{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:545NGEN63H6DU4THNT7E3VMOAT","short_pith_number":"pith:545NGEN6","schema_version":"1.0","canonical_sha256":"ef3ad311bed9fc3a72676cfe4dd58e04e61e8d06f09b174d6b8b2e606f70e7c5","source":{"kind":"arxiv","id":"1907.02614","version":3},"attestation_state":"computed","paper":{"title":"On the topology and the boundary of N-dimensional RCD(K,N) spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Andrea Mondino, Vitali Kapovitch","submitted_at":"2019-07-04T22:16:54Z","abstract_excerpt":"We establish topological regularity and stability of N-dimensional RCD(K,N) spaces (up to a small singular set), also called non-collapsed RCD(K,N) in the literature. We also introduce the notion of a boundary of such spaces and study its properties, including its behavior under Gromov-Hausdorff convergence."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1907.02614","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-07-04T22:16:54Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"ed89b3a20ce41a67459865a0a8917f96e8f7bf098c1d02c63fb36a2083c2759b","abstract_canon_sha256":"fd2a3855efee1f807e87068328d645a9da098bf28a6f4f54b5873aec780e1c7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:21:32.850282Z","signature_b64":"5Jl72dD7gbzPz2Dzfi/vAexZCtzCbff1OOT6PiZ7aMwIbNy52uA+fYo/Bm7dssA/5Pzk7w2+u5WzFcfE8qfPAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef3ad311bed9fc3a72676cfe4dd58e04e61e8d06f09b174d6b8b2e606f70e7c5","last_reissued_at":"2026-07-05T02:21:32.849724Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:21:32.849724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the topology and the boundary of N-dimensional RCD(K,N) spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Andrea Mondino, Vitali Kapovitch","submitted_at":"2019-07-04T22:16:54Z","abstract_excerpt":"We establish topological regularity and stability of N-dimensional RCD(K,N) spaces (up to a small singular set), also called non-collapsed RCD(K,N) in the literature. We also introduce the notion of a boundary of such spaces and study its properties, including its behavior under Gromov-Hausdorff convergence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02614","kind":"arxiv","version":3},"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/1907.02614/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.02614","created_at":"2026-07-05T02:21:32.849788+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.02614v3","created_at":"2026-07-05T02:21:32.849788+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02614","created_at":"2026-07-05T02:21:32.849788+00:00"},{"alias_kind":"pith_short_12","alias_value":"545NGEN63H6D","created_at":"2026-07-05T02:21:32.849788+00:00"},{"alias_kind":"pith_short_16","alias_value":"545NGEN63H6DU4TH","created_at":"2026-07-05T02:21:32.849788+00:00"},{"alias_kind":"pith_short_8","alias_value":"545NGEN6","created_at":"2026-07-05T02:21:32.849788+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.24380","citing_title":"Fibrations, the First Betti Number, and Almost Nonnegative Ricci Curvature","ref_index":53,"is_internal_anchor":false},{"citing_arxiv_id":"2112.06962","citing_title":"One-phase Free Boundary Problems on RCD Metric Measure Spaces","ref_index":64,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/545NGEN63H6DU4THNT7E3VMOAT","json":"https://pith.science/pith/545NGEN63H6DU4THNT7E3VMOAT.json","graph_json":"https://pith.science/api/pith-number/545NGEN63H6DU4THNT7E3VMOAT/graph.json","events_json":"https://pith.science/api/pith-number/545NGEN63H6DU4THNT7E3VMOAT/events.json","paper":"https://pith.science/paper/545NGEN6"},"agent_actions":{"view_html":"https://pith.science/pith/545NGEN63H6DU4THNT7E3VMOAT","download_json":"https://pith.science/pith/545NGEN63H6DU4THNT7E3VMOAT.json","view_paper":"https://pith.science/paper/545NGEN6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.02614&json=true","fetch_graph":"https://pith.science/api/pith-number/545NGEN63H6DU4THNT7E3VMOAT/graph.json","fetch_events":"https://pith.science/api/pith-number/545NGEN63H6DU4THNT7E3VMOAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/545NGEN63H6DU4THNT7E3VMOAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/545NGEN63H6DU4THNT7E3VMOAT/action/storage_attestation","attest_author":"https://pith.science/pith/545NGEN63H6DU4THNT7E3VMOAT/action/author_attestation","sign_citation":"https://pith.science/pith/545NGEN63H6DU4THNT7E3VMOAT/action/citation_signature","submit_replication":"https://pith.science/pith/545NGEN63H6DU4THNT7E3VMOAT/action/replication_record"}},"created_at":"2026-07-05T02:21:32.849788+00:00","updated_at":"2026-07-05T02:21:32.849788+00:00"}