{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6VWAY7BN74W6SV4NYN7E3D4EBP","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":"cd4fcd1cfa46585f1f10392e9e1ec9f3b7b18fa4777ec78ee1cdc970f0df5a25","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-12T00:15:17Z","title_canon_sha256":"c1e330df43a48c4e80f793c35da8d394b64d4bb73b45aa4b76d191bca48a0975"},"schema_version":"1.0","source":{"id":"1804.04263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.04263","created_at":"2026-05-18T00:18:35Z"},{"alias_kind":"arxiv_version","alias_value":"1804.04263v2","created_at":"2026-05-18T00:18:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04263","created_at":"2026-05-18T00:18:35Z"},{"alias_kind":"pith_short_12","alias_value":"6VWAY7BN74W6","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6VWAY7BN74W6SV4N","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6VWAY7BN","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:b54a20e6beeec06629c94ee699463f48ad045c425247015fc08f5f098357d0b3","target":"graph","created_at":"2026-05-18T00:18:35Z","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":"A characterization of the tree $T^*$ such that $\\mathrm{BP}(T^*)=\\overleftrightarrow{\\mathrm{DFUDS}(T)}$, the reversal of $\\mathrm{DFUDS}(T)$ is given. An immediate consequence is a rigorous characterization of the tree $\\hat{T}$ such that $\\mathrm{BP}(\\hat{T})=\\mathrm{DFUDS}(T)$. In summary, $\\mathrm{BP}$ and $\\mathrm{DFUDS}$ are unified within an encompassing framework, which might have the potential to imply future simplifications with regard to queries in $\\mathrm{BP}$ and/or $\\mathrm{DFUDS}$. Immediate benefits displayed here are to identify so far unnoted commonalities in most recent wor","authors_text":"Alexander Sch\\\"onhuth, Rayan Chikhi","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-12T00:15:17Z","title":"Dualities in Tree Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04263","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":"sha256:20175b82a714ce10777c827978422710ded921b2e051f86fa91b64185f5eeb25","target":"record","created_at":"2026-05-18T00:18:35Z","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":"cd4fcd1cfa46585f1f10392e9e1ec9f3b7b18fa4777ec78ee1cdc970f0df5a25","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-12T00:15:17Z","title_canon_sha256":"c1e330df43a48c4e80f793c35da8d394b64d4bb73b45aa4b76d191bca48a0975"},"schema_version":"1.0","source":{"id":"1804.04263","kind":"arxiv","version":2}},"canonical_sha256":"f56c0c7c2dff2de9578dc37e4d8f840bdf22cd42256c4972632c0b2c2fc05206","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f56c0c7c2dff2de9578dc37e4d8f840bdf22cd42256c4972632c0b2c2fc05206","first_computed_at":"2026-05-18T00:18:35.410849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:35.410849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tog2zUF1FxEn2qIRDiz2rhxfC3u9AwX7SV23q+B6g0Z1SeehLR0RCfOfmvaHRdKdNa0ME8dUQc12tswghCJ4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:35.411580Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.04263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20175b82a714ce10777c827978422710ded921b2e051f86fa91b64185f5eeb25","sha256:b54a20e6beeec06629c94ee699463f48ad045c425247015fc08f5f098357d0b3"],"state_sha256":"4757dc7365ce368aa420ab721800f369e74c2f971aa4f076c9b25ac0ca345eaf"}