{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P3UIU6FI7XEVODQSCOUMYNWQYP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"25ed72dfd28731e1694cf1aea4253a9ac46ceb84d5f427d2e0367d8ba1230142","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-09-06T19:30:38Z","title_canon_sha256":"a97703875a2211056586cc280c40f2b63b4cbd762e45f007021d56cc759b142d"},"schema_version":"1.0","source":{"id":"1309.1748","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1748","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1748v3","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1748","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"pith_short_12","alias_value":"P3UIU6FI7XEV","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P3UIU6FI7XEVODQS","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P3UIU6FI","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:e094dc890368c02a4a65a5810c012dfeadaf481bf515873b9e6d927c3bd9a60c","target":"graph","created_at":"2026-05-18T03:09:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Eliahu Levy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-09-06T19:30:38Z","title":"Inflated Cauchy Filters - A Way to Construct the Completion of a General Uniform Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1748","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:29cf2db721fb0f6963a84afba6fbcfac2317c209c5ecbc4cb7184bcb3a0c7a66","target":"record","created_at":"2026-05-18T03:09:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"25ed72dfd28731e1694cf1aea4253a9ac46ceb84d5f427d2e0367d8ba1230142","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-09-06T19:30:38Z","title_canon_sha256":"a97703875a2211056586cc280c40f2b63b4cbd762e45f007021d56cc759b142d"},"schema_version":"1.0","source":{"id":"1309.1748","kind":"arxiv","version":3}},"canonical_sha256":"7ee88a78a8fdc9570e1213a8cc36d0c3dd9b3614958e9db4c18553a364327c3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ee88a78a8fdc9570e1213a8cc36d0c3dd9b3614958e9db4c18553a364327c3b","first_computed_at":"2026-05-18T03:09:47.689878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:47.689878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a1ewBWJZfolUmfSvYHzkkHOC5zghf0fZFfzVptrqvGJ7OEBUIASAKBUml+aFVb8s2R8pzLdXnYVny9HVcFDLDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:47.690581Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1748","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29cf2db721fb0f6963a84afba6fbcfac2317c209c5ecbc4cb7184bcb3a0c7a66","sha256:e094dc890368c02a4a65a5810c012dfeadaf481bf515873b9e6d927c3bd9a60c"],"state_sha256":"72ba074c60b103be1d3feab60cb468d165ee455ef1ef1042ae4cc263f621e4b2"}