{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:EFZI3QJ4MQB2JPXCORQS6DWBNC","short_pith_number":"pith:EFZI3QJ4","schema_version":"1.0","canonical_sha256":"21728dc13c6403a4bee274612f0ec168945b873046bd8f235276f25f0a739533","source":{"kind":"arxiv","id":"2605.17328","version":1},"attestation_state":"computed","paper":{"title":"Transportation cost inequalities for mean reflection SPDEs with white noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Solutions to mean-reflected SPDEs satisfy a quadratic transportation cost inequality under the uniform norm.","cross_cats":[],"primary_cat":"math.PR","authors_text":"Beibei Zhang, Bin Qian","submitted_at":"2026-05-17T08:35:17Z","abstract_excerpt":"We establish a quadratic transportation cost inequality under the uniform norm for solutions to mean reflected stochastic partial differential equations, a new type of equation in which the compensating reflection part depends not on the paths but on the law of the solution."},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.17328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-17T08:35:17Z","cross_cats_sorted":[],"title_canon_sha256":"767fa4961a2dd08ad05e494873c0eb61b5c5bd1d43b9ce703a4e8393978379e1","abstract_canon_sha256":"bf237602065156a880bfa1670afc563bf601dd6addaf18922fa075a2d6dd9cc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:52.365621Z","signature_b64":"vHPJvmuD3xJ8HNoyLZV8jiQ0eE7x0bnZQ3juqzAvvg2dARK9KzPdQkTQaJ9MdFZ6+DgordC5q6U7o11Ss0D2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21728dc13c6403a4bee274612f0ec168945b873046bd8f235276f25f0a739533","last_reissued_at":"2026-05-20T00:03:52.364837Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:52.364837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transportation cost inequalities for mean reflection SPDEs with white noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Solutions to mean-reflected SPDEs satisfy a quadratic transportation cost inequality under the uniform norm.","cross_cats":[],"primary_cat":"math.PR","authors_text":"Beibei Zhang, Bin Qian","submitted_at":"2026-05-17T08:35:17Z","abstract_excerpt":"We establish a quadratic transportation cost inequality under the uniform norm for solutions to mean reflected stochastic partial differential equations, a new type of equation in which the compensating reflection part depends not on the paths but on the law of the solution."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish a quadratic transportation cost inequality under the uniform norm for solutions to mean reflected stochastic partial differential equations, a new type of equation in which the compensating reflection part depends not on the paths but on the law of the solution.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The mean-reflected SPDE admits a unique solution whose law satisfies the necessary integrability and continuity properties to make the transportation cost inequality well-defined under the uniform norm (implicit in the abstract's claim that such an inequality can be established for this new equation class).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Establishes quadratic transportation cost inequality under uniform norm for mean-reflected SPDEs with white noise where reflection depends on the solution's law.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Solutions to mean-reflected SPDEs satisfy a quadratic transportation cost inequality under the uniform norm.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"54b9fd1d00ff2b6b68164baf62b16734696b45c266252fc38e16bd14bf7f12ba"},"source":{"id":"2605.17328","kind":"arxiv","version":1},"verdict":{"id":"6741d9fa-b14d-4c28-a845-9a99a1c60553","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:03:32.693093Z","strongest_claim":"We establish a quadratic transportation cost inequality under the uniform norm for solutions to mean reflected stochastic partial differential equations, a new type of equation in which the compensating reflection part depends not on the paths but on the law of the solution.","one_line_summary":"Establishes quadratic transportation cost inequality under uniform norm for mean-reflected SPDEs with white noise where reflection depends on the solution's law.