{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:6OIQZAREET47KK2II4NUNBGF74","short_pith_number":"pith:6OIQZARE","canonical_record":{"source":{"id":"1902.10876","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-28T03:05:03Z","cross_cats_sorted":[],"title_canon_sha256":"6268d82ddd37155a9abace32b57162a6ed25f13caa3d402723de2036ee97ee55","abstract_canon_sha256":"0c45f4f86de39025cc4728edc72cb191f59432712b1ff97236dd3321d9fe68ef"},"schema_version":"1.0"},"canonical_sha256":"f3910c822424f9f52b48471b4684c5ff0c6e851024852931cb83715e9861306d","source":{"kind":"arxiv","id":"1902.10876","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:6OIQZAREET47KK2II4NUNBGF74","target":"record","payload":{"canonical_record":{"source":{"id":"1902.10876","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-28T03:05:03Z","cross_cats_sorted":[],"title_canon_sha256":"6268d82ddd37155a9abace32b57162a6ed25f13caa3d402723de2036ee97ee55","abstract_canon_sha256":"0c45f4f86de39025cc4728edc72cb191f59432712b1ff97236dd3321d9fe68ef"},"schema_version":"1.0"},"canonical_sha256":"f3910c822424f9f52b48471b4684c5ff0c6e851024852931cb83715e9861306d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:58.454267Z","signature_b64":"cPjizJnvPY+Z0OGDZaGbFK8ygzdMchBJj75kFgaPcYyYFddMWls2+G986l6IUbWYc8k74Aq4ck4ZQoiKNPTLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3910c822424f9f52b48471b4684c5ff0c6e851024852931cb83715e9861306d","last_reissued_at":"2026-05-17T23:42:58.453805Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:58.453805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.10876","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bObOrTS6j4Xi5+YA4GByoxAjnV7fqUggG/moZ/xDxtnfXwqDGTZOd4Su+nealKYMDAspwsKp/Ly9kfgRujJNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:23:47.280395Z"},"content_sha256":"4a4e2464c6883e69203f54045ba15ba7c58bfc3fe7dc5f72d27e41081e29da38","schema_version":"1.0","event_id":"sha256:4a4e2464c6883e69203f54045ba15ba7c58bfc3fe7dc5f72d27e41081e29da38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:6OIQZAREET47KK2II4NUNBGF74","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on metric-measure spaces supporting Poincar\\'e inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Piotr Haj{\\l}asz, Ryan Alvarado","submitted_at":"2019-02-28T03:05:03Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10876","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b0WJdJJe75Icys3PLD2bjMMQ/0/6Y4jyeodfrFElO+fk8zLqD9SG67NU06rtKlzMA08Q6RDfDRyqH1y0OrQGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:23:47.280736Z"},"content_sha256":"c9db52352985e702aea6e39bfddbc2a25ea45b00c076c3f924ebfaf7aa714c73","schema_version":"1.0","event_id":"sha256:c9db52352985e702aea6e39bfddbc2a25ea45b00c076c3f924ebfaf7aa714c73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6OIQZAREET47KK2II4NUNBGF74/bundle.json","state_url":"https://pith.science/pith/6OIQZAREET47KK2II4NUNBGF74/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6OIQZAREET47KK2II4NUNBGF74/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-12T00:23:47Z","links":{"resolver":"https://pith.science/pith/6OIQZAREET47KK2II4NUNBGF74","bundle":"https://pith.science/pith/6OIQZAREET47KK2II4NUNBGF74/bundle.json","state":"https://pith.science/pith/6OIQZAREET47KK2II4NUNBGF74/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6OIQZAREET47KK2II4NUNBGF74/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dv2xwMzLqHtuhbWVtRBpBEUfVqN4o7fSmyq4Jnj4MvFw8F/LrUNpz/+2sFdHMlNoVNxqqTQIZMdZUEkCfL01Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:23:47.282592Z","bundle_sha256":"5f307743a4a8ecadc5c6f5f4e1707d110344b818c46d007be360788b234ea488"}}