{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:P27LJ2LS6WUCHSAEZJKEIKWSXJ","short_pith_number":"pith:P27LJ2LS","schema_version":"1.0","canonical_sha256":"7ebeb4e972f5a823c804ca54442ad2ba6c1d1106e264568cb9d72c2c981c5481","source":{"kind":"arxiv","id":"1906.00351","version":1},"attestation_state":"computed","paper":{"title":"The Scott rank of Polish metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.MG","authors_text":"Andre Nies, Katia Fokina, Martin Koerwien, Sy Friedman","submitted_at":"2019-06-02T06:31:55Z","abstract_excerpt":"We study the usual notion of Scott rank but in the setting of Polish metric spaces. The signature consists of distance relations: for each rational $q > 0$, there is a relation $R_{<q}(x,y)$ stating that the distance of $x$ and $y $ is less than $q$. We show that compact spaces have Scott rank at most $\\omega$, and that there are discrete ultrametric spaces of arbitrarily high countable Scott rank."},"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":"1906.00351","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-06-02T06:31:55Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"371932e071d4cadd47d9fc2bd553f4a7512e03e1ebd160692d002aac966eca18","abstract_canon_sha256":"f1c546694318eeceef6d295259e0c46106efd1a05c6a51a6cb4d9c5b6ca2e24b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:27.352740Z","signature_b64":"QkapSnRBNb+8RkhLG5SLE/7DzLAlm5XkX6gJcG+rnzuAkrJPRCofT1rjmm4Jzk5XlwXCb31m3uqsGJ9C1/bpCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ebeb4e972f5a823c804ca54442ad2ba6c1d1106e264568cb9d72c2c981c5481","last_reissued_at":"2026-05-17T23:44:27.352233Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:27.352233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Scott rank of Polish metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.MG","authors_text":"Andre Nies, Katia Fokina, Martin Koerwien, Sy Friedman","submitted_at":"2019-06-02T06:31:55Z","abstract_excerpt":"We study the usual notion of Scott rank but in the setting of Polish metric spaces. The signature consists of distance relations: for each rational $q > 0$, there is a relation $R_{<q}(x,y)$ stating that the distance of $x$ and $y $ is less than $q$. We show that compact spaces have Scott rank at most $\\omega$, and that there are discrete ultrametric spaces of arbitrarily high countable Scott rank."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00351","kind":"arxiv","version":1},"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":"1906.00351","created_at":"2026-05-17T23:44:27.352324+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.00351v1","created_at":"2026-05-17T23:44:27.352324+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.00351","created_at":"2026-05-17T23:44:27.352324+00:00"},{"alias_kind":"pith_short_12","alias_value":"P27LJ2LS6WUC","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"P27LJ2LS6WUCHSAE","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"P27LJ2LS","created_at":"2026-05-18T12:33:24.271573+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P27LJ2LS6WUCHSAEZJKEIKWSXJ","json":"https://pith.science/pith/P27LJ2LS6WUCHSAEZJKEIKWSXJ.json","graph_json":"https://pith.science/api/pith-number/P27LJ2LS6WUCHSAEZJKEIKWSXJ/graph.json","events_json":"https://pith.science/api/pith-number/P27LJ2LS6WUCHSAEZJKEIKWSXJ/events.json","paper":"https://pith.science/paper/P27LJ2LS"},"agent_actions":{"view_html":"https://pith.science/pith/P27LJ2LS6WUCHSAEZJKEIKWSXJ","download_json":"https://pith.science/pith/P27LJ2LS6WUCHSAEZJKEIKWSXJ.json","view_paper":"https://pith.science/paper/P27LJ2LS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.00351&json=true","fetch_graph":"https://pith.science/api/pith-number/P27LJ2LS6WUCHSAEZJKEIKWSXJ/graph.json","fetch_events":"https://pith.science/api/pith-number/P27LJ2LS6WUCHSAEZJKEIKWSXJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P27LJ2LS6WUCHSAEZJKEIKWSXJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P27LJ2LS6WUCHSAEZJKEIKWSXJ/action/storage_attestation","attest_author":"https://pith.science/pith/P27LJ2LS6WUCHSAEZJKEIKWSXJ/action/author_attestation","sign_citation":"https://pith.science/pith/P27LJ2LS6WUCHSAEZJKEIKWSXJ/action/citation_signature","submit_replication":"https://pith.science/pith/P27LJ2LS6WUCHSAEZJKEIKWSXJ/action/replication_record"}},"created_at":"2026-05-17T23:44:27.352324+00:00","updated_at":"2026-05-17T23:44:27.352324+00:00"}