{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OUY77IL3ODQSJU5EMZGDHBJSC5","short_pith_number":"pith:OUY77IL3","canonical_record":{"source":{"id":"1603.05236","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-13T23:39:57Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"32a1bcaa762ac37fd2785f2564ee5867c0ab2d5aa74a204b40be82c68205cae5","abstract_canon_sha256":"d786a522a8583719e3a66b8eaf6d24f35802202b2a0b6237c9d9bd567015a19a"},"schema_version":"1.0"},"canonical_sha256":"7531ffa17b70e124d3a4664c33853217523a4786546c09a8e49a5297dee3c160","source":{"kind":"arxiv","id":"1603.05236","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05236","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05236v2","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05236","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"OUY77IL3ODQS","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OUY77IL3ODQSJU5E","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OUY77IL3","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OUY77IL3ODQSJU5EMZGDHBJSC5","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05236","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-13T23:39:57Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"32a1bcaa762ac37fd2785f2564ee5867c0ab2d5aa74a204b40be82c68205cae5","abstract_canon_sha256":"d786a522a8583719e3a66b8eaf6d24f35802202b2a0b6237c9d9bd567015a19a"},"schema_version":"1.0"},"canonical_sha256":"7531ffa17b70e124d3a4664c33853217523a4786546c09a8e49a5297dee3c160","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:22.499978Z","signature_b64":"UZqT8Md4ennwKMQGORXktypyEu5sLxwR6YtP1GaDLOpY2xZ+65e3OhK8g/0IhKCVWp9VMEWGJlP1U8Qc+ugLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7531ffa17b70e124d3a4664c33853217523a4786546c09a8e49a5297dee3c160","last_reissued_at":"2026-05-18T01:11:22.499292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:22.499292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05236","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":"2026-05-18T01:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9+3q1NL4Ix1z+oLetaj3G63ygoslwAaNxsTZ0vYYxjRITWRs97tTNjYWKEYhw1ngVgV/WsJyxcsMoeifZQxHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:53:08.900614Z"},"content_sha256":"b4ebdcb435dc279d6d6f6619baeeed1e127f342036f5109c41ceda3dd2bcf1d6","schema_version":"1.0","event_id":"sha256:b4ebdcb435dc279d6d6f6619baeeed1e127f342036f5109c41ceda3dd2bcf1d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OUY77IL3ODQSJU5EMZGDHBJSC5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structure theory of singular spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Richard H. Bamler","submitted_at":"2016-03-13T23:39:57Z","abstract_excerpt":"In this paper we generalize the theory of Cheeger, Colding and Naber to certain singular spaces that arise as limits of sequences of Riemannian manifolds. This theory will have applications in the analysis of Ricci flows of bounded curvature, which we will describe in a subsequent paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05236","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":"2026-05-18T01:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7dxT4dRaXUDYoQVJaK3MFkQCT4vyyp3fgH/D9MWK9ryL/ezmegfz9NvhA0qBxqczQ8qn8o47PWiQ/YWC5lgqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:53:08.901280Z"},"content_sha256":"73a30c4346765e98629a67dba2c96b348310e2f5f9ea617284b32b921f544610","schema_version":"1.0","event_id":"sha256:73a30c4346765e98629a67dba2c96b348310e2f5f9ea617284b32b921f544610"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OUY77IL3ODQSJU5EMZGDHBJSC5/bundle.json","state_url":"https://pith.science/pith/OUY77IL3ODQSJU5EMZGDHBJSC5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OUY77IL3ODQSJU5EMZGDHBJSC5/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":"2026-05-28T22:53:08Z","links":{"resolver":"https://pith.science/pith/OUY77IL3ODQSJU5EMZGDHBJSC5","bundle":"https://pith.science/pith/OUY77IL3ODQSJU5EMZGDHBJSC5/bundle.json","state":"https://pith.science/pith/OUY77IL3ODQSJU5EMZGDHBJSC5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OUY77IL3ODQSJU5EMZGDHBJSC5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OUY77IL3ODQSJU5EMZGDHBJSC5","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":"d786a522a8583719e3a66b8eaf6d24f35802202b2a0b6237c9d9bd567015a19a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-13T23:39:57Z","title_canon_sha256":"32a1bcaa762ac37fd2785f2564ee5867c0ab2d5aa74a204b40be82c68205cae5"},"schema_version":"1.0","source":{"id":"1603.05236","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05236","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05236v2","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05236","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"OUY77IL3ODQS","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OUY77IL3ODQSJU5E","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OUY77IL3","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:73a30c4346765e98629a67dba2c96b348310e2f5f9ea617284b32b921f544610","target":"graph","created_at":"2026-05-18T01:11:22Z","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 paper we generalize the theory of Cheeger, Colding and Naber to certain singular spaces that arise as limits of sequences of Riemannian manifolds. This theory will have applications in the analysis of Ricci flows of bounded curvature, which we will describe in a subsequent paper.","authors_text":"Richard H. Bamler","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-13T23:39:57Z","title":"Structure theory of singular spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05236","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:b4ebdcb435dc279d6d6f6619baeeed1e127f342036f5109c41ceda3dd2bcf1d6","target":"record","created_at":"2026-05-18T01:11:22Z","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":"d786a522a8583719e3a66b8eaf6d24f35802202b2a0b6237c9d9bd567015a19a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-13T23:39:57Z","title_canon_sha256":"32a1bcaa762ac37fd2785f2564ee5867c0ab2d5aa74a204b40be82c68205cae5"},"schema_version":"1.0","source":{"id":"1603.05236","kind":"arxiv","version":2}},"canonical_sha256":"7531ffa17b70e124d3a4664c33853217523a4786546c09a8e49a5297dee3c160","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7531ffa17b70e124d3a4664c33853217523a4786546c09a8e49a5297dee3c160","first_computed_at":"2026-05-18T01:11:22.499292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:22.499292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UZqT8Md4ennwKMQGORXktypyEu5sLxwR6YtP1GaDLOpY2xZ+65e3OhK8g/0IhKCVWp9VMEWGJlP1U8Qc+ugLDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:22.499978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05236","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4ebdcb435dc279d6d6f6619baeeed1e127f342036f5109c41ceda3dd2bcf1d6","sha256:73a30c4346765e98629a67dba2c96b348310e2f5f9ea617284b32b921f544610"],"state_sha256":"8f210da4ce3a51e61194d5440b50ead111bac0d4ce2a3bb4219abecc68136464"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0mKhRrGufjZm/SQginzAA1SDdwf8cQ+ZO8lnYMAteJPRu6pyMtIVRN3haIwpbwdQqHiJXo6h/vC1RdgfTVFBBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:53:08.904753Z","bundle_sha256":"5119cc8eb80818e4eabf8f6fac262685ae19bb3575cfbb8e8acc3abe8ddf3fa7"}}