-05-18T03:59:48.355844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:48.355844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3F1owtlz34lYtC+e52OrgxozaZ5dn8bqcvD9JC/chh94n847xxtJYTJzS/4sW4ftfyZ8HWmOtE8NM2aMeDezAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:48.356350Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.4067","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43baf7f0c77fcefdc355ef3599b495d9bea0c92a27f7185f6a5d70b7b459d69b","sha256:48d274e690e11ccc30281c1816587e623646f8153ff5373085e8e8b9cb7af2b1"],"state_sha256":"255d55c0fd3b6ea779e2679c757d4f0027dc1aef1e551a8937092b118973b2b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UxT++sja115OAB62eTwXxc5RPSKhdOtmMyJzbKnjg6fnukds+KZ0fNeQO+eo9Lx4BWZwrSlU61i46Cj34i1PCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:28:31.442088Z","bundle_sha256":"3f84130fa858696ec1912aaa65ed8b49c8f16fc4bec2322891d76e1e95c886d2"}}