{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IM5VVYTYCXDT6ZJC2YFCIPA445","short_pith_number":"pith:IM5VVYTY","canonical_record":{"source":{"id":"1812.02571","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-06T14:54:54Z","cross_cats_sorted":[],"title_canon_sha256":"b1a1a5a025b1673af891cd78e8c780adac4c8aae6ab3ed2e589731a2237a0d86","abstract_canon_sha256":"7aa77ffc104b08fe6da13308c9f2630112d10bea538edabd6eb2c2787f639c5e"},"schema_version":"1.0"},"canonical_sha256":"433b5ae27815c73f6522d60a243c1ce74cdb5875e2ae8586fcbdb6bbfc368c73","source":{"kind":"arxiv","id":"1812.02571","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02571","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02571v1","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02571","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"IM5VVYTYCXDT","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IM5VVYTYCXDT6ZJC","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IM5VVYTY","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IM5VVYTYCXDT6ZJC2YFCIPA445","target":"record","payload":{"canonical_record":{"source":{"id":"1812.02571","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-06T14:54:54Z","cross_cats_sorted":[],"title_canon_sha256":"b1a1a5a025b1673af891cd78e8c780adac4c8aae6ab3ed2e589731a2237a0d86","abstract_canon_sha256":"7aa77ffc104b08fe6da13308c9f2630112d10bea538edabd6eb2c2787f639c5e"},"schema_version":"1.0"},"canonical_sha256":"433b5ae27815c73f6522d60a243c1ce74cdb5875e2ae8586fcbdb6bbfc368c73","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:55.402214Z","signature_b64":"n2EraQN73mNfYttqfMim+GFRTKkkjBNdLsGV4NQTWY3f7kkif5DDppLXKLJQIpYitJfivYy0g8mn1xOr7nFgDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"433b5ae27815c73f6522d60a243c1ce74cdb5875e2ae8586fcbdb6bbfc368c73","last_reissued_at":"2026-05-17T23:58:55.401766Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:55.401766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.02571","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"17L/QeFBvHqILemOuRfrNBvri9OeoTMNCprkMI1xEyOQbNVZuzcsldOSPri24Za6FUcEPhR8ELc5irVgJcZ7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:06:34.818531Z"},"content_sha256":"d6106fa8d034a79558ee3aea1edfd4ab11f7b65ec70b088983923cbaa848284c","schema_version":"1.0","event_id":"sha256:d6106fa8d034a79558ee3aea1edfd4ab11f7b65ec70b088983923cbaa848284c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IM5VVYTYCXDT6ZJC2YFCIPA445","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Radius estimates for Alexandrov space with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jian Ge, Ronggang Li","submitted_at":"2018-12-06T14:54:54Z","abstract_excerpt":"In this note, we study the radius of positively curved or non-negatively curved Alexandrov space with strictly convex boundary, with convexity measured by the Base-Angle defined by Alexander and Bishop. We also estimate the volume of the boundary of non-negatively curved spaces as well as the rigidity case, which can be thought as a non-negatively curved version of a recent result of Grove-Petersen."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02571","kind":"arxiv","version":1},"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":"2026-05-17T23:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2GeeSr7ToZ96hdo4xJguCSw371ILrpmoqOS1WeNxcclQxL4nTbsbfzq85XfIqZvNCg2fRRihpyDtR7ibCLLZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:06:34.819169Z"},"content_sha256":"b52de6826a0c9d2b2a02a67158014395147c749d99cfe6e540097493255cd687","schema_version":"1.0","event_id":"sha256:b52de6826a0c9d2b2a02a67158014395147c749d99cfe6e540097493255cd687"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IM5VVYTYCXDT6ZJC2YFCIPA445/bundle.json","state_url":"https://pith.science/pith/IM5VVYTYCXDT6ZJC2YFCIPA445/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IM5VVYTYCXDT6ZJC2YFCIPA445/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":"2026-05-30T23:06:34Z","links":{"resolver":"https://pith.science/pith/IM5VVYTYCXDT6ZJC2YFCIPA445","bundle":"https://pith.science/pith/IM5VVYTYCXDT6ZJC2YFCIPA445/bundle.json","state":"https://pith.science/pith/IM5VVYTYCXDT6ZJC2YFCIPA445/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IM5VVYTYCXDT6ZJC2YFCIPA445/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IM5VVYTYCXDT6ZJC2YFCIPA445","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":"7aa77ffc104b08fe6da13308c9f2630112d10bea538edabd6eb2c2787f639c5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-06T14:54:54Z","title_canon_sha256":"b1a1a5a025b1673af891cd78e8c780adac4c8aae6ab3ed2e589731a2237a0d86"},"schema_version":"1.0","source":{"id":"1812.02571","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02571","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02571v1","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02571","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"IM5VVYTYCXDT","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IM5VVYTYCXDT6ZJC","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IM5VVYTY","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:b52de6826a0c9d2b2a02a67158014395147c749d99cfe6e540097493255cd687","target":"graph","created_at":"2026-05-17T23:58:55Z","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":"In this note, we study the radius of positively curved or non-negatively curved Alexandrov space with strictly convex boundary, with convexity measured by the Base-Angle defined by Alexander and Bishop. We also estimate the volume of the boundary of non-negatively curved spaces as well as the rigidity case, which can be thought as a non-negatively curved version of a recent result of Grove-Petersen.","authors_text":"Jian Ge, Ronggang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-06T14:54:54Z","title":"Radius estimates for Alexandrov space with boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02571","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:d6106fa8d034a79558ee3aea1edfd4ab11f7b65ec70b088983923cbaa848284c","target":"record","created_at":"2026-05-17T23:58:55Z","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":"7aa77ffc104b08fe6da13308c9f2630112d10bea538edabd6eb2c2787f639c5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-06T14:54:54Z","title_canon_sha256":"b1a1a5a025b1673af891cd78e8c780adac4c8aae6ab3ed2e589731a2237a0d86"},"schema_version":"1.0","source":{"id":"1812.02571","kind":"arxiv","version":1}},"canonical_sha256":"433b5ae27815c73f6522d60a243c1ce74cdb5875e2ae8586fcbdb6bbfc368c73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"433b5ae27815c73f6522d60a243c1ce74cdb5875e2ae8586fcbdb6bbfc368c73","first_computed_at":"2026-05-17T23:58:55.401766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:55.401766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n2EraQN73mNfYttqfMim+GFRTKkkjBNdLsGV4NQTWY3f7kkif5DDppLXKLJQIpYitJfivYy0g8mn1xOr7nFgDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:55.402214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02571","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6106fa8d034a79558ee3aea1edfd4ab11f7b65ec70b088983923cbaa848284c","sha256:b52de6826a0c9d2b2a02a67158014395147c749d99cfe6e540097493255cd687"],"state_sha256":"9c73ce732699eb2acbf2cf5c33eaf7b3501ac219b7e9d86372b81d19e08febd3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q7RfrlYUEgPbMZZH1Y+CsIaWvSC41HNp+0feH2Wc8zD58rFaDd9jXueE4K73DvQTGBc9tECPjufl0sSEqUhGCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:06:34.822475Z","bundle_sha256":"c09cdee033d19b09c67168fd9bedf3489962a38e20dc4914addb7e953a8b9f2b"}}