{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XAOJUDS3N2H7WZBJC673JT3BKV","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":"e72f591ab2acb3d93ef7f20addc52130312dcd11a3489d3a7c01eeb23a5def4c","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-06-27T12:13:34Z","title_canon_sha256":"735bafeeecb5a1d081d5344a30244f6d64dbb5f406e67a1f819392476b19a407"},"schema_version":"1.0","source":{"id":"1506.08287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.08287","created_at":"2026-05-18T01:20:11Z"},{"alias_kind":"arxiv_version","alias_value":"1506.08287v1","created_at":"2026-05-18T01:20:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08287","created_at":"2026-05-18T01:20:11Z"},{"alias_kind":"pith_short_12","alias_value":"XAOJUDS3N2H7","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XAOJUDS3N2H7WZBJ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XAOJUDS3","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:c85ac1d729194b835d68083ce7b79d3032d8f4fd3e1bcd4bc987e1d02339c0fc","target":"graph","created_at":"2026-05-18T01:20:11Z","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":"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","authors_text":"Jerzy Dydak, Ziga Virk","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-06-27T12:13:34Z","title":"Preserving Coarse Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08287","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":"sha256:2fa8f3ce1fd7f65208f70acfa073ea614c4258508ce2c18d7d5c1bc35a89ecc0","target":"record","created_at":"2026-05-18T01:20:11Z","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":"e72f591ab2acb3d93ef7f20addc52130312dcd11a3489d3a7c01eeb23a5def4c","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-06-27T12:13:34Z","title_canon_sha256":"735bafeeecb5a1d081d5344a30244f6d64dbb5f406e67a1f819392476b19a407"},"schema_version":"1.0","source":{"id":"1506.08287","kind":"arxiv","version":1}},"canonical_sha256":"b81c9a0e5b6e8ffb642917bfb4cf61554f1768cb32a3912ea994ce109edfe572","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b81c9a0e5b6e8ffb642917bfb4cf61554f1768cb32a3912ea994ce109edfe572","first_computed_at":"2026-05-18T01:20:11.681640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:11.681640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9GMtJUkFfRQExrHoJvDWsUYW4IwKzIE58wkHZibq+l/mF5VzEXgai6+jfTAohVob1QUoe/Of+cFC6Qo0pO5KCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:11.682112Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.08287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fa8f3ce1fd7f65208f70acfa073ea614c4258508ce2c18d7d5c1bc35a89ecc0","sha256:c85ac1d729194b835d68083ce7b79d3032d8f4fd3e1bcd4bc987e1d02339c0fc"],"state_sha256":"8b9b97f7f3628f213dd15e8e4079aff54fa8302809671ab0deb467144cfc9a69"}