{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:GI6CVRWC7MFJCP6XVPAQ33CBWT","short_pith_number":"pith:GI6CVRWC","schema_version":"1.0","canonical_sha256":"323c2ac6c2fb0a913fd7abc10dec41b4c9f76cef65d10d1d3e2dc3c5546f52d6","source":{"kind":"arxiv","id":"1405.0568","version":4},"attestation_state":"computed","paper":{"title":"On Superstable Expansions of Free Abelian Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Daniel Palacin, Rizos Sklinos","submitted_at":"2014-05-03T11:20:12Z","abstract_excerpt":"We prove that $(\\Z,+,0)$ has no proper superstable expansions of finite Lascar rank. Nevertheless, this structure equipped with a predicate defining powers of a given natural number is superstable of Lascar rank $\\omega$. Additionally, our methods yield other superstable expansions such as $(\\Z,+,0)$ equipped with the set of factorial elements."},"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":"1405.0568","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-05-03T11:20:12Z","cross_cats_sorted":[],"title_canon_sha256":"4db91e1e2803f4508b2f49717caca5ae1156c0d9759084a61a28a21e06864467","abstract_canon_sha256":"0c8ea32c6e3ff54ef66821fef487a987cae19cc17f375a4f54c3aa2af61f6090"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:25.068478Z","signature_b64":"YAw7blr4dE+Qilrm5MR4/4qgUie9nRoQTao5rS8f67IMRntVOwv/T02fnsptBP/FcgFUc/mEN3hPXXeNaVXLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"323c2ac6c2fb0a913fd7abc10dec41b4c9f76cef65d10d1d3e2dc3c5546f52d6","last_reissued_at":"2026-05-18T00:15:25.067669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:25.067669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Superstable Expansions of Free Abelian Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Daniel Palacin, Rizos Sklinos","submitted_at":"2014-05-03T11:20:12Z","abstract_excerpt":"We prove that $(\\Z,+,0)$ has no proper superstable expansions of finite Lascar rank. Nevertheless, this structure equipped with a predicate defining powers of a given natural number is superstable of Lascar rank $\\omega$. Additionally, our methods yield other superstable expansions such as $(\\Z,+,0)$ equipped with the set of factorial elements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0568","kind":"arxiv","version":4},"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":"1405.0568","created_at":"2026-05-18T00:15:25.067814+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.0568v4","created_at":"2026-05-18T00:15:25.067814+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0568","created_at":"2026-05-18T00:15:25.067814+00:00"},{"alias_kind":"pith_short_12","alias_value":"GI6CVRWC7MFJ","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"GI6CVRWC7MFJCP6X","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"GI6CVRWC","created_at":"2026-05-18T12:28:30.664211+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/GI6CVRWC7MFJCP6XVPAQ33CBWT","json":"https://pith.science/pith/GI6CVRWC7MFJCP6XVPAQ33CBWT.json","graph_json":"https://pith.science/api/pith-number/GI6CVRWC7MFJCP6XVPAQ33CBWT/graph.json","events_json":"https://pith.science/api/pith-number/GI6CVRWC7MFJCP6XVPAQ33CBWT/events.json","paper":"https://pith.science/paper/GI6CVRWC"},"agent_actions":{"view_html":"https://pith.science/pith/GI6CVRWC7MFJCP6XVPAQ33CBWT","download_json":"https://pith.science/pith/GI6CVRWC7MFJCP6XVPAQ33CBWT.json","view_paper":"https://pith.science/paper/GI6CVRWC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.0568&json=true","fetch_graph":"https://pith.science/api/pith-number/GI6CVRWC7MFJCP6XVPAQ33CBWT/graph.json","fetch_events":"https://pith.science/api/pith-number/GI6CVRWC7MFJCP6XVPAQ33CBWT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GI6CVRWC7MFJCP6XVPAQ33CBWT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GI6CVRWC7MFJCP6XVPAQ33CBWT/action/storage_attestation","attest_author":"https://pith.science/pith/GI6CVRWC7MFJCP6XVPAQ33CBWT/action/author_attestation","sign_citation":"https://pith.science/pith/GI6CVRWC7MFJCP6XVPAQ33CBWT/action/citation_signature","submit_replication":"https://pith.science/pith/GI6CVRWC7MFJCP6XVPAQ33CBWT/action/replication_record"}},"created_at":"2026-05-18T00:15:25.067814+00:00","updated_at":"2026-05-18T00:15:25.067814+00:00"}