{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:P3UIU6FI7XEVODQSCOUMYNWQYP","short_pith_number":"pith:P3UIU6FI","schema_version":"1.0","canonical_sha256":"7ee88a78a8fdc9570e1213a8cc36d0c3dd9b3614958e9db4c18553a364327c3b","source":{"kind":"arxiv","id":"1309.1748","version":3},"attestation_state":"computed","paper":{"title":"Inflated Cauchy Filters - A Way to Construct the Completion of a General Uniform Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Eliahu Levy","submitted_at":"2013-09-06T19:30:38Z","abstract_excerpt":"Treatises about General Topology that emphasize the notion of uniformity and uniform space find, of course, no difficulty in defining the notion of a complete uniform space and in constructing the completion of a metric space, via its Cauchy sequences. In contrast, constructing the completion of a general uniform space, especially without recourse to pseudometrics, presents itself as somewhat awkward. In this note the notion of an inflated Cauchy filter is proposed as a way to accomplish that. As the author learned later, all that was actually expounded in Bourbaki, Topologie Generale, 1966 ed"},"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":"1309.1748","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-09-06T19:30:38Z","cross_cats_sorted":[],"title_canon_sha256":"a97703875a2211056586cc280c40f2b63b4cbd762e45f007021d56cc759b142d","abstract_canon_sha256":"25ed72dfd28731e1694cf1aea4253a9ac46ceb84d5f427d2e0367d8ba1230142"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:47.690581Z","signature_b64":"a1ewBWJZfolUmfSvYHzkkHOC5zghf0fZFfzVptrqvGJ7OEBUIASAKBUml+aFVb8s2R8pzLdXnYVny9HVcFDLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ee88a78a8fdc9570e1213a8cc36d0c3dd9b3614958e9db4c18553a364327c3b","last_reissued_at":"2026-05-18T03:09:47.689878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:47.689878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inflated Cauchy Filters - A Way to Construct the Completion of a General Uniform Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Eliahu Levy","submitted_at":"2013-09-06T19:30:38Z","abstract_excerpt":"Treatises about General Topology that emphasize the notion of uniformity and uniform space find, of course, no difficulty in defining the notion of a complete uniform space and in constructing the completion of a metric space, via its Cauchy sequences. In contrast, constructing the completion of a general uniform space, especially without recourse to pseudometrics, presents itself as somewhat awkward. In this note the notion of an inflated Cauchy filter is proposed as a way to accomplish that. As the author learned later, all that was actually expounded in Bourbaki, Topologie Generale, 1966 ed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1748","kind":"arxiv","version":3},"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":"1309.1748","created_at":"2026-05-18T03:09:47.689991+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.1748v3","created_at":"2026-05-18T03:09:47.689991+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1748","created_at":"2026-05-18T03:09:47.689991+00:00"},{"alias_kind":"pith_short_12","alias_value":"P3UIU6FI7XEV","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"P3UIU6FI7XEVODQS","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"P3UIU6FI","created_at":"2026-05-18T12:27:54.935989+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/P3UIU6FI7XEVODQSCOUMYNWQYP","json":"https://pith.science/pith/P3UIU6FI7XEVODQSCOUMYNWQYP.json","graph_json":"https://pith.science/api/pith-number/P3UIU6FI7XEVODQSCOUMYNWQYP/graph.json","events_json":"https://pith.science/api/pith-number/P3UIU6FI7XEVODQSCOUMYNWQYP/events.json","paper":"https://pith.science/paper/P3UIU6FI"},"agent_actions":{"view_html":"https://pith.science/pith/P3UIU6FI7XEVODQSCOUMYNWQYP","download_json":"https://pith.science/pith/P3UIU6FI7XEVODQSCOUMYNWQYP.json","view_paper":"https://pith.science/paper/P3UIU6FI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.1748&json=true","fetch_graph":"https://pith.science/api/pith-number/P3UIU6FI7XEVODQSCOUMYNWQYP/graph.json","fetch_events":"https://pith.science/api/pith-number/P3UIU6FI7XEVODQSCOUMYNWQYP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P3UIU6FI7XEVODQSCOUMYNWQYP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P3UIU6FI7XEVODQSCOUMYNWQYP/action/storage_attestation","attest_author":"https://pith.science/pith/P3UIU6FI7XEVODQSCOUMYNWQYP/action/author_attestation","sign_citation":"https://pith.science/pith/P3UIU6FI7XEVODQSCOUMYNWQYP/action/citation_signature","submit_replication":"https://pith.science/pith/P3UIU6FI7XEVODQSCOUMYNWQYP/action/replication_record"}},"created_at":"2026-05-18T03:09:47.689991+00:00","updated_at":"2026-05-18T03:09:47.689991+00:00"}