{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MBLAEDUECAMZAAYT37RPLAHDJK","short_pith_number":"pith:MBLAEDUE","schema_version":"1.0","canonical_sha256":"6056020e841019900313dfe2f580e34a9585bfd5cc4d6f70462ac8d22a804ce7","source":{"kind":"arxiv","id":"1310.4264","version":3},"attestation_state":"computed","paper":{"title":"Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ivan Gentil (ICJ)","submitted_at":"2013-10-16T04:24:01Z","abstract_excerpt":"We prove a refined contraction inequality for diffusion semigroups with respect to the Wasserstein distance on a compact Riemannian manifold taking account of the dimension. The result generalizes in a Riemannian context, the dimensional contraction established in [BGG13] for the Euclidean heat equation. It is proved by using a dimensional coercive estimate for the Hodge-de Rham semigroup on 1-forms."},"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":"1310.4264","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T04:24:01Z","cross_cats_sorted":[],"title_canon_sha256":"86d705997fc99b50578a4ddcadb38366d5a206d9cf46a6ea1494ac3b06c0837c","abstract_canon_sha256":"24f6965adcf2e2be587de5271030a74bf66a2fd3c91f2e280160161aa0bbeea1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:21.610018Z","signature_b64":"YWXSUcoziIKi3AIKSWbX5A/gWOKimZ+FgrqcSqmjk2DWG65z9bzj54AzzKZ3dZPHHwwGYlwb4NjD+IB/B278Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6056020e841019900313dfe2f580e34a9585bfd5cc4d6f70462ac8d22a804ce7","last_reissued_at":"2026-05-18T02:31:21.609544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:21.609544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ivan Gentil (ICJ)","submitted_at":"2013-10-16T04:24:01Z","abstract_excerpt":"We prove a refined contraction inequality for diffusion semigroups with respect to the Wasserstein distance on a compact Riemannian manifold taking account of the dimension. The result generalizes in a Riemannian context, the dimensional contraction established in [BGG13] for the Euclidean heat equation. It is proved by using a dimensional coercive estimate for the Hodge-de Rham semigroup on 1-forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4264","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":""},"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":"1310.4264","created_at":"2026-05-18T02:31:21.609613+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.4264v3","created_at":"2026-05-18T02:31:21.609613+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4264","created_at":"2026-05-18T02:31:21.609613+00:00"},{"alias_kind":"pith_short_12","alias_value":"MBLAEDUECAMZ","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"MBLAEDUECAMZAAYT","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"MBLAEDUE","created_at":"2026-05-18T12:27:51.066281+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MBLAEDUECAMZAAYT37RPLAHDJK","json":"https://pith.science/pith/MBLAEDUECAMZAAYT37RPLAHDJK.json","graph_json":"https://pith.science/api/pith-number/MBLAEDUECAMZAAYT37RPLAHDJK/graph.json","events_json":"https://pith.science/api/pith-number/MBLAEDUECAMZAAYT37RPLAHDJK/events.json","paper":"https://pith.science/paper/MBLAEDUE"},"agent_actions":{"view_html":"https://pith.science/pith/MBLAEDUECAMZAAYT37RPLAHDJK","download_json":"https://pith.science/pith/MBLAEDUECAMZAAYT37RPLAHDJK.json","view_paper":"https://pith.science/paper/MBLAEDUE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.4264&json=true","fetch_graph":"https://pith.science/api/pith-number/MBLAEDUECAMZAAYT37RPLAHDJK/graph.json","fetch_events":"https://pith.science/api/pith-number/MBLAEDUECAMZAAYT37RPLAHDJK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MBLAEDUECAMZAAYT37RPLAHDJK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MBLAEDUECAMZAAYT37RPLAHDJK/action/storage_attestation","attest_author":"https://pith.science/pith/MBLAEDUECAMZAAYT37RPLAHDJK/action/author_attestation","sign_citation":"https://pith.science/pith/MBLAEDUECAMZAAYT37RPLAHDJK/action/citation_signature","submit_replication":"https://pith.science/pith/MBLAEDUECAMZAAYT37RPLAHDJK/action/replication_record"}},"created_at":"2026-05-18T02:31:21.609613+00:00","updated_at":"2026-05-18T02:31:21.609613+00:00"}