{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LBFGMVT6KIYQQR44US6SKKEDWG","short_pith_number":"pith:LBFGMVT6","canonical_record":{"source":{"id":"1510.07547","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-26T16:53:07Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"6fd4921063fa3db0b678cca12acdf2d9ab67630dffd634429ce7bd2b21a15fd1","abstract_canon_sha256":"28f5d4fbfc8a35c4e16daba4da1ca3f58ada004ddf86ff56e8b3d52efa544cf5"},"schema_version":"1.0"},"canonical_sha256":"584a66567e523108479ca4bd252883b1924ceef35c3a8913984d550635269b7d","source":{"kind":"arxiv","id":"1510.07547","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07547","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07547v1","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07547","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"LBFGMVT6KIYQ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LBFGMVT6KIYQQR44","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LBFGMVT6","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LBFGMVT6KIYQQR44US6SKKEDWG","target":"record","payload":{"canonical_record":{"source":{"id":"1510.07547","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-26T16:53:07Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"6fd4921063fa3db0b678cca12acdf2d9ab67630dffd634429ce7bd2b21a15fd1","abstract_canon_sha256":"28f5d4fbfc8a35c4e16daba4da1ca3f58ada004ddf86ff56e8b3d52efa544cf5"},"schema_version":"1.0"},"canonical_sha256":"584a66567e523108479ca4bd252883b1924ceef35c3a8913984d550635269b7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:13.874188Z","signature_b64":"rydLhtKptGCe9OnYDevtyttugHy8E2M6r5LEE65u+cvCxJ0OQyIm3ZUlSStQK5nilFveuOkOQBOtGOrK9i0aAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"584a66567e523108479ca4bd252883b1924ceef35c3a8913984d550635269b7d","last_reissued_at":"2026-05-18T01:29:13.873583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:13.873583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.07547","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":"2026-05-18T01:29:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"exQfmtZqDyYGYLZVRzrka5CeVaXCel4ArPyVWFRlZNWTPrMfySXGbHMeRr8Xs/MTWu4MT8LmjqqN7hM8ep/pAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:17:49.162653Z"},"content_sha256":"a8eac83a674fc30ea298b3519206c50fc5a95d6da9c472c04c8b447502a28adf","schema_version":"1.0","event_id":"sha256:a8eac83a674fc30ea298b3519206c50fc5a95d6da9c472c04c8b447502a28adf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LBFGMVT6KIYQQR44US6SKKEDWG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intrinsic flat and Gromov-Hausdorff convergence of manifolds with Ricci curvature bounded below","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Jacobus W. Portegies, Rostislav Matveev","submitted_at":"2015-10-26T16:53:07Z","abstract_excerpt":"We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature uniformly bounded from below and diameter uniformly bounded above, Gromov-Hausdorff convergence essentially agrees with intrinsic flat convergence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07547","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":"2026-05-18T01:29:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Igh0gweR+vNDlVnl47xXBSRT/7I6PznfdhnHsCUoxV+jbuA9tPsSBlo5sX5AFCBAzSXbraWnfhEgNKDJq0ipCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:17:49.162989Z"},"content_sha256":"42a55035f19c05b73b5549336fc005748d39878d604247419b406fbdd6aaf507","schema_version":"1.0","event_id":"sha256:42a55035f19c05b73b5549336fc005748d39878d604247419b406fbdd6aaf507"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBFGMVT6KIYQQR44US6SKKEDWG/bundle.json","state_url":"https://pith.science/pith/LBFGMVT6KIYQQR44US6SKKEDWG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBFGMVT6KIYQQR44US6SKKEDWG/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":"2026-06-02T04:17:49Z","links":{"resolver":"https://pith.science/pith/LBFGMVT6KIYQQR44US6SKKEDWG","bundle":"https://pith.science/pith/LBFGMVT6KIYQQR44US6SKKEDWG/bundle.json","state":"https://pith.science/pith/LBFGMVT6KIYQQR44US6SKKEDWG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBFGMVT6KIYQQR44US6SKKEDWG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LBFGMVT6KIYQQR44US6SKKEDWG","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":"28f5d4fbfc8a35c4e16daba4da1ca3f58ada004ddf86ff56e8b3d52efa544cf5","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-26T16:53:07Z","title_canon_sha256":"6fd4921063fa3db0b678cca12acdf2d9ab67630dffd634429ce7bd2b21a15fd1"},"schema_version":"1.0","source":{"id":"1510.07547","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07547","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07547v1","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07547","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"LBFGMVT6KIYQ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LBFGMVT6KIYQQR44","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LBFGMVT6","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:42a55035f19c05b73b5549336fc005748d39878d604247419b406fbdd6aaf507","target":"graph","created_at":"2026-05-18T01:29:13Z","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 show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature uniformly bounded from below and diameter uniformly bounded above, Gromov-Hausdorff convergence essentially agrees with intrinsic flat convergence.","authors_text":"Jacobus W. Portegies, Rostislav Matveev","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-26T16:53:07Z","title":"Intrinsic flat and Gromov-Hausdorff convergence of manifolds with Ricci curvature bounded below"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07547","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:a8eac83a674fc30ea298b3519206c50fc5a95d6da9c472c04c8b447502a28adf","target":"record","created_at":"2026-05-18T01:29:13Z","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":"28f5d4fbfc8a35c4e16daba4da1ca3f58ada004ddf86ff56e8b3d52efa544cf5","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-26T16:53:07Z","title_canon_sha256":"6fd4921063fa3db0b678cca12acdf2d9ab67630dffd634429ce7bd2b21a15fd1"},"schema_version":"1.0","source":{"id":"1510.07547","kind":"arxiv","version":1}},"canonical_sha256":"584a66567e523108479ca4bd252883b1924ceef35c3a8913984d550635269b7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"584a66567e523108479ca4bd252883b1924ceef35c3a8913984d550635269b7d","first_computed_at":"2026-05-18T01:29:13.873583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:13.873583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rydLhtKptGCe9OnYDevtyttugHy8E2M6r5LEE65u+cvCxJ0OQyIm3ZUlSStQK5nilFveuOkOQBOtGOrK9i0aAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:13.874188Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07547","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8eac83a674fc30ea298b3519206c50fc5a95d6da9c472c04c8b447502a28adf","sha256:42a55035f19c05b73b5549336fc005748d39878d604247419b406fbdd6aaf507"],"state_sha256":"c398e4358f457c31afbc1f2485f18cd76e141ebd9de1a6a2fa4019696150e0ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xJjXMtYTtAwTmgXAXhkQpSVrRTTb82fUq1xrud0B9lpzaqSnO36NhI4uOaCtbL1aM7pvJj6v3OL0kROcqHc8Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:17:49.165011Z","bundle_sha256":"75f67a4f6d5decafe5e505fb6b6c46d468bea320caa213a0c933b3f4d72eaee9"}}