{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:G7RDB6C6FC62ANZMKKWIHDXLEW","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":"7bf0f642b1d16b9b26f21189e1234b7b0e2c57950aade8733f0eaef72ad3e667","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2020-08-02T09:42:17Z","title_canon_sha256":"0091c5e51997b7e7e0cde43fe1d3b23876927bbf18baba1dd01c0a13662bd80f"},"schema_version":"1.0","source":{"id":"2008.00438","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.00438","created_at":"2026-07-05T01:24:07Z"},{"alias_kind":"arxiv_version","alias_value":"2008.00438v1","created_at":"2026-07-05T01:24:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.00438","created_at":"2026-07-05T01:24:07Z"},{"alias_kind":"pith_short_12","alias_value":"G7RDB6C6FC62","created_at":"2026-07-05T01:24:07Z"},{"alias_kind":"pith_short_16","alias_value":"G7RDB6C6FC62ANZM","created_at":"2026-07-05T01:24:07Z"},{"alias_kind":"pith_short_8","alias_value":"G7RDB6C6","created_at":"2026-07-05T01:24:07Z"}],"graph_snapshots":[{"event_id":"sha256:d419b8efdffa2d947fd47e8d410b5874950cdce6295106873e6bef1b1f1e4f58","target":"graph","created_at":"2026-07-05T01:24:07Z","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/2008.00438/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a vertex $u$ of a tree $T$, the leaf (internal, respectively) status of $u$ is the sum of the distances from $u$ to all leaves (internal vertices, respectively) of $T$. The minimum (maximum, respectively) leaf status of a tree $T$ is the minimum (maximum, respectively) leaf statuses of all vertices of $T$. The minimum (maximum, respectively) internal status of a tree $T$ is the minimum (maximum, respectively) internal statuses of all vertices of $T$. We give the smallest and largest values for the minimum leaf status, maximum leaf status, minimum internal status, and maximum internal statu","authors_text":"Bo Zhou, Haiyan Guo","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2020-08-02T09:42:17Z","title":"On extremal leaf status and internal status of trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.00438","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":"sha256:8b16d12247ebb573b9c2674a26547e30a90f270e4bc90362e2de9f39ff463b35","target":"record","created_at":"2026-07-05T01:24:07Z","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":"7bf0f642b1d16b9b26f21189e1234b7b0e2c57950aade8733f0eaef72ad3e667","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2020-08-02T09:42:17Z","title_canon_sha256":"0091c5e51997b7e7e0cde43fe1d3b23876927bbf18baba1dd01c0a13662bd80f"},"schema_version":"1.0","source":{"id":"2008.00438","kind":"arxiv","version":1}},"canonical_sha256":"37e230f85e28bda0372c52ac838eeb25b5e2babb69b573455d16c0602d9ddf58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37e230f85e28bda0372c52ac838eeb25b5e2babb69b573455d16c0602d9ddf58","first_computed_at":"2026-07-05T01:24:07.741193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:24:07.741193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JiYXTQYNsQzuUa3f9ujEqur2XNfzz+8ennMmqhvFqL3/MFAamsglIf35hfLkfAbp5zdZ4l7Md1ST+HkjLLqgAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:24:07.741807Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.00438","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b16d12247ebb573b9c2674a26547e30a90f270e4bc90362e2de9f39ff463b35","sha256:d419b8efdffa2d947fd47e8d410b5874950cdce6295106873e6bef1b1f1e4f58"],"state_sha256":"fb01f256cd100888fb3993b24dff24da48f0d7a31fb3b8e420793c851e297087"}