{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PZZHCEDAC44QLXPA4JUFCUQYDO","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":"911caf0eeb21fdbfbb574cc35b615eceaff56c0aade7e7f3de215c3e5a596065","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-06-08T21:03:27Z","title_canon_sha256":"11e256cfbf4ed4abbdf78d9721ab28e154deb7f4c185edf83aa5123a9fac6f90"},"schema_version":"1.0","source":{"id":"1106.1672","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1672","created_at":"2026-07-04T23:56:14Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1672v3","created_at":"2026-07-04T23:56:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1672","created_at":"2026-07-04T23:56:14Z"},{"alias_kind":"pith_short_12","alias_value":"PZZHCEDAC44Q","created_at":"2026-07-04T23:56:14Z"},{"alias_kind":"pith_short_16","alias_value":"PZZHCEDAC44QLXPA","created_at":"2026-07-04T23:56:14Z"},{"alias_kind":"pith_short_8","alias_value":"PZZHCEDA","created_at":"2026-07-04T23:56:14Z"}],"graph_snapshots":[{"event_id":"sha256:f83c05278ce10484645cdc0a702d350f96a098cff64d85d0b864ff2fb80b220d","target":"graph","created_at":"2026-07-04T23:56:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1106.1672/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathbf{TB}$ be the category of totally bounded, locally compact metric spaces with the $C_0$ coarse structures. We show that if $X$ and $Y$ are in $\\mathbf{TB}$ then $X$ and $Y$ are coarsely equivalent if and only if their Higson coronas are homeomorphic. In fact, the Higson corona functor gives an equivalence of categories $\\mathbf{TB}\\to\\mathbf{K}$, where $\\mathbf{K}$ is the category of compact metrizable spaces. We use this fact to show that the continuously controlled coarse structure on a locally compact space $X$ induced by some metrizable compactification $\\tilde{X}$ is determined","authors_text":"Atsushi Yamashita, Kotaro Mine","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-06-08T21:03:27Z","title":"Metric compactifications and coarse structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1672","kind":"arxiv","version":3},"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:fe524b70d0003dc95f27be5d665f41ce5becda1d579acb4b24f7f35530ab9642","target":"record","created_at":"2026-07-04T23:56:14Z","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":"911caf0eeb21fdbfbb574cc35b615eceaff56c0aade7e7f3de215c3e5a596065","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-06-08T21:03:27Z","title_canon_sha256":"11e256cfbf4ed4abbdf78d9721ab28e154deb7f4c185edf83aa5123a9fac6f90"},"schema_version":"1.0","source":{"id":"1106.1672","kind":"arxiv","version":3}},"canonical_sha256":"7e72711060173905dde0e2685152181bb453b8dfd4948f531a9fc9c39ab68e98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e72711060173905dde0e2685152181bb453b8dfd4948f531a9fc9c39ab68e98","first_computed_at":"2026-07-04T23:56:14.069446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:56:14.069446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L6Rv01epsAb4QK0d23kRnIvDb3+dDxJ3ns32JJvCX15X+c0wE/ftsnpU2qA7wsHmVCuudhtl//rrJXfNTlBfBg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:56:14.069910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1672","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe524b70d0003dc95f27be5d665f41ce5becda1d579acb4b24f7f35530ab9642","sha256:f83c05278ce10484645cdc0a702d350f96a098cff64d85d0b864ff2fb80b220d"],"state_sha256":"765bcc2b9e93afa4443a2f331e069b38cc9525be5c2e701604ee50c79fdb64b6"}