{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BC5TVPP5UWDEHBVIRQC44DJ53T","short_pith_number":"pith:BC5TVPP5","canonical_record":{"source":{"id":"1701.06345","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-23T11:46:53Z","cross_cats_sorted":[],"title_canon_sha256":"872049775bc28793d49fd2a9835cd6de6200a8949408ccb23522e5115153c683","abstract_canon_sha256":"4dd5dc2e377a9d817af76f621cd3101a20ef0e49a0be2f8c8d0a1469abecfd67"},"schema_version":"1.0"},"canonical_sha256":"08bb3abdfda5864386a88c05ce0d3ddced687d197e6d5fa0d3b781269d202a49","source":{"kind":"arxiv","id":"1701.06345","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06345","created_at":"2026-05-18T00:33:52Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06345v2","created_at":"2026-05-18T00:33:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06345","created_at":"2026-05-18T00:33:52Z"},{"alias_kind":"pith_short_12","alias_value":"BC5TVPP5UWDE","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BC5TVPP5UWDEHBVI","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BC5TVPP5","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BC5TVPP5UWDEHBVIRQC44DJ53T","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06345","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-23T11:46:53Z","cross_cats_sorted":[],"title_canon_sha256":"872049775bc28793d49fd2a9835cd6de6200a8949408ccb23522e5115153c683","abstract_canon_sha256":"4dd5dc2e377a9d817af76f621cd3101a20ef0e49a0be2f8c8d0a1469abecfd67"},"schema_version":"1.0"},"canonical_sha256":"08bb3abdfda5864386a88c05ce0d3ddced687d197e6d5fa0d3b781269d202a49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:52.730480Z","signature_b64":"ldWeIgd5CLDhXTi8McKNILjaZ+lHOF0RnTCZ1j3XBJkn3h726FEZkXp7ppetr/1k3xqmyOyUSBaofnLaWy9GDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08bb3abdfda5864386a88c05ce0d3ddced687d197e6d5fa0d3b781269d202a49","last_reissued_at":"2026-05-18T00:33:52.729883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:52.729883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06345","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WUmw2j8v4q16SWys/j8qOgT3SgkheYoKCsIif7N3M0f+EMj+uUdwnzyL4QMIqUzr9/2tKVuR0EHpOQQGbXB8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:17:15.668675Z"},"content_sha256":"aa2d3f98e637b9d5e9dc22bf3e6be777b821577eee7c2dfba35c0a38a3413033","schema_version":"1.0","event_id":"sha256:aa2d3f98e637b9d5e9dc22bf3e6be777b821577eee7c2dfba35c0a38a3413033"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BC5TVPP5UWDEHBVIRQC44DJ53T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasispheres and metric doubling measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Atte Lohvansuu, Kai Rajala, Martti Rasimus","submitted_at":"2017-01-23T11:46:53Z","abstract_excerpt":"Applying the Bonk-Kleiner characterization of Ahlfors 2-regular quasispheres, we show that a metric two-sphere $X$ is a quasisphere if and only if $X$ is linearly locally connected and carries a weak metric doubling measure, i.e., a measure that deforms the metric on $X$ without much shrinking."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06345","kind":"arxiv","version":2},"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":"2026-05-18T00:33:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PHX0Iu2MgUFZ1Lxy37A6jS0gK3lilPcI1WvXDpnSxEAj907y/SttrplnsBF1aJ+K4ITxh39nvHMMfQYFaJ1LBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:17:15.669022Z"},"content_sha256":"55d8a4f465ff6b652fa3557b53e2fa7a28b9f031ff2710e21223090c5aa894ec","schema_version":"1.0","event_id":"sha256:55d8a4f465ff6b652fa3557b53e2fa7a28b9f031ff2710e21223090c5aa894ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BC5TVPP5UWDEHBVIRQC44DJ53T/bundle.json","state_url":"https://pith.science/pith/BC5TVPP5UWDEHBVIRQC44DJ53T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BC5TVPP5UWDEHBVIRQC44DJ53T/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":"2026-06-24T18:17:15Z","links":{"resolver":"https://pith.science/pith/BC5TVPP5UWDEHBVIRQC44DJ53T","bundle":"https://pith.science/pith/BC5TVPP5UWDEHBVIRQC44DJ53T/bundle.json","state":"https://pith.science/pith/BC5TVPP5UWDEHBVIRQC44DJ53T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BC5TVPP5UWDEHBVIRQC44DJ53T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BC5TVPP5UWDEHBVIRQC44DJ53T","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":"4dd5dc2e377a9d817af76f621cd3101a20ef0e49a0be2f8c8d0a1469abecfd67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-23T11:46:53Z","title_canon_sha256":"872049775bc28793d49fd2a9835cd6de6200a8949408ccb23522e5115153c683"},"schema_version":"1.0","source":{"id":"1701.06345","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06345","created_at":"2026-05-18T00:33:52Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06345v2","created_at":"2026-05-18T00:33:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06345","created_at":"2026-05-18T00:33:52Z"},{"alias_kind":"pith_short_12","alias_value":"BC5TVPP5UWDE","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BC5TVPP5UWDEHBVI","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BC5TVPP5","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:55d8a4f465ff6b652fa3557b53e2fa7a28b9f031ff2710e21223090c5aa894ec","target":"graph","created_at":"2026-05-18T00:33:52Z","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":"Applying the Bonk-Kleiner characterization of Ahlfors 2-regular quasispheres, we show that a metric two-sphere $X$ is a quasisphere if and only if $X$ is linearly locally connected and carries a weak metric doubling measure, i.e., a measure that deforms the metric on $X$ without much shrinking.","authors_text":"Atte Lohvansuu, Kai Rajala, Martti Rasimus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-23T11:46:53Z","title":"Quasispheres and metric doubling measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06345","kind":"arxiv","version":2},"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:aa2d3f98e637b9d5e9dc22bf3e6be777b821577eee7c2dfba35c0a38a3413033","target":"record","created_at":"2026-05-18T00:33:52Z","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":"4dd5dc2e377a9d817af76f621cd3101a20ef0e49a0be2f8c8d0a1469abecfd67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-23T11:46:53Z","title_canon_sha256":"872049775bc28793d49fd2a9835cd6de6200a8949408ccb23522e5115153c683"},"schema_version":"1.0","source":{"id":"1701.06345","kind":"arxiv","version":2}},"canonical_sha256":"08bb3abdfda5864386a88c05ce0d3ddced687d197e6d5fa0d3b781269d202a49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08bb3abdfda5864386a88c05ce0d3ddced687d197e6d5fa0d3b781269d202a49","first_computed_at":"2026-05-18T00:33:52.729883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:52.729883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ldWeIgd5CLDhXTi8McKNILjaZ+lHOF0RnTCZ1j3XBJkn3h726FEZkXp7ppetr/1k3xqmyOyUSBaofnLaWy9GDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:52.730480Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06345","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa2d3f98e637b9d5e9dc22bf3e6be777b821577eee7c2dfba35c0a38a3413033","sha256:55d8a4f465ff6b652fa3557b53e2fa7a28b9f031ff2710e21223090c5aa894ec"],"state_sha256":"6b5d2e60d6658b68d33f758bfc41c6aead890ea9cb8faffeb42d63d6ab642374"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vXLCiieQy9zHHFFrPbiZJ1bmZ7CEdU7OVJqDgtQv0EPi93ibntq7fCWAsv7V3Q7fNkaZyxv5dsJ8ZJ8TnauMDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:17:15.670994Z","bundle_sha256":"ba5d6ab59714fb75e18780d440a8ef48901dd66a6e3f9a761c31c89dbe3f6b26"}}