{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZMKVSBW6ZQQVI2IKCJ2I7ZYI75","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":"6ddec220b8932e33ac35370f35933c0fd4018ce0ad7fae3acdf63b3ff1207dbb","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-02-25T11:20:18Z","title_canon_sha256":"a68788920b08f2d181e5cdbade325dc7f4cd606799c49dd4fce7641e4b2e62a2"},"schema_version":"1.0","source":{"id":"2602.22281","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.22281","created_at":"2026-06-12T01:10:19Z"},{"alias_kind":"arxiv_version","alias_value":"2602.22281v3","created_at":"2026-06-12T01:10:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.22281","created_at":"2026-06-12T01:10:19Z"},{"alias_kind":"pith_short_12","alias_value":"ZMKVSBW6ZQQV","created_at":"2026-06-12T01:10:19Z"},{"alias_kind":"pith_short_16","alias_value":"ZMKVSBW6ZQQVI2IK","created_at":"2026-06-12T01:10:19Z"},{"alias_kind":"pith_short_8","alias_value":"ZMKVSBW6","created_at":"2026-06-12T01:10:19Z"}],"graph_snapshots":[{"event_id":"sha256:ed00bc22afaea449dcb19cf56b9c31779db82384103bc2530b62844ee40df500","target":"graph","created_at":"2026-06-12T01:10:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2602.22281/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The maximum agreement forest (MAF) problem in phylogenetics takes as input a set t >= 2 of binary phylogenetic trees T on the same set of taxa X. It asks for a partition of X into the smallest number of blocks such that the subtrees induced by these blocks are disjoint and have common topology across all the trees in T. We produce a modified version of the well-known chain reduction rule in order to prove that after exhaustive application of reduction rules each tree has O( t * r * k ) leaves, where k is the natural parameter (the number of blocks) and r=min{max{k,3},t+1}}. We prove this bound","authors_text":"Leo van Iersel, Ruben Meuwese, Steven Kelk","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-02-25T11:20:18Z","title":"A kernel for the maximum agreement forest problem on multiple binary phylogenetic trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.22281","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":"sha256:0fcf8bed6108131aeb61d8dbd687974480920e6e056a673106e550385672f0e6","target":"record","created_at":"2026-06-12T01:10:19Z","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":"6ddec220b8932e33ac35370f35933c0fd4018ce0ad7fae3acdf63b3ff1207dbb","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-02-25T11:20:18Z","title_canon_sha256":"a68788920b08f2d181e5cdbade325dc7f4cd606799c49dd4fce7641e4b2e62a2"},"schema_version":"1.0","source":{"id":"2602.22281","kind":"arxiv","version":3}},"canonical_sha256":"cb155906decc2154690a12748fe708ff7828275b958e36f27f11b305961b20d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb155906decc2154690a12748fe708ff7828275b958e36f27f11b305961b20d1","first_computed_at":"2026-06-12T01:10:19.968551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:10:19.968551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yIN+a8n7rBj2G/XMtn7sfGrm3bQm/l8VBGZMZpGcjetEgu5BZ8aYg2jfhUgAZ/pZ4cVDxxbU6hTFwTyXXg4mAw==","signature_status":"signed_v1","signed_at":"2026-06-12T01:10:19.969333Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.22281","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fcf8bed6108131aeb61d8dbd687974480920e6e056a673106e550385672f0e6","sha256:ed00bc22afaea449dcb19cf56b9c31779db82384103bc2530b62844ee40df500"],"state_sha256":"52c03207babb294f3a903cfd8995284c54668d603eb49705625dd3ca8108f992"}