{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:SPJXR4H6GWWS7SZHRTCFSJIJVU","short_pith_number":"pith:SPJXR4H6","schema_version":"1.0","canonical_sha256":"93d378f0fe35ad2fcb278cc4592509ad2eabc47e094834cda48951bf605f933f","source":{"kind":"arxiv","id":"1309.6903","version":4},"attestation_state":"computed","paper":{"title":"The algebra of conditional sets and the concepts of conditional topology and compactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Asgar Jamneshan, Martin Karliczek, Michael Kupper, Samuel Drapeau","submitted_at":"2013-09-21T15:54:22Z","abstract_excerpt":"The concepts of a conditional set, a conditional inclusion relation and a conditional Cartesian product are introduced. The resulting conditional set theory is sufficiently rich in order to construct a conditional topology, a conditional real and functional analysis indicating the possibility of a mathematical discourse based on conditional sets. It is proved that the conditional power set is a complete Boolean algebra, and a conditional version of the axiom of choice, the ultrafilter lemma, Tychonoff's theorem, the Borel-Lebesgue theorem, the Hahn-Banach theorem, the Banach-Alaoglu theorem an"},"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":"1309.6903","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-09-21T15:54:22Z","cross_cats_sorted":[],"title_canon_sha256":"f93ed4de974d1265d58eb5fe22a0cb8f5092c76f5a797cc428aa03de762481f5","abstract_canon_sha256":"3e5c537b4a70d61316f6cfd1089bfa10174bc370883b4a7b627876cb11acffd5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:21.410725Z","signature_b64":"PwcTs8LlLLCA0ML5UDQpztD+v87zDHxOj2gkJMoNrJ5HePxBjQWEaBEoBkZ68vE6N09vZgBWO19ZdHrRmGWjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93d378f0fe35ad2fcb278cc4592509ad2eabc47e094834cda48951bf605f933f","last_reissued_at":"2026-05-18T01:07:21.410311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:21.410311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The algebra of conditional sets and the concepts of conditional topology and compactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Asgar Jamneshan, Martin Karliczek, Michael Kupper, Samuel Drapeau","submitted_at":"2013-09-21T15:54:22Z","abstract_excerpt":"The concepts of a conditional set, a conditional inclusion relation and a conditional Cartesian product are introduced. The resulting conditional set theory is sufficiently rich in order to construct a conditional topology, a conditional real and functional analysis indicating the possibility of a mathematical discourse based on conditional sets. It is proved that the conditional power set is a complete Boolean algebra, and a conditional version of the axiom of choice, the ultrafilter lemma, Tychonoff's theorem, the Borel-Lebesgue theorem, the Hahn-Banach theorem, the Banach-Alaoglu theorem an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6903","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":"1309.6903","created_at":"2026-05-18T01:07:21.410394+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.6903v4","created_at":"2026-05-18T01:07:21.410394+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6903","created_at":"2026-05-18T01:07:21.410394+00:00"},{"alias_kind":"pith_short_12","alias_value":"SPJXR4H6GWWS","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SPJXR4H6GWWS7SZH","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SPJXR4H6","created_at":"2026-05-18T12:27:59.945178+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/SPJXR4H6GWWS7SZHRTCFSJIJVU","json":"https://pith.science/pith/SPJXR4H6GWWS7SZHRTCFSJIJVU.json","graph_json":"https://pith.science/api/pith-number/SPJXR4H6GWWS7SZHRTCFSJIJVU/graph.json","events_json":"https://pith.science/api/pith-number/SPJXR4H6GWWS7SZHRTCFSJIJVU/events.json","paper":"https://pith.science/paper/SPJXR4H6"},"agent_actions":{"view_html":"https://pith.science/pith/SPJXR4H6GWWS7SZHRTCFSJIJVU","download_json":"https://pith.science/pith/SPJXR4H6GWWS7SZHRTCFSJIJVU.json","view_paper":"https://pith.science/paper/SPJXR4H6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.6903&json=true","fetch_graph":"https://pith.science/api/pith-number/SPJXR4H6GWWS7SZHRTCFSJIJVU/graph.json","fetch_events":"https://pith.science/api/pith-number/SPJXR4H6GWWS7SZHRTCFSJIJVU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SPJXR4H6GWWS7SZHRTCFSJIJVU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SPJXR4H6GWWS7SZHRTCFSJIJVU/action/storage_attestation","attest_author":"https://pith.science/pith/SPJXR4H6GWWS7SZHRTCFSJIJVU/action/author_attestation","sign_citation":"https://pith.science/pith/SPJXR4H6GWWS7SZHRTCFSJIJVU/action/citation_signature","submit_replication":"https://pith.science/pith/SPJXR4H6GWWS7SZHRTCFSJIJVU/action/replication_record"}},"created_at":"2026-05-18T01:07:21.410394+00:00","updated_at":"2026-05-18T01:07:21.410394+00:00"}