{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:SIM3IU52LEHWRZP7X3BTED7MY3","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":"fd54baeb528f4a588c4def30f8ab625cea063f08b2a128fd80be7bcd4072e244","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-02-16T20:05:41Z","title_canon_sha256":"7a900184cd08a2cd4b81ef38ffb4117bab6c623cb85163d117f2d34c00f4bf6f"},"schema_version":"1.0","source":{"id":"2302.08557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.08557","created_at":"2026-07-05T05:42:51Z"},{"alias_kind":"arxiv_version","alias_value":"2302.08557v1","created_at":"2026-07-05T05:42:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.08557","created_at":"2026-07-05T05:42:51Z"},{"alias_kind":"pith_short_12","alias_value":"SIM3IU52LEHW","created_at":"2026-07-05T05:42:51Z"},{"alias_kind":"pith_short_16","alias_value":"SIM3IU52LEHWRZP7","created_at":"2026-07-05T05:42:51Z"},{"alias_kind":"pith_short_8","alias_value":"SIM3IU52","created_at":"2026-07-05T05:42:51Z"}],"graph_snapshots":[{"event_id":"sha256:31effe367603f8314b8400e6859809e1fdb392d2907132e108a38a0cd54d5e35","target":"graph","created_at":"2026-07-05T05:42:51Z","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/2302.08557/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study multicolour, oriented and high-dimensional discrepancies of the set of all subtrees of a tree. As our main result, we show that the $r$-colour discrepancy of the subtrees of any tree is a linear function of the number of leaves $\\ell$ of that tree. More concretely, we show that it is bounded by $\\lceil(r-1)\\ell/r\\rceil$ from below and $\\lceil(r-1)\\ell/2\\rceil$ from above, and that these bounds are asymptotically sharp. Motivated by this result, we introduce natural notions of oriented and high-dimensional discrepancies and prove bounds for the corresponding discrepancies of the set of","authors_text":"Fenglin Wang, Michail Sarantis, Peleg Michaeli, Tarun Krishna, Yiqing Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-02-16T20:05:41Z","title":"Discrepancies of subtrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.08557","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":"sha256:2e5fe4c08bf941a3196da533d78a4b9e6cfa103b3eeba0cebf0501b8192708f7","target":"record","created_at":"2026-07-05T05:42:51Z","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":"fd54baeb528f4a588c4def30f8ab625cea063f08b2a128fd80be7bcd4072e244","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-02-16T20:05:41Z","title_canon_sha256":"7a900184cd08a2cd4b81ef38ffb4117bab6c623cb85163d117f2d34c00f4bf6f"},"schema_version":"1.0","source":{"id":"2302.08557","kind":"arxiv","version":1}},"canonical_sha256":"9219b453ba590f68e5ffbec3320fecc6c1de415c6dd84a84478953ae678084fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9219b453ba590f68e5ffbec3320fecc6c1de415c6dd84a84478953ae678084fd","first_computed_at":"2026-07-05T05:42:51.846061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:42:51.846061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9r9nHGihRTKyl8phFxTERXX0C+9+FMOLvQByjLVONps4/14XEeoXqpV7rRJ1zabkSOYfQOrTz2+j9HClzttQCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:42:51.846516Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.08557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e5fe4c08bf941a3196da533d78a4b9e6cfa103b3eeba0cebf0501b8192708f7","sha256:31effe367603f8314b8400e6859809e1fdb392d2907132e108a38a0cd54d5e35"],"state_sha256":"6737bdbcf8dd609d969f050352e241d46a7a3b2bd1aa7b8d4a90df31459ac6a0"}