{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RPW4EEKJDVXO3EK65FXV5ZF4KJ","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":"ff3d9486c96b177b8742456f42bd2aa1a6a51297801c5b36f550cb0b9395f844","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-12-08T12:45:50Z","title_canon_sha256":"731f695fdcd9478e9fa4020f9b8e67727055572cf70cd8c9fbcbd879ded52ea5"},"schema_version":"1.0","source":{"id":"1812.03313","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03313","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03313v1","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03313","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"pith_short_12","alias_value":"RPW4EEKJDVXO","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RPW4EEKJDVXO3EK6","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RPW4EEKJ","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:d62c3d5c3693361f6403876600bd3ef0d226f20455025b2a59951830815fe128","target":"graph","created_at":"2026-05-17T23:58:46Z","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":"We study locally compact metric spaces that enjoy various forms of homogeneity with respect to M\\\"obius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with invertibility. In particular, we provide a new characterization of snowflakes of boundaries of rank-one symmetric spaces of non-compact type among locally compact and connected metric spaces. Furthermore, we investigate the metric implications of homogeneity with respect to uniformly strongly quasi-M\\\"obius self-homeomorphisms, connecting such homogeneity with the combin","authors_text":"David Freeman, Enrico Le Donne","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-12-08T12:45:50Z","title":"Toward a quasi-M\\\"obius characterization of Invertible Homogeneous Metric Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03313","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:b190d4f821ad4e70d4ed8cc9ccd5cbf71fd6f18b4226a863bfc057e80c6bc3b9","target":"record","created_at":"2026-05-17T23:58:46Z","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":"ff3d9486c96b177b8742456f42bd2aa1a6a51297801c5b36f550cb0b9395f844","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-12-08T12:45:50Z","title_canon_sha256":"731f695fdcd9478e9fa4020f9b8e67727055572cf70cd8c9fbcbd879ded52ea5"},"schema_version":"1.0","source":{"id":"1812.03313","kind":"arxiv","version":1}},"canonical_sha256":"8bedc211491d6eed915ee96f5ee4bc527f6c9785503a92e624f96f0476d01503","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8bedc211491d6eed915ee96f5ee4bc527f6c9785503a92e624f96f0476d01503","first_computed_at":"2026-05-17T23:58:46.568226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:46.568226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PPCrdeyOA5H6hP4BksxWsIIWuNcd7c7pYN4u/tPKlDeolnmZodVIK5PaLUHQagrRxqlyUpZHv2FWzjAdP913Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:46.568703Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.03313","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b190d4f821ad4e70d4ed8cc9ccd5cbf71fd6f18b4226a863bfc057e80c6bc3b9","sha256:d62c3d5c3693361f6403876600bd3ef0d226f20455025b2a59951830815fe128"],"state_sha256":"485de62ee0a407ed29d54f54d03182f9e81d0711189ebb743b1b0d8661c2e19a"}