{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Q24T3JGHPCZKGGC6IAS5QGORKI","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":"cd7256f74c2bc9543a76451ebca31e0498cf02f83f362f905872404bd3f270a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-07-16T15:08:34Z","title_canon_sha256":"52676c457eb432f360e9765e443c21e12dc00a67c36b70a4365db09ff7f557a9"},"schema_version":"1.0","source":{"id":"2607.15096","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.15096","created_at":"2026-07-17T01:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"2607.15096v1","created_at":"2026-07-17T01:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.15096","created_at":"2026-07-17T01:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"Q24T3JGHPCZK","created_at":"2026-07-17T01:22:09Z"},{"alias_kind":"pith_short_16","alias_value":"Q24T3JGHPCZKGGC6","created_at":"2026-07-17T01:22:09Z"},{"alias_kind":"pith_short_8","alias_value":"Q24T3JGH","created_at":"2026-07-17T01:22:09Z"}],"graph_snapshots":[{"event_id":"sha256:01d73afd248d41172f5161e7790c15546b0983c52c48295f8a7e1b8d2caee2c1","target":"graph","created_at":"2026-07-17T01:22:09Z","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/2607.15096/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $(X,\\mathcal E)$ and $(Y,\\mathcal F)$ be uniformly locally finite coarse spaces. We prove that every $C^*$-algebra isomorphism $C_u^*(X,\\mathcal E)\\cong C_u^*(Y,\\mathcal F)$ forces $(X,\\mathcal E)$ and $(Y,\\mathcal F)$ to be bijectively coarsely equivalent. This completely resolves the isomorphism rigidity problem for uniform Roe algebras over arbitrary uniformly locally finite coarse spaces.","authors_text":"Teng Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-07-16T15:08:34Z","title":"Isomorphism rigidity of uniform Roe algebras over arbitrary uniformly locally finite coarse spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.15096","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":"sha256:3f76708579440d86da3db77d06238bad225c94c04087483cd67ca8624ff32bbf","target":"record","created_at":"2026-07-17T01:22:09Z","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":"cd7256f74c2bc9543a76451ebca31e0498cf02f83f362f905872404bd3f270a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-07-16T15:08:34Z","title_canon_sha256":"52676c457eb432f360e9765e443c21e12dc00a67c36b70a4365db09ff7f557a9"},"schema_version":"1.0","source":{"id":"2607.15096","kind":"arxiv","version":1}},"canonical_sha256":"86b93da4c778b2a3185e4025d819d15233d1f4e85c7f3fd6567b5958a42c8cb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86b93da4c778b2a3185e4025d819d15233d1f4e85c7f3fd6567b5958a42c8cb2","first_computed_at":"2026-07-17T01:22:09.210713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-17T01:22:09.210713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XdOmdzbPZHlbeZYR/GYYC5blCmOGp1VDz3VpdFZTkQyZG5yKh1R2KUALlNJDqGDCab8j5+lGWemvQNiucLl/Dw==","signature_status":"signed_v1","signed_at":"2026-07-17T01:22:09.211577Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.15096","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f76708579440d86da3db77d06238bad225c94c04087483cd67ca8624ff32bbf","sha256:01d73afd248d41172f5161e7790c15546b0983c52c48295f8a7e1b8d2caee2c1"],"state_sha256":"8e6981ea2d7758a8c394da6ee8f606d9223527f5101b5b7eb691baecae685f1b"}