{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XAOJUDS3N2H7WZBJC673JT3BKV","short_pith_number":"pith:XAOJUDS3","schema_version":"1.0","canonical_sha256":"b81c9a0e5b6e8ffb642917bfb4cf61554f1768cb32a3912ea994ce109edfe572","source":{"kind":"arxiv","id":"1506.08287","version":1},"attestation_state":"computed","paper":{"title":"Preserving Coarse Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"Jerzy Dydak, Ziga Virk","submitted_at":"2015-06-27T12:13:34Z","abstract_excerpt":"The aim of this paper is to investigate properties preserved and co-preserved by coarsely $n$-to-1 functions, in particular by the quotient maps $X\\to X/\\sim$ induced by a finite group $G$ acting by isometries on a metric space $X$. The coarse properties we are mainly interested in are related to asymptotic dimension and its generalizations: having finite asymptotic dimension, asymptotic Property C, straight finite decomposition complexity, countable asymptotic dimension, and metric sparsification property. We provide an alternative description of asymptotic Property C and we prove that the cl"},"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":"1506.08287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-06-27T12:13:34Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"735bafeeecb5a1d081d5344a30244f6d64dbb5f406e67a1f819392476b19a407","abstract_canon_sha256":"e72f591ab2acb3d93ef7f20addc52130312dcd11a3489d3a7c01eeb23a5def4c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:11.682112Z","signature_b64":"9GMtJUkFfRQExrHoJvDWsUYW4IwKzIE58wkHZibq+l/mF5VzEXgai6+jfTAohVob1QUoe/Of+cFC6Qo0pO5KCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b81c9a0e5b6e8ffb642917bfb4cf61554f1768cb32a3912ea994ce109edfe572","last_reissued_at":"2026-05-18T01:20:11.681640Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:11.681640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Preserving Coarse Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"Jerzy Dydak, Ziga Virk","submitted_at":"2015-06-27T12:13:34Z","abstract_excerpt":"The aim of this paper is to investigate properties preserved and co-preserved by coarsely $n$-to-1 functions, in particular by the quotient maps $X\\to X/\\sim$ induced by a finite group $G$ acting by isometries on a metric space $X$. The coarse properties we are mainly interested in are related to asymptotic dimension and its generalizations: having finite asymptotic dimension, asymptotic Property C, straight finite decomposition complexity, countable asymptotic dimension, and metric sparsification property. We provide an alternative description of asymptotic Property C and we prove that the cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08287","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":"1506.08287","created_at":"2026-05-18T01:20:11.681701+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.08287v1","created_at":"2026-05-18T01:20:11.681701+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08287","created_at":"2026-05-18T01:20:11.681701+00:00"},{"alias_kind":"pith_short_12","alias_value":"XAOJUDS3N2H7","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XAOJUDS3N2H7WZBJ","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XAOJUDS3","created_at":"2026-05-18T12:29:50.041715+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/XAOJUDS3N2H7WZBJC673JT3BKV","json":"https://pith.science/pith/XAOJUDS3N2H7WZBJC673JT3BKV.json","graph_json":"https://pith.science/api/pith-number/XAOJUDS3N2H7WZBJC673JT3BKV/graph.json","events_json":"https://pith.science/api/pith-number/XAOJUDS3N2H7WZBJC673JT3BKV/events.json","paper":"https://pith.science/paper/XAOJUDS3"},"agent_actions":{"view_html":"https://pith.science/pith/XAOJUDS3N2H7WZBJC673JT3BKV","download_json":"https://pith.science/pith/XAOJUDS3N2H7WZBJC673JT3BKV.json","view_paper":"https://pith.science/paper/XAOJUDS3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.08287&json=true","fetch_graph":"https://pith.science/api/pith-number/XAOJUDS3N2H7WZBJC673JT3BKV/graph.json","fetch_events":"https://pith.science/api/pith-number/XAOJUDS3N2H7WZBJC673JT3BKV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XAOJUDS3N2H7WZBJC673JT3BKV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XAOJUDS3N2H7WZBJC673JT3BKV/action/storage_attestation","attest_author":"https://pith.science/pith/XAOJUDS3N2H7WZBJC673JT3BKV/action/author_attestation","sign_citation":"https://pith.science/pith/XAOJUDS3N2H7WZBJC673JT3BKV/action/citation_signature","submit_replication":"https://pith.science/pith/XAOJUDS3N2H7WZBJC673JT3BKV/action/replication_record"}},"created_at":"2026-05-18T01:20:11.681701+00:00","updated_at":"2026-05-18T01:20:11.681701+00:00"}