{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:575JYDWSNBHFRL7HAPZERLN7WN","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":"c804709db2d2ae0c9f167a5982d3c95a8a1b95ea43e8286fc6e724b7f7edb801","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-05-28T16:41:33Z","title_canon_sha256":"92eabd813a2023d37b9392ac2956d6506ad45255f2e3d470cb17b829dbeafc10"},"schema_version":"1.0","source":{"id":"1805.11034","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11034","created_at":"2026-05-18T00:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11034v1","created_at":"2026-05-18T00:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11034","created_at":"2026-05-18T00:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"575JYDWSNBHF","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"575JYDWSNBHFRL7H","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"575JYDWS","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:1b19c7bca0652b628d70ecd9275bcd57463eee82dcc6da699566cab57481033a","target":"graph","created_at":"2026-05-18T00:14:48Z","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":"Coarse geometry, the branch of topology that studies the global properties of spaces, was originally developed for metric spaces and then Roe introduced coarse structures as a large-scale counterpart of uniformities. In the literature, there are very important generalisations of uniform spaces, such as semi-uniform and quasi-uniform spaces. In this paper, we introduce and start to study their large-scale counterparts, which generalise coarse spaces: semi-coarse spaces and quasi-coarse spaces.","authors_text":"Nicol\\`o Zava","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-05-28T16:41:33Z","title":"Generalisations of coarse spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11034","kind":"arxiv","version":1},"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:f9403bc91b579880cd1a05f062c95510b1c397acf09cd7540ebdff6580ba5278","target":"record","created_at":"2026-05-18T00:14:48Z","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":"c804709db2d2ae0c9f167a5982d3c95a8a1b95ea43e8286fc6e724b7f7edb801","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-05-28T16:41:33Z","title_canon_sha256":"92eabd813a2023d37b9392ac2956d6506ad45255f2e3d470cb17b829dbeafc10"},"schema_version":"1.0","source":{"id":"1805.11034","kind":"arxiv","version":1}},"canonical_sha256":"effa9c0ed2684e58afe703f248adbfb350e5c453d63e0452d89b6210df049569","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"effa9c0ed2684e58afe703f248adbfb350e5c453d63e0452d89b6210df049569","first_computed_at":"2026-05-18T00:14:48.448853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:48.448853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hXsQDqR+AV8SoDCdPDvCOmaen+qESX7FxE9OckB3zaqlNiurAYfzfunzf+QTiuXaqTepMgkKVXCi78vOs+bLAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:48.449468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.11034","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9403bc91b579880cd1a05f062c95510b1c397acf09cd7540ebdff6580ba5278","sha256:1b19c7bca0652b628d70ecd9275bcd57463eee82dcc6da699566cab57481033a"],"state_sha256":"c026a27c1840175b0f66b2dfad92a5250b8ec67e9a06be9a0d47c2216cb15f12"}