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Combinatorial characterizations are also obtained for poset-valued ultrametric distances recently defined by Priess-Crampe and Ribenboim."},"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":"1908.08349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-08-22T13:04:49Z","cross_cats_sorted":[],"title_canon_sha256":"9eb5362ea2cb1f03b9ca6628b80d7355c574c4503b8a2cc72b15f2cd671bba86","abstract_canon_sha256":"61f25763afa8470ec2f2c146dce90dcba277b60ae127a255492f47481c5d2376"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:12.020348Z","signature_b64":"dFsOXrUAxLEbe+BzVN3FAU5Wg/fmDAVnBm9UFf7OELlyCTd4g4OlVbYoZ2foVPss4DyPzCy910ySkPjB+7ogCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4338fc007eacc77d5ab132e2ec902217cc7cd276c063d53b5d079d031053fd69","last_reissued_at":"2026-07-04T23:59:12.019943Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:12.019943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial properties of ultrametrics and generalized ultrametrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"O. 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