{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6OIQZAREET47KK2II4NUNBGF74","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":"0c45f4f86de39025cc4728edc72cb191f59432712b1ff97236dd3321d9fe68ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-28T03:05:03Z","title_canon_sha256":"6268d82ddd37155a9abace32b57162a6ed25f13caa3d402723de2036ee97ee55"},"schema_version":"1.0","source":{"id":"1902.10876","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10876","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10876v3","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10876","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"pith_short_12","alias_value":"6OIQZAREET47","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6OIQZAREET47KK2I","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6OIQZARE","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:c9db52352985e702aea6e39bfddbc2a25ea45b00c076c3f924ebfaf7aa714c73","target":"graph","created_at":"2026-05-17T23:42:58Z","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":"Using a method of Korobenko, Maldonado and Rios we show a new characterization of doubling metric-measure spaces supporting Poincar\\'e inequalities without assuming a priori that the measure is doubling.","authors_text":"Piotr Haj{\\l}asz, Ryan Alvarado","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-28T03:05:03Z","title":"A note on metric-measure spaces supporting Poincar\\'e inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10876","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":"sha256:4a4e2464c6883e69203f54045ba15ba7c58bfc3fe7dc5f72d27e41081e29da38","target":"record","created_at":"2026-05-17T23:42:58Z","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":"0c45f4f86de39025cc4728edc72cb191f59432712b1ff97236dd3321d9fe68ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-28T03:05:03Z","title_canon_sha256":"6268d82ddd37155a9abace32b57162a6ed25f13caa3d402723de2036ee97ee55"},"schema_version":"1.0","source":{"id":"1902.10876","kind":"arxiv","version":3}},"canonical_sha256":"f3910c822424f9f52b48471b4684c5ff0c6e851024852931cb83715e9861306d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3910c822424f9f52b48471b4684c5ff0c6e851024852931cb83715e9861306d","first_computed_at":"2026-05-17T23:42:58.453805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:58.453805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cPjizJnvPY+Z0OGDZaGbFK8ygzdMchBJj75kFgaPcYyYFddMWls2+G986l6IUbWYc8k74Aq4ck4ZQoiKNPTLBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:58.454267Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.10876","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a4e2464c6883e69203f54045ba15ba7c58bfc3fe7dc5f72d27e41081e29da38","sha256:c9db52352985e702aea6e39bfddbc2a25ea45b00c076c3f924ebfaf7aa714c73"],"state_sha256":"c4eb6b4393e9c918dad330359cbcf786bf16513b91f080a9b39d98259ba98e5f"}