{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BP2D6WVCQK527TBGAHHHV4W25W","short_pith_number":"pith:BP2D6WVC","canonical_record":{"source":{"id":"1804.08563","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-23T16:57:58Z","cross_cats_sorted":[],"title_canon_sha256":"c2cf706b05ae089295be12c09a941decee57fa3c3abac58f4eabc61e3a646daf","abstract_canon_sha256":"fc5caee859e3e1ca87098d34ebe5168b85f01be8fbe3264d1b17730861ecb9ff"},"schema_version":"1.0"},"canonical_sha256":"0bf43f5aa282bbafcc2601ce7af2daedbe182010ece5bf439f36ebba10feddf9","source":{"kind":"arxiv","id":"1804.08563","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BP2D6WVCQK527TBGAHHHV4W25W","target":"record","payload":{"canonical_record":{"source":{"id":"1804.08563","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-23T16:57:58Z","cross_cats_sorted":[],"title_canon_sha256":"c2cf706b05ae089295be12c09a941decee57fa3c3abac58f4eabc61e3a646daf","abstract_canon_sha256":"fc5caee859e3e1ca87098d34ebe5168b85f01be8fbe3264d1b17730861ecb9ff"},"schema_version":"1.0"},"canonical_sha256":"0bf43f5aa282bbafcc2601ce7af2daedbe182010ece5bf439f36ebba10feddf9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:18.002944Z","signature_b64":"z9bDS22XMojeI0nRr6dyqdupKc+rNgbUOcq0HKqPXaBNTZK5ysIUEpz2T47U8hXIgMF+WLosLdC3JEfiHoyAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bf43f5aa282bbafcc2601ce7af2daedbe182010ece5bf439f36ebba10feddf9","last_reissued_at":"2026-05-18T00:02:18.002442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:18.002442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.08563","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tn/LmFM0E4+m/dwNCrCShXnQv/Vb5FLw9OYAw1zAGE91ICuDP3Qhwf5FfrxB06GioEaKhbHsWwhsKFf8OiWfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:47:43.024855Z"},"content_sha256":"56e2e81fff62f8d8aa8a7cf6804feae30378e42418437cb662c7299214f659db","schema_version":"1.0","event_id":"sha256:56e2e81fff62f8d8aa8a7cf6804feae30378e42418437cb662c7299214f659db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BP2D6WVCQK527TBGAHHHV4W25W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Theory of Transfers: Duality and convolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Malcolm Bowles, Nassif Ghoussoub","submitted_at":"2018-04-23T16:57:58Z","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 Schrodinger 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08563","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x5DP2tFMYRFlMPWzU55OX8fHnqsQRHCF+Y8xh+/axLWhkxyWKi6lJNLFe4+OV0hG0m5B0BJ2Qcewn2xD+68TCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:47:43.025468Z"},"content_sha256":"4c31760637f94af2d6b5cb1a6600961a3080ea191fca942ea2f7fcdcf08e2164","schema_version":"1.0","event_id":"sha256:4c31760637f94af2d6b5cb1a6600961a3080ea191fca942ea2f7fcdcf08e2164"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BP2D6WVCQK527TBGAHHHV4W25W/bundle.json","state_url":"https://pith.science/pith/BP2D6WVCQK527TBGAHHHV4W25W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BP2D6WVCQK527TBGAHHHV4W25W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-01T23:47:43Z","links":{"resolver":"https://pith.science/pith/BP2D6WVCQK527TBGAHHHV4W25W","bundle":"https://pith.science/pith/BP2D6WVCQK527TBGAHHHV4W25W/bundle.json","state":"https://pith.science/pith/BP2D6WVCQK527TBGAHHHV4W25W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BP2D6WVCQK527TBGAHHHV4W25W/bundle.json"},"state":{"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 Schrodinger 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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pLHL3n4nFoXXgx5sa9K1bZwiqZmX9/keCTob+Z4PqH5vLmYP9VzUMEWM8TIJws2piPs5qkEV74CvOhdK4O53Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T23:47:43.028741Z","bundle_sha256":"30f217986e403cfc6f686e0b652802c4550c715475108738a3b851401e55766d"}}