{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BP2D6WVCQK527TBGAHHHV4W25W","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fc5caee859e3e1ca87098d34ebe5168b85f01be8fbe3264d1b17730861ecb9ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-23T16:57:58Z","title_canon_sha256":"c2cf706b05ae089295be12c09a941decee57fa3c3abac58f4eabc61e3a646daf"},"schema_version":"1.0","source":{"id":"1804.08563","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08563","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08563v3","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08563","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"pith_short_12","alias_value":"BP2D6WVCQK52","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BP2D6WVCQK527TBG","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BP2D6WVC","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:4c31760637f94af2d6b5cb1a6600961a3080ea191fca942ea2f7fcdcf08e2164","target":"graph","created_at":"2026-05-18T00:02:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We introduce and study the permanence properties of the class of linear transfers between probability measures. This class contains all cost minimizing mass transports, but also martingale mass transports, the Schrodinger bridge associated to a reversible Markov process, and the weak mass transports of Tala- grand, Marton, Gozlan and others. The class also includes various stochastic mass transports to which Monge-Kantorovich theory does not apply. We also introduce the cone of convex transfers, which include any p-power (p > 1) of a linear transfer, but also the logarithmic entropy, the Dons","authors_text":"Malcolm Bowles, Nassif Ghoussoub","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-23T16:57:58Z","title":"A Theory of Transfers: Duality and convolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08563","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:56e2e81fff62f8d8aa8a7cf6804feae30378e42418437cb662c7299214f659db","target":"record","created_at":"2026-05-18T00:02:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fc5caee859e3e1ca87098d34ebe5168b85f01be8fbe3264d1b17730861ecb9ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-23T16:57:58Z","title_canon_sha256":"c2cf706b05ae089295be12c09a941decee57fa3c3abac58f4eabc61e3a646daf"},"schema_version":"1.0","source":{"id":"1804.08563","kind":"arxiv","version":3}},"canonical_sha256":"0bf43f5aa282bbafcc2601ce7af2daedbe182010ece5bf439f36ebba10feddf9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bf43f5aa282bbafcc2601ce7af2daedbe182010ece5bf439f36ebba10feddf9","first_computed_at":"2026-05-18T00:02:18.002442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:18.002442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z9bDS22XMojeI0nRr6dyqdupKc+rNgbUOcq0HKqPXaBNTZK5ysIUEpz2T47U8hXIgMF+WLosLdC3JEfiHoyAAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:18.002944Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.08563","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56e2e81fff62f8d8aa8a7cf6804feae30378e42418437cb662c7299214f659db","sha256:4c31760637f94af2d6b5cb1a6600961a3080ea191fca942ea2f7fcdcf08e2164"],"state_sha256":"fd45c4cd48af21f7d1008f1965801385fb17938ba2fc1e019e980020744054a2"}