{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:Y2BIV4UC3VUPIV7SDUHMMJMQ64","short_pith_number":"pith:Y2BIV4UC","schema_version":"1.0","canonical_sha256":"c6828af282dd68f457f21d0ec62590f718df4710f74c09fea84093b0f80e603f","source":{"kind":"arxiv","id":"1905.00123","version":2},"attestation_state":"computed","paper":{"title":"New differential operator and non-collapsed $RCD$ spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Shouhei Honda","submitted_at":"2019-04-30T22:51:13Z","abstract_excerpt":"We show characterizations of non-collapsed compact $RCD(K, N)$ spaces, which in particular confirm a conjecture of De Philippis-Gigli on the implication from the weakly non-collapsed condition to the non-collapsed one in the compact case. The key idea is to give the explicit formula of the Laplacian associated to the pull-back Riemannian metric by embedding in $L^2$ via the heat kernel. This seems the first application of geometric flow to the study of RCD spaces."},"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":"1905.00123","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-04-30T22:51:13Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"0d5301ed84e9c30f41cd2fc639246dfdee82bcac6c593ff4394f2454da5dbed6","abstract_canon_sha256":"03db27da815feb14cfa946f317ec6cae3f3682e22db02bd95d557fdcbd4895e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:52:14.699226Z","signature_b64":"BkoMhJOna0fjR9msO5XFvQVicnCLe8fv7fXWzAbpQ8oyHyimMlsmD/YELR4upuns3SWwVs34llueUpzdlFVoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6828af282dd68f457f21d0ec62590f718df4710f74c09fea84093b0f80e603f","last_reissued_at":"2026-07-05T01:52:14.698876Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:52:14.698876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New differential operator and non-collapsed $RCD$ spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Shouhei Honda","submitted_at":"2019-04-30T22:51:13Z","abstract_excerpt":"We show characterizations of non-collapsed compact $RCD(K, N)$ spaces, which in particular confirm a conjecture of De Philippis-Gigli on the implication from the weakly non-collapsed condition to the non-collapsed one in the compact case. The key idea is to give the explicit formula of the Laplacian associated to the pull-back Riemannian metric by embedding in $L^2$ via the heat kernel. This seems the first application of geometric flow to the study of RCD spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00123","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/1905.00123/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":"1905.00123","created_at":"2026-07-05T01:52:14.698932+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.00123v2","created_at":"2026-07-05T01:52:14.698932+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00123","created_at":"2026-07-05T01:52:14.698932+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y2BIV4UC3VUP","created_at":"2026-07-05T01:52:14.698932+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y2BIV4UC3VUPIV7S","created_at":"2026-07-05T01:52:14.698932+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y2BIV4UC","created_at":"2026-07-05T01:52:14.698932+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.07036","citing_title":"On the structure of RCD spaces with upper curvature bounds","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y2BIV4UC3VUPIV7SDUHMMJMQ64","json":"https://pith.science/pith/Y2BIV4UC3VUPIV7SDUHMMJMQ64.json","graph_json":"https://pith.science/api/pith-number/Y2BIV4UC3VUPIV7SDUHMMJMQ64/graph.json","events_json":"https://pith.science/api/pith-number/Y2BIV4UC3VUPIV7SDUHMMJMQ64/events.json","paper":"https://pith.science/paper/Y2BIV4UC"},"agent_actions":{"view_html":"https://pith.science/pith/Y2BIV4UC3VUPIV7SDUHMMJMQ64","download_json":"https://pith.science/pith/Y2BIV4UC3VUPIV7SDUHMMJMQ64.json","view_paper":"https://pith.science/paper/Y2BIV4UC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.00123&json=true","fetch_graph":"https://pith.science/api/pith-number/Y2BIV4UC3VUPIV7SDUHMMJMQ64/graph.json","fetch_events":"https://pith.science/api/pith-number/Y2BIV4UC3VUPIV7SDUHMMJMQ64/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y2BIV4UC3VUPIV7SDUHMMJMQ64/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y2BIV4UC3VUPIV7SDUHMMJMQ64/action/storage_attestation","attest_author":"https://pith.science/pith/Y2BIV4UC3VUPIV7SDUHMMJMQ64/action/author_attestation","sign_citation":"https://pith.science/pith/Y2BIV4UC3VUPIV7SDUHMMJMQ64/action/citation_signature","submit_replication":"https://pith.science/pith/Y2BIV4UC3VUPIV7SDUHMMJMQ64/action/replication_record"}},"created_at":"2026-07-05T01:52:14.698932+00:00","updated_at":"2026-07-05T01:52:14.698932+00:00"}