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The mean-reflected SPDE admits a unique solution whose law satisfies the necessary integrability and continuity properties to make the transportation cost inequality well-defined under the uniform norm (implicit in the abstract's claim that such an inequality can be established for this new equation class).","pith_extraction_headline":"Solutions to mean-reflected SPDEs satisfy a quadratic transportation cost inequality under the uniform norm."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17328/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:20.139870Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:13:08.585903Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.811730Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.745063Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"3228d62bb2b0bc7226f5200fe0fdd7cf4392e9f068a3530d08fa99fa916791ad"},"references":{"count":33,"sample":[{"doi":"","year":2013,"title":"Transportation cost inequalities for neutral func- tional stochastic equations","work_id":"4ffd7823-537d-4236-9373-89feaa577296","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"Transportation inequalities for stochastic heat equations","work_id":"e7cad145-dc64-423f-9b92-ba510865e17b","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"A note on Harnack and Transportation inequalities For Stochastic Differential Equations with reflections","work_id":"6924cd47-ae5a-4dba-a627-9b1e635954e9","ref_index":3,"cited_arxiv_id":"1905.01083","is_internal_anchor":true},{"doi":"","year":1999,"title":"G., G¨ otze, F., 1999","work_id":"8cb4eba6-1352-4afe-9130-5ac24337524a","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2000,"title":"G., Houdr´ e, C., 2000","work_id":"42c9b060-76a8-42f1-aadc-3fd6d8652fed","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":33,"snapshot_sha256":"c864e8c922689eab996f5a0c2477e5c53a7813ffb3ef65e08ee5477d78d27c27","internal_anchors":1},"formal_canon":{"evidence_count":1,"snapshot_sha256":"bad0b9c712ca9cb47e9142ddb6a3e0314282dde6751f12f6f2bfe4a5ed5941aa"},"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":"2605.17328","created_at":"2026-05-20T00:03:52.364945+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.17328v1","created_at":"2026-05-20T00:03:52.364945+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17328","created_at":"2026-05-20T00:03:52.364945+00:00"},{"alias_kind":"pith_short_12","alias_value":"EFZI3QJ4MQB2","created_at":"2026-05-20T00:03:52.364945+00:00"},{"alias_kind":"pith_short_16","alias_value":"EFZI3QJ4MQB2JPXC","created_at":"2026-05-20T00:03:52.364945+00:00"},{"alias_kind":"pith_short_8","alias_value":"EFZI3QJ4","created_at":"2026-05-20T00:03:52.364945+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":1,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EFZI3QJ4MQB2JPXCORQS6DWBNC","json":"https://pith.science/pith/EFZI3QJ4MQB2JPXCORQS6DWBNC.json","graph_json":"https://pith.science/api/pith-number/EFZI3QJ4MQB2JPXCORQS6DWBNC/graph.json","events_json":"https://pith.science/api/pith-number/EFZI3QJ4MQB2JPXCORQS6DWBNC/events.json","paper":"https://pith.science/paper/EFZI3QJ4"},"agent_actions":{"view_html":"https://pith.science/pith/EFZI3QJ4MQB2JPXCORQS6DWBNC","download_json":"https://pith.science/pith/EFZI3QJ4MQB2JPXCORQS6DWBNC.json","view_paper":"https://pith.science/paper/EFZI3QJ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.17328&json=true","fetch_graph":"https://pith.science/api/pith-number/EFZI3QJ4MQB2JPXCORQS6DWBNC/graph.json","fetch_events":"https://pith.science/api/pith-number/EFZI3QJ4MQB2JPXCORQS6DWBNC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EFZI3QJ4MQB2JPXCORQS6DWBNC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EFZI3QJ4MQB2JPXCORQS6DWBNC/action/storage_attestation","attest_author":"https://pith.science/pith/EFZI3QJ4MQB2JPXCORQS6DWBNC/action/author_attestation","sign_citation":"https://pith.science/pith/EFZI3QJ4MQB2JPXCORQS6DWBNC/action/citation_signature","submit_replication":"https://pith.science/pith/EFZI3QJ4MQB2JPXCORQS6DWBNC/action/replication_record"}},"created_at":"2026-05-20T00:03:52.364945+00:00","updated_at":"2026-05-20T00:03:52.364945+00:00"}