{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:R3OSDR6OVHYPNU3GNDKXQRECUR","short_pith_number":"pith:R3OSDR6O","schema_version":"1.0","canonical_sha256":"8edd21c7cea9f0f6d36668d5784482a47ad27a44c0c7be56446bb7fc95461bc4","source":{"kind":"arxiv","id":"1710.10536","version":1},"attestation_state":"computed","paper":{"title":"A partial Laplacian as an infinitesimal generator on the Wasserstein space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wilfrid Gangbo, Yat Tin Chow","submitted_at":"2017-10-28T23:40:55Z","abstract_excerpt":"We study stochastic processes on the Wasserstein space, together with their infinitesimal generators. One of these processes is modeled after Brownian motion and plays a central role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel probability measures, and we use it to define heat flow on the Wasserstein space. We verify a distinctive smoothing effect of this flow for a particular class of initial conditions. To this end, we will develop a theory of Fourier analysis and conic surfaces in metric spaces. We note that the use of the infinitesimal generat"},"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":"1710.10536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-28T23:40:55Z","cross_cats_sorted":[],"title_canon_sha256":"c2bcb77d590f57c50bb98af81f5384792b6023197b77f8dc50021f14aa68bb9d","abstract_canon_sha256":"cb2daf11e7c7239f6906b00882e2c5428b5990a7fe290c76dfcf0d1831f78005"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:47.196033Z","signature_b64":"z9agz4VSwpkVVi+aiLTHVIfjg7P37Yj89AcnkOS+Nf2+aDeqB27nF/3Bk5YSmiJJ/qIabiAmDiSfBlB7jJgZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8edd21c7cea9f0f6d36668d5784482a47ad27a44c0c7be56446bb7fc95461bc4","last_reissued_at":"2026-05-18T00:31:47.195257Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:47.195257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A partial Laplacian as an infinitesimal generator on the Wasserstein space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wilfrid Gangbo, Yat Tin Chow","submitted_at":"2017-10-28T23:40:55Z","abstract_excerpt":"We study stochastic processes on the Wasserstein space, together with their infinitesimal generators. One of these processes is modeled after Brownian motion and plays a central role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel probability measures, and we use it to define heat flow on the Wasserstein space. We verify a distinctive smoothing effect of this flow for a particular class of initial conditions. To this end, we will develop a theory of Fourier analysis and conic surfaces in metric spaces. We note that the use of the infinitesimal generat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10536","kind":"arxiv","version":1},"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":"1710.10536","created_at":"2026-05-18T00:31:47.195394+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.10536v1","created_at":"2026-05-18T00:31:47.195394+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10536","created_at":"2026-05-18T00:31:47.195394+00:00"},{"alias_kind":"pith_short_12","alias_value":"R3OSDR6OVHYP","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_16","alias_value":"R3OSDR6OVHYPNU3G","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_8","alias_value":"R3OSDR6O","created_at":"2026-05-18T12:31:39.905425+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/R3OSDR6OVHYPNU3GNDKXQRECUR","json":"https://pith.science/pith/R3OSDR6OVHYPNU3GNDKXQRECUR.json","graph_json":"https://pith.science/api/pith-number/R3OSDR6OVHYPNU3GNDKXQRECUR/graph.json","events_json":"https://pith.science/api/pith-number/R3OSDR6OVHYPNU3GNDKXQRECUR/events.json","paper":"https://pith.science/paper/R3OSDR6O"},"agent_actions":{"view_html":"https://pith.science/pith/R3OSDR6OVHYPNU3GNDKXQRECUR","download_json":"https://pith.science/pith/R3OSDR6OVHYPNU3GNDKXQRECUR.json","view_paper":"https://pith.science/paper/R3OSDR6O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.10536&json=true","fetch_graph":"https://pith.science/api/pith-number/R3OSDR6OVHYPNU3GNDKXQRECUR/graph.json","fetch_events":"https://pith.science/api/pith-number/R3OSDR6OVHYPNU3GNDKXQRECUR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R3OSDR6OVHYPNU3GNDKXQRECUR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R3OSDR6OVHYPNU3GNDKXQRECUR/action/storage_attestation","attest_author":"https://pith.science/pith/R3OSDR6OVHYPNU3GNDKXQRECUR/action/author_attestation","sign_citation":"https://pith.science/pith/R3OSDR6OVHYPNU3GNDKXQRECUR/action/citation_signature","submit_replication":"https://pith.science/pith/R3OSDR6OVHYPNU3GNDKXQRECUR/action/replication_record"}},"created_at":"2026-05-18T00:31:47.195394+00:00","updated_at":"2026-05-18T00:31:47.195394+00:00"}