{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:PSS7YL3BTU3WBEYYBNNKD5GZWY","short_pith_number":"pith:PSS7YL3B","schema_version":"1.0","canonical_sha256":"7ca5fc2f619d376093180b5aa1f4d9b611e6acf2e2b19af0cd513ac758786f3d","source":{"kind":"arxiv","id":"1905.05474","version":1},"attestation_state":"computed","paper":{"title":"Categories of coarse groups: quasi-homomorphisms and functorial coarse structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Dikran Dikranjan, Nicol\\`o Zava","submitted_at":"2019-05-14T09:10:46Z","abstract_excerpt":"Coarse geometry is the study of large-scale properties of spaces. In this paper we study group coarse structures (i.e., coarse structures on groups that agree with the algebraic structures), by using group ideals. We introduce a large class of examples of group coarse structures induced by cardinal invariants. In order to enhance the categorical treatment of the subject, we use quasi-homomorphisms, as a large-scale counterpart of homomorphisms. In particular, the localisation of a category plays a fundamental role. We then define the notion of functorial coarse structures and we give various e"},"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":"1905.05474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-05-14T09:10:46Z","cross_cats_sorted":[],"title_canon_sha256":"dc1797fbc3e5c3511e589f8994368668b17b242eac5f696b192358a1dd13e48d","abstract_canon_sha256":"1c44f5640ce46137af043c40ae39c2f4d7c9b3b8d169fb4101192d4679ba8b17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:16.352148Z","signature_b64":"jtttx1BZRL7vwdjTapFJkmHfENbKZTK8eYZLUlZHKAUv95SCtaPWK0tM4+j6xrEkmYkdgWTL/NpXwlFmQvY6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ca5fc2f619d376093180b5aa1f4d9b611e6acf2e2b19af0cd513ac758786f3d","last_reissued_at":"2026-05-17T23:46:16.351502Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:16.351502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Categories of coarse groups: quasi-homomorphisms and functorial coarse structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Dikran Dikranjan, Nicol\\`o Zava","submitted_at":"2019-05-14T09:10:46Z","abstract_excerpt":"Coarse geometry is the study of large-scale properties of spaces. In this paper we study group coarse structures (i.e., coarse structures on groups that agree with the algebraic structures), by using group ideals. We introduce a large class of examples of group coarse structures induced by cardinal invariants. In order to enhance the categorical treatment of the subject, we use quasi-homomorphisms, as a large-scale counterpart of homomorphisms. In particular, the localisation of a category plays a fundamental role. We then define the notion of functorial coarse structures and we give various e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05474","kind":"arxiv","version":1},"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":"1905.05474","created_at":"2026-05-17T23:46:16.351598+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.05474v1","created_at":"2026-05-17T23:46:16.351598+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05474","created_at":"2026-05-17T23:46:16.351598+00:00"},{"alias_kind":"pith_short_12","alias_value":"PSS7YL3BTU3W","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"PSS7YL3BTU3WBEYY","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"PSS7YL3B","created_at":"2026-05-18T12:33:24.271573+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/PSS7YL3BTU3WBEYYBNNKD5GZWY","json":"https://pith.science/pith/PSS7YL3BTU3WBEYYBNNKD5GZWY.json","graph_json":"https://pith.science/api/pith-number/PSS7YL3BTU3WBEYYBNNKD5GZWY/graph.json","events_json":"https://pith.science/api/pith-number/PSS7YL3BTU3WBEYYBNNKD5GZWY/events.json","paper":"https://pith.science/paper/PSS7YL3B"},"agent_actions":{"view_html":"https://pith.science/pith/PSS7YL3BTU3WBEYYBNNKD5GZWY","download_json":"https://pith.science/pith/PSS7YL3BTU3WBEYYBNNKD5GZWY.json","view_paper":"https://pith.science/paper/PSS7YL3B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.05474&json=true","fetch_graph":"https://pith.science/api/pith-number/PSS7YL3BTU3WBEYYBNNKD5GZWY/graph.json","fetch_events":"https://pith.science/api/pith-number/PSS7YL3BTU3WBEYYBNNKD5GZWY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PSS7YL3BTU3WBEYYBNNKD5GZWY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PSS7YL3BTU3WBEYYBNNKD5GZWY/action/storage_attestation","attest_author":"https://pith.science/pith/PSS7YL3BTU3WBEYYBNNKD5GZWY/action/author_attestation","sign_citation":"https://pith.science/pith/PSS7YL3BTU3WBEYYBNNKD5GZWY/action/citation_signature","submit_replication":"https://pith.science/pith/PSS7YL3BTU3WBEYYBNNKD5GZWY/action/replication_record"}},"created_at":"2026-05-17T23:46:16.351598+00:00","updated_at":"2026-05-17T23:46:16.351598+00:00"}