{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5YIYGSVGQ4UJL7RJY6QL3KZQH3","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":"111097dcf6991a881458c412f2e036c8a9e1bc4e989428b16c370fbd3245c4f3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-12T09:47:00Z","title_canon_sha256":"1b5c2933bc68baa230956e1af918902176fdf72e08957ed98f1f2958a85b2412"},"schema_version":"1.0","source":{"id":"2502.08251","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.08251","created_at":"2026-07-05T10:13:20Z"},{"alias_kind":"arxiv_version","alias_value":"2502.08251v1","created_at":"2026-07-05T10:13:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.08251","created_at":"2026-07-05T10:13:20Z"},{"alias_kind":"pith_short_12","alias_value":"5YIYGSVGQ4UJ","created_at":"2026-07-05T10:13:20Z"},{"alias_kind":"pith_short_16","alias_value":"5YIYGSVGQ4UJL7RJ","created_at":"2026-07-05T10:13:20Z"},{"alias_kind":"pith_short_8","alias_value":"5YIYGSVG","created_at":"2026-07-05T10:13:20Z"}],"graph_snapshots":[{"event_id":"sha256:c69e377c9a4cb3c2f67fb6c258108cf2f423561237ba5ebc3df2d6c7d8a5a082","target":"graph","created_at":"2026-07-05T10:13:20Z","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/2502.08251/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Arboreal networks are a generalization of rooted trees, defined by keeping the tree-like structure, but dropping the requirement for a single root. Just as the class of cographs is precisely the class of undirected graphs that can be explained by a labelled rooted tree (T,t), we show that the class of distance-hereditary graphs is precisely the class of undirected graphs that can be explained by a labelled arboreal network (N,t).","authors_text":"Guillaume E. Scholz","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-12T09:47:00Z","title":"Representing distance-hereditary graphs with multi-rooted trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08251","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":"sha256:69ae5cccdac65656bd818c026a6f3c064e1a08abfed1600bf0d2a90aa6440116","target":"record","created_at":"2026-07-05T10:13:20Z","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":"111097dcf6991a881458c412f2e036c8a9e1bc4e989428b16c370fbd3245c4f3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-12T09:47:00Z","title_canon_sha256":"1b5c2933bc68baa230956e1af918902176fdf72e08957ed98f1f2958a85b2412"},"schema_version":"1.0","source":{"id":"2502.08251","kind":"arxiv","version":1}},"canonical_sha256":"ee11834aa6872895fe29c7a0bdab303eec3ebafa6bb7220fb2be19a1ff51a024","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee11834aa6872895fe29c7a0bdab303eec3ebafa6bb7220fb2be19a1ff51a024","first_computed_at":"2026-07-05T10:13:20.012368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:13:20.012368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SZ6yoUw5KE5TEKVldTjSK6mA+YyhWN0CsXteaNTH+lPc7Eue2Gw+q7cC2wv/MEaKUxJWE8dKlPgJ7C4dJpUyAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:13:20.013467Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.08251","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69ae5cccdac65656bd818c026a6f3c064e1a08abfed1600bf0d2a90aa6440116","sha256:c69e377c9a4cb3c2f67fb6c258108cf2f423561237ba5ebc3df2d6c7d8a5a082"],"state_sha256":"8d8c73d8c0246971f920aa396a49852c28be48ba72f38ee3b2382c0fb117b2e1"}