{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:T4UXNXJBIB3JKSQVPFCAPXGAGG","short_pith_number":"pith:T4UXNXJB","canonical_record":{"source":{"id":"1809.04386","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-12T12:45:11Z","cross_cats_sorted":[],"title_canon_sha256":"a5aa60fdef31ab38bed593b5270a0bce3acfbd00b30aa9a9b1e6f39387358a02","abstract_canon_sha256":"7b3cf7c177ff3f5156e9f58d18fbd5177fce20f13d0bbad70a6ff72da6a22103"},"schema_version":"1.0"},"canonical_sha256":"9f2976dd214076954a15794407dcc031b4f9f1ace1edafedc623a044bcb20c76","source":{"kind":"arxiv","id":"1809.04386","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.04386","created_at":"2026-07-05T01:06:06Z"},{"alias_kind":"arxiv_version","alias_value":"1809.04386v2","created_at":"2026-07-05T01:06:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04386","created_at":"2026-07-05T01:06:06Z"},{"alias_kind":"pith_short_12","alias_value":"T4UXNXJBIB3J","created_at":"2026-07-05T01:06:06Z"},{"alias_kind":"pith_short_16","alias_value":"T4UXNXJBIB3JKSQV","created_at":"2026-07-05T01:06:06Z"},{"alias_kind":"pith_short_8","alias_value":"T4UXNXJB","created_at":"2026-07-05T01:06:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:T4UXNXJBIB3JKSQVPFCAPXGAGG","target":"record","payload":{"canonical_record":{"source":{"id":"1809.04386","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-12T12:45:11Z","cross_cats_sorted":[],"title_canon_sha256":"a5aa60fdef31ab38bed593b5270a0bce3acfbd00b30aa9a9b1e6f39387358a02","abstract_canon_sha256":"7b3cf7c177ff3f5156e9f58d18fbd5177fce20f13d0bbad70a6ff72da6a22103"},"schema_version":"1.0"},"canonical_sha256":"9f2976dd214076954a15794407dcc031b4f9f1ace1edafedc623a044bcb20c76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:06:06.609620Z","signature_b64":"JCWKzSUhHf+gQkoGuNK5jIInMDnyV2jIxGEL8u4lCsAZkee1Lx2uFwp/B0kVaEAWwyu6FvBVUNWvvd/mtLoNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f2976dd214076954a15794407dcc031b4f9f1ace1edafedc623a044bcb20c76","last_reissued_at":"2026-07-05T01:06:06.608827Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:06:06.608827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.04386","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":"2026-07-05T01:06:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/HPJHhb58w2dotc+PMKImuEO32oTofP2EY7qEnTT2KWqgAByTfgmcmKmoWPU6VJg2E99p2R/sZVlw7BxVyUnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T19:33:38.683448Z"},"content_sha256":"9a6ebe33c29ed10f8df3b2a061fee6e9deb151cd2d4acf97232e7ad004df9541","schema_version":"1.0","event_id":"sha256:9a6ebe33c29ed10f8df3b2a061fee6e9deb151cd2d4acf97232e7ad004df9541"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:T4UXNXJBIB3JKSQVPFCAPXGAGG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the regular-convexity of Ricci shrinker limit spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bing Wang, Shaosai Huang, Yu Li","submitted_at":"2018-09-12T12:45:11Z","abstract_excerpt":"In this paper, we study the structure of the pointed-Gromov-Hausdorff limits of sequences of Ricci shrinkers. We define a regular-singular decomposition following the work of Cheeger-Colding for manifolds with a uniform Ricci curvature lower bound, and prove that the regular part of any Ricci shrinker limit space is convex, inspired by Colding-Naber's original idea of parabolic smoothing of the distance functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04386","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1809.04386/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:06:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZOtwqsMhnpfwF45gfjwGRGgdA5B+U4Km4c+ygxItOaFrhPVbVyOHC6A8+VYW/FfdUkYwsxBLo6BKqMvouT+1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T19:33:38.684044Z"},"content_sha256":"d602d4b90f011c6766875d2862aa02e147c8dc83384457f360638f7dd55c7b39","schema_version":"1.0","event_id":"sha256:d602d4b90f011c6766875d2862aa02e147c8dc83384457f360638f7dd55c7b39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4UXNXJBIB3JKSQVPFCAPXGAGG/bundle.json","state_url":"https://pith.science/pith/T4UXNXJBIB3JKSQVPFCAPXGAGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4UXNXJBIB3JKSQVPFCAPXGAGG/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":"2026-08-11T19:33:38Z","links":{"resolver":"https://pith.science/pith/T4UXNXJBIB3JKSQVPFCAPXGAGG","bundle":"https://pith.science/pith/T4UXNXJBIB3JKSQVPFCAPXGAGG/bundle.json","state":"https://pith.science/pith/T4UXNXJBIB3JKSQVPFCAPXGAGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4UXNXJBIB3JKSQVPFCAPXGAGG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:T4UXNXJBIB3JKSQVPFCAPXGAGG","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":"7b3cf7c177ff3f5156e9f58d18fbd5177fce20f13d0bbad70a6ff72da6a22103","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-12T12:45:11Z","title_canon_sha256":"a5aa60fdef31ab38bed593b5270a0bce3acfbd00b30aa9a9b1e6f39387358a02"},"schema_version":"1.0","source":{"id":"1809.04386","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.04386","created_at":"2026-07-05T01:06:06Z"},{"alias_kind":"arxiv_version","alias_value":"1809.04386v2","created_at":"2026-07-05T01:06:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04386","created_at":"2026-07-05T01:06:06Z"},{"alias_kind":"pith_short_12","alias_value":"T4UXNXJBIB3J","created_at":"2026-07-05T01:06:06Z"},{"alias_kind":"pith_short_16","alias_value":"T4UXNXJBIB3JKSQV","created_at":"2026-07-05T01:06:06Z"},{"alias_kind":"pith_short_8","alias_value":"T4UXNXJB","created_at":"2026-07-05T01:06:06Z"}],"graph_snapshots":[{"event_id":"sha256:d602d4b90f011c6766875d2862aa02e147c8dc83384457f360638f7dd55c7b39","target":"graph","created_at":"2026-07-05T01:06:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1809.04386/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the structure of the pointed-Gromov-Hausdorff limits of sequences of Ricci shrinkers. We define a regular-singular decomposition following the work of Cheeger-Colding for manifolds with a uniform Ricci curvature lower bound, and prove that the regular part of any Ricci shrinker limit space is convex, inspired by Colding-Naber's original idea of parabolic smoothing of the distance functions.","authors_text":"Bing Wang, Shaosai Huang, Yu Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-12T12:45:11Z","title":"On the regular-convexity of Ricci shrinker limit spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04386","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":"sha256:9a6ebe33c29ed10f8df3b2a061fee6e9deb151cd2d4acf97232e7ad004df9541","target":"record","created_at":"2026-07-05T01:06:06Z","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":"7b3cf7c177ff3f5156e9f58d18fbd5177fce20f13d0bbad70a6ff72da6a22103","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-12T12:45:11Z","title_canon_sha256":"a5aa60fdef31ab38bed593b5270a0bce3acfbd00b30aa9a9b1e6f39387358a02"},"schema_version":"1.0","source":{"id":"1809.04386","kind":"arxiv","version":2}},"canonical_sha256":"9f2976dd214076954a15794407dcc031b4f9f1ace1edafedc623a044bcb20c76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f2976dd214076954a15794407dcc031b4f9f1ace1edafedc623a044bcb20c76","first_computed_at":"2026-07-05T01:06:06.608827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:06:06.608827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JCWKzSUhHf+gQkoGuNK5jIInMDnyV2jIxGEL8u4lCsAZkee1Lx2uFwp/B0kVaEAWwyu6FvBVUNWvvd/mtLoNCA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:06:06.609620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.04386","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a6ebe33c29ed10f8df3b2a061fee6e9deb151cd2d4acf97232e7ad004df9541","sha256:d602d4b90f011c6766875d2862aa02e147c8dc83384457f360638f7dd55c7b39"],"state_sha256":"e01a29576afdd5bdd8c4298668d812dcdd74a0c2241079a15c4961f9d6355da3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LwcMkh+hAPoqhPho3Q1YHnuE/Sf68s0vDbzQBmMuOyfuf9Llxf2vtMboU9Oo7XXpr5+85vGDQk5ZnJKDC4mnAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T19:33:38.695058Z","bundle_sha256":"d72105bf9d52ca82a08199d38683d2f96912b6f85f5e48807a0231afe777f21f"}}