{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QKYOBHIVPFZDRBWNV5LDTOOVPL","short_pith_number":"pith:QKYOBHIV","canonical_record":{"source":{"id":"1310.6815","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-25T04:19:32Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"726bf3a88115018096067288ce770acd08553e12d86f089c02b133bd6826cb4c","abstract_canon_sha256":"3b6a5026f4fcdf30ffb115007a38bc6d85e9ee569c01d78aacf588c0246e1c73"},"schema_version":"1.0"},"canonical_sha256":"82b0e09d1579723886cdaf5639b9d57aeebf0d8846258a69197e231ae87d8f98","source":{"kind":"arxiv","id":"1310.6815","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6815","created_at":"2026-05-18T01:41:00Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6815v2","created_at":"2026-05-18T01:41:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6815","created_at":"2026-05-18T01:41:00Z"},{"alias_kind":"pith_short_12","alias_value":"QKYOBHIVPFZD","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QKYOBHIVPFZDRBWN","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QKYOBHIV","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QKYOBHIVPFZDRBWNV5LDTOOVPL","target":"record","payload":{"canonical_record":{"source":{"id":"1310.6815","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-25T04:19:32Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"726bf3a88115018096067288ce770acd08553e12d86f089c02b133bd6826cb4c","abstract_canon_sha256":"3b6a5026f4fcdf30ffb115007a38bc6d85e9ee569c01d78aacf588c0246e1c73"},"schema_version":"1.0"},"canonical_sha256":"82b0e09d1579723886cdaf5639b9d57aeebf0d8846258a69197e231ae87d8f98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:00.241178Z","signature_b64":"inCtQ0Rfi2a8lletDEdRYUylIUDQflyxLi0Bdy6G/J6QOXKmpCDv7az2VTrrGS36NRjtGOfhOD54t3JwOSlYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82b0e09d1579723886cdaf5639b9d57aeebf0d8846258a69197e231ae87d8f98","last_reissued_at":"2026-05-18T01:41:00.240704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:00.240704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.6815","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":"2026-05-18T01:41:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rNS/pSaF+ZBziqB2c0hUXhiXiZdiDw4RZiy/diczMinWgNYM+erClE8UclUkPP3DEmvyvVpldC7sO4kSO0zNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:00:43.131760Z"},"content_sha256":"9299080b82518b8decc456825e049775b1f19fb6a0d177298c5f7af00cdacf31","schema_version":"1.0","event_id":"sha256:9299080b82518b8decc456825e049775b1f19fb6a0d177298c5f7af00cdacf31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QKYOBHIVPFZDRBWNV5LDTOOVPL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Globalization with probabilistic convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Nan Li","submitted_at":"2013-10-25T04:19:32Z","abstract_excerpt":"We introduce a notion of probabilistic convexity and generalize some classical globalization theorems in Alexandrov geometry. A weighted Alexandrov's lemma is developed as a basic tool."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6815","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":"2026-05-18T01:41:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9/iST38Pn+gXnPq/HBV3EexdKSpTNPrrtuSY4yh4H1sk5mWYo7+o0HYeAVYAFQP8fBAlXiBP5WlewanK70rfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:00:43.132347Z"},"content_sha256":"60fa7a4d6f5854cbcd70b766433dd50ab0eb9d269076b964e105018329c92524","schema_version":"1.0","event_id":"sha256:60fa7a4d6f5854cbcd70b766433dd50ab0eb9d269076b964e105018329c92524"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QKYOBHIVPFZDRBWNV5LDTOOVPL/bundle.json","state_url":"https://pith.science/pith/QKYOBHIVPFZDRBWNV5LDTOOVPL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QKYOBHIVPFZDRBWNV5LDTOOVPL/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":"2026-05-22T23:00:43Z","links":{"resolver":"https://pith.science/pith/QKYOBHIVPFZDRBWNV5LDTOOVPL","bundle":"https://pith.science/pith/QKYOBHIVPFZDRBWNV5LDTOOVPL/bundle.json","state":"https://pith.science/pith/QKYOBHIVPFZDRBWNV5LDTOOVPL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QKYOBHIVPFZDRBWNV5LDTOOVPL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QKYOBHIVPFZDRBWNV5LDTOOVPL","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":"3b6a5026f4fcdf30ffb115007a38bc6d85e9ee569c01d78aacf588c0246e1c73","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-25T04:19:32Z","title_canon_sha256":"726bf3a88115018096067288ce770acd08553e12d86f089c02b133bd6826cb4c"},"schema_version":"1.0","source":{"id":"1310.6815","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6815","created_at":"2026-05-18T01:41:00Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6815v2","created_at":"2026-05-18T01:41:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6815","created_at":"2026-05-18T01:41:00Z"},{"alias_kind":"pith_short_12","alias_value":"QKYOBHIVPFZD","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QKYOBHIVPFZDRBWN","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QKYOBHIV","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:60fa7a4d6f5854cbcd70b766433dd50ab0eb9d269076b964e105018329c92524","target":"graph","created_at":"2026-05-18T01:41:00Z","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":"We introduce a notion of probabilistic convexity and generalize some classical globalization theorems in Alexandrov geometry. A weighted Alexandrov's lemma is developed as a basic tool.","authors_text":"Nan Li","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-25T04:19:32Z","title":"Globalization with probabilistic convexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6815","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":"sha256:9299080b82518b8decc456825e049775b1f19fb6a0d177298c5f7af00cdacf31","target":"record","created_at":"2026-05-18T01:41:00Z","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":"3b6a5026f4fcdf30ffb115007a38bc6d85e9ee569c01d78aacf588c0246e1c73","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-25T04:19:32Z","title_canon_sha256":"726bf3a88115018096067288ce770acd08553e12d86f089c02b133bd6826cb4c"},"schema_version":"1.0","source":{"id":"1310.6815","kind":"arxiv","version":2}},"canonical_sha256":"82b0e09d1579723886cdaf5639b9d57aeebf0d8846258a69197e231ae87d8f98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82b0e09d1579723886cdaf5639b9d57aeebf0d8846258a69197e231ae87d8f98","first_computed_at":"2026-05-18T01:41:00.240704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:00.240704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"inCtQ0Rfi2a8lletDEdRYUylIUDQflyxLi0Bdy6G/J6QOXKmpCDv7az2VTrrGS36NRjtGOfhOD54t3JwOSlYCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:00.241178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6815","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9299080b82518b8decc456825e049775b1f19fb6a0d177298c5f7af00cdacf31","sha256:60fa7a4d6f5854cbcd70b766433dd50ab0eb9d269076b964e105018329c92524"],"state_sha256":"7b548fef601f664090d7aef70e4346476fa3d03dc30f854433f888c433c42cd0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nBUlM/vYDtCP1wITXMtCLAbBpAQWWMy5VRPzS4Sp0FcIOmUK7AWreieRWNOborqTcuhi+N9Ygm7t/QFx/AXcCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T23:00:43.135743Z","bundle_sha256":"e6db4ab6c60fb642f3ad41fa7e18f67c3587843725d616d06005cf0d8255f9d8"}}