{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:3MCDAWCVPIHSQRLCAFADNEH35J","short_pith_number":"pith:3MCDAWCV","schema_version":"1.0","canonical_sha256":"db043058557a0f28456201403690fbea7e7a5ebd83e26a9e17c5cd65eca3dd7f","source":{"kind":"arxiv","id":"1902.08747","version":2},"attestation_state":"computed","paper":{"title":"On ultrametric-preserving functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Oleksiy Dovgoshey","submitted_at":"2019-02-23T06:58:35Z","abstract_excerpt":"Characterizations of pseudoultrametric-preserving functions and semimetric-preserving functions are found. The structural properties of pseudoultrametrics which can be represented as a composition of an ultrametric and ultrametric-pseudoultrametric-preserving function are found. A dual form of Pongsriiam-Termwuttipong characterization of the ultrametric-preserving functions is described. We also introduce a concept of $k$-separating family of functions and use it to characterize the ultrametric spaces."},"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":"1902.08747","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-02-23T06:58:35Z","cross_cats_sorted":[],"title_canon_sha256":"fb0159f91c49375b492233aa0aa875e05ad6f3b8b47bd4f72a256f727f0daa62","abstract_canon_sha256":"15eb04dda7424c62b612bd257dc4dfb31686a0218156c8ecbf9c4ccd02a55f62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:11.984233Z","signature_b64":"+tFsyrNK7jM7cpM7DAf3uUbFxtfHOYTI1Uqn9Hb+mAuj4bhvVSC1orhz84KejBchIQvp6/ov9yhoN0PDRuKeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db043058557a0f28456201403690fbea7e7a5ebd83e26a9e17c5cd65eca3dd7f","last_reissued_at":"2026-05-17T23:41:11.983634Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:11.983634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On ultrametric-preserving functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Oleksiy Dovgoshey","submitted_at":"2019-02-23T06:58:35Z","abstract_excerpt":"Characterizations of pseudoultrametric-preserving functions and semimetric-preserving functions are found. The structural properties of pseudoultrametrics which can be represented as a composition of an ultrametric and ultrametric-pseudoultrametric-preserving function are found. A dual form of Pongsriiam-Termwuttipong characterization of the ultrametric-preserving functions is described. We also introduce a concept of $k$-separating family of functions and use it to characterize the ultrametric spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08747","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1902.08747","created_at":"2026-05-17T23:41:11.983721+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.08747v2","created_at":"2026-05-17T23:41:11.983721+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08747","created_at":"2026-05-17T23:41:11.983721+00:00"},{"alias_kind":"pith_short_12","alias_value":"3MCDAWCVPIHS","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"3MCDAWCVPIHSQRLC","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"3MCDAWCV","created_at":"2026-05-18T12:33:07.085635+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.08349","citing_title":"Combinatorial properties of ultrametrics and generalized ultrametrics","ref_index":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3MCDAWCVPIHSQRLCAFADNEH35J","json":"https://pith.science/pith/3MCDAWCVPIHSQRLCAFADNEH35J.json","graph_json":"https://pith.science/api/pith-number/3MCDAWCVPIHSQRLCAFADNEH35J/graph.json","events_json":"https://pith.science/api/pith-number/3MCDAWCVPIHSQRLCAFADNEH35J/events.json","paper":"https://pith.science/paper/3MCDAWCV"},"agent_actions":{"view_html":"https://pith.science/pith/3MCDAWCVPIHSQRLCAFADNEH35J","download_json":"https://pith.science/pith/3MCDAWCVPIHSQRLCAFADNEH35J.json","view_paper":"https://pith.science/paper/3MCDAWCV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.08747&json=true","fetch_graph":"https://pith.science/api/pith-number/3MCDAWCVPIHSQRLCAFADNEH35J/graph.json","fetch_events":"https://pith.science/api/pith-number/3MCDAWCVPIHSQRLCAFADNEH35J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3MCDAWCVPIHSQRLCAFADNEH35J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3MCDAWCVPIHSQRLCAFADNEH35J/action/storage_attestation","attest_author":"https://pith.science/pith/3MCDAWCVPIHSQRLCAFADNEH35J/action/author_attestation","sign_citation":"https://pith.science/pith/3MCDAWCVPIHSQRLCAFADNEH35J/action/citation_signature","submit_replication":"https://pith.science/pith/3MCDAWCVPIHSQRLCAFADNEH35J/action/replication_record"}},"created_at":"2026-05-17T23:41:11.983721+00:00","updated_at":"2026-05-17T23:41:11.983721+00:00"}