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We present labels of size $1/4\\log^2n+o(\\log^2n)$, matching (up to low order terms) the recent $1/4\\log^2n-O(\\log n)$ lower bound [ICALP'16].\n  Prior to our work, all distance"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1608.00212","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-07-31T12:30:27Z","cross_cats_sorted":[],"title_canon_sha256":"e628437eed8f842905366988e84edfa15b7193c5ff356db4b000e4dd1bbbf80c","abstract_canon_sha256":"a93853223947f555e2e41b9624544e45cb6abaaedc7ebd5049b928193c8dbbc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:33.755790Z","signature_b64":"lMwNQ2o5NjcxunCE1c6FxGTDQqSc9xeFGP1pMSbGjwmNBu+or5XR3O/G5JCqB+p+DDUfoMKpagkTJc87Y6arCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26c21acb37816f09b37e1efbdfd46381cd2ed329650bc552d21641eac590653f","last_reissued_at":"2026-05-18T00:44:33.755337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:33.755337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Distance Labeling Schemes for Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ofer Freedman, Oren Weimann, Patrick K. 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