{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:57DD3LX4L3JL6FNC2GYJFKWFHL","short_pith_number":"pith:57DD3LX4","schema_version":"1.0","canonical_sha256":"efc63daefc5ed2bf15a2d1b092aac53ae14ac76b70027fdbe7bc859689804127","source":{"kind":"arxiv","id":"1410.3144","version":1},"attestation_state":"computed","paper":{"title":"Locally constant functions in C-minimal structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Pablo Cubides Kovacsics","submitted_at":"2014-10-12T20:09:51Z","abstract_excerpt":"Let $M$ be a $C$-minimal structure and $T$ its canonical tree (which corresponds in an ultrametric space to the set of closed balls with radius different than $\\infty$ ordered by inclusion). We present a description of definable locally constant functions $f:M\\rightarrow T$ in $C$-minimal structures having a canonical tree with infinitely many branches at each node and densely ordered branches. This provides both a description of definable subsets of $T$ in one variable and analogues of known results in algebraically closed valued fields."},"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":"1410.3144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-10-12T20:09:51Z","cross_cats_sorted":[],"title_canon_sha256":"6362a4c2748578203e2f1e17a553c7ce91109e8646dafc413f75a8e2155d35e2","abstract_canon_sha256":"ec304e569bca4591e3527d2c6fc5b120b4ed2ca63b61b138fd7ef17ed2df3135"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:16.917286Z","signature_b64":"eEKReGoZy32DT6RxzfuDw50ms3Z8sNUIqD0wzRfYV/F02oHdOPiRtjDgcYqQWS34CWh9RCJ0beo+dNyA+u2KCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efc63daefc5ed2bf15a2d1b092aac53ae14ac76b70027fdbe7bc859689804127","last_reissued_at":"2026-05-18T02:40:16.916794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:16.916794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Locally constant functions in C-minimal structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Pablo Cubides Kovacsics","submitted_at":"2014-10-12T20:09:51Z","abstract_excerpt":"Let $M$ be a $C$-minimal structure and $T$ its canonical tree (which corresponds in an ultrametric space to the set of closed balls with radius different than $\\infty$ ordered by inclusion). We present a description of definable locally constant functions $f:M\\rightarrow T$ in $C$-minimal structures having a canonical tree with infinitely many branches at each node and densely ordered branches. This provides both a description of definable subsets of $T$ in one variable and analogues of known results in algebraically closed valued fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3144","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":"1410.3144","created_at":"2026-05-18T02:40:16.916889+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.3144v1","created_at":"2026-05-18T02:40:16.916889+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3144","created_at":"2026-05-18T02:40:16.916889+00:00"},{"alias_kind":"pith_short_12","alias_value":"57DD3LX4L3JL","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"57DD3LX4L3JL6FNC","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"57DD3LX4","created_at":"2026-05-18T12:28:14.216126+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/57DD3LX4L3JL6FNC2GYJFKWFHL","json":"https://pith.science/pith/57DD3LX4L3JL6FNC2GYJFKWFHL.json","graph_json":"https://pith.science/api/pith-number/57DD3LX4L3JL6FNC2GYJFKWFHL/graph.json","events_json":"https://pith.science/api/pith-number/57DD3LX4L3JL6FNC2GYJFKWFHL/events.json","paper":"https://pith.science/paper/57DD3LX4"},"agent_actions":{"view_html":"https://pith.science/pith/57DD3LX4L3JL6FNC2GYJFKWFHL","download_json":"https://pith.science/pith/57DD3LX4L3JL6FNC2GYJFKWFHL.json","view_paper":"https://pith.science/paper/57DD3LX4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.3144&json=true","fetch_graph":"https://pith.science/api/pith-number/57DD3LX4L3JL6FNC2GYJFKWFHL/graph.json","fetch_events":"https://pith.science/api/pith-number/57DD3LX4L3JL6FNC2GYJFKWFHL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/57DD3LX4L3JL6FNC2GYJFKWFHL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/57DD3LX4L3JL6FNC2GYJFKWFHL/action/storage_attestation","attest_author":"https://pith.science/pith/57DD3LX4L3JL6FNC2GYJFKWFHL/action/author_attestation","sign_citation":"https://pith.science/pith/57DD3LX4L3JL6FNC2GYJFKWFHL/action/citation_signature","submit_replication":"https://pith.science/pith/57DD3LX4L3JL6FNC2GYJFKWFHL/action/replication_record"}},"created_at":"2026-05-18T02:40:16.916889+00:00","updated_at":"2026-05-18T02:40:16.916889+00:00"}