{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:ZYX52KOQVVAR5VFH43OQUCHSMB","short_pith_number":"pith:ZYX52KOQ","canonical_record":{"source":{"id":"2102.06379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-02-12T07:53:22Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"3b3edf247cd8f1f84dc01369a83a298ff289475568286cc634301cd39589da1d","abstract_canon_sha256":"6331228b620ef67d51f299375bb166cc82b05beaa59f121239b03052a39467b6"},"schema_version":"1.0"},"canonical_sha256":"ce2fdd29d0ad411ed4a7e6dd0a08f2605dbd7665b7902acb1a7eb81ba0770235","source":{"kind":"arxiv","id":"2102.06379","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.06379","created_at":"2026-07-05T02:17:50Z"},{"alias_kind":"arxiv_version","alias_value":"2102.06379v2","created_at":"2026-07-05T02:17:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.06379","created_at":"2026-07-05T02:17:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZYX52KOQVVAR","created_at":"2026-07-05T02:17:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZYX52KOQVVAR5VFH","created_at":"2026-07-05T02:17:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZYX52KOQ","created_at":"2026-07-05T02:17:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:ZYX52KOQVVAR5VFH43OQUCHSMB","target":"record","payload":{"canonical_record":{"source":{"id":"2102.06379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-02-12T07:53:22Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"3b3edf247cd8f1f84dc01369a83a298ff289475568286cc634301cd39589da1d","abstract_canon_sha256":"6331228b620ef67d51f299375bb166cc82b05beaa59f121239b03052a39467b6"},"schema_version":"1.0"},"canonical_sha256":"ce2fdd29d0ad411ed4a7e6dd0a08f2605dbd7665b7902acb1a7eb81ba0770235","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:17:50.832461Z","signature_b64":"aaVr3p9dXuAd+v3A6OsxBxHS8gbkR9ZlnN6M0/RkiZbSfIxJdNtv9OjeDsi1zFoEkINwe9duV9cyrrIUtffaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce2fdd29d0ad411ed4a7e6dd0a08f2605dbd7665b7902acb1a7eb81ba0770235","last_reissued_at":"2026-07-05T02:17:50.831973Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:17:50.831973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.06379","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:17:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3CM/BL8++qZkJuXk/sQPcGn9zBLltzP9636MGtjS9jFyl8fCWCv7OASRYv88qAx3FPhhJrSZp74f6iOiW13nAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T20:56:29.595850Z"},"content_sha256":"f73e161a37534a2b58dc6229a7f47086aceb20ab46029aacd4c119093ef707cc","schema_version":"1.0","event_id":"sha256:f73e161a37534a2b58dc6229a7f47086aceb20ab46029aacd4c119093ef707cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:ZYX52KOQVVAR5VFH43OQUCHSMB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central Limit Theorems for General Transportation Costs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alberto Gonz\\'alez-Sanz (IMT, Eustasio del Barrio (IMUVA), IMUVA), Jean-Michel Loubes (IMT)","submitted_at":"2021-02-12T07:53:22Z","abstract_excerpt":"We consider the problem of optimal transportation with general cost between a empirical measure and a general target probability on R d , with d $\\ge$ 1. We extend results in [19] and prove asymptotic stability of both optimal transport maps and potentials for a large class of costs in R d. We derive a central limit theorem (CLT) towards a Gaussian distribution for the empirical transportation cost under minimal assumptions, with a new proof based on the Efron-Stein inequality and on the sequential compactness of the closed unit ball in L 2 (P) for the weak topology. We provide also CLTs for e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.06379","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.06379/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:17:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gbku0JJ8L+C1wfpGLWyI6cHDN6uJnbzjfu4lKUlxekWfsLTqfYFKMFyj6SRwJvay7VB3z0AhIYEu3QbgKlxmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T20:56:29.596373Z"},"content_sha256":"22f35f4cb3c0544ee3b97724816a02af32158893dc9ad0ec39efd1dfff0781a9","schema_version":"1.0","event_id":"sha256:22f35f4cb3c0544ee3b97724816a02af32158893dc9ad0ec39efd1dfff0781a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZYX52KOQVVAR5VFH43OQUCHSMB/bundle.json","state_url":"https://pith.science/pith/ZYX52KOQVVAR5VFH43OQUCHSMB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZYX52KOQVVAR5VFH43OQUCHSMB/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":"2026-08-18T20:56:29Z","links":{"resolver":"https://pith.science/pith/ZYX52KOQVVAR5VFH43OQUCHSMB","bundle":"https://pith.science/pith/ZYX52KOQVVAR5VFH43OQUCHSMB/bundle.json","state":"https://pith.science/pith/ZYX52KOQVVAR5VFH43OQUCHSMB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZYX52KOQVVAR5VFH43OQUCHSMB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:ZYX52KOQVVAR5VFH43OQUCHSMB","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":"6331228b620ef67d51f299375bb166cc82b05beaa59f121239b03052a39467b6","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-02-12T07:53:22Z","title_canon_sha256":"3b3edf247cd8f1f84dc01369a83a298ff289475568286cc634301cd39589da1d"},"schema_version":"1.0","source":{"id":"2102.06379","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.06379","created_at":"2026-07-05T02:17:50Z"},{"alias_kind":"arxiv_version","alias_value":"2102.06379v2","created_at":"2026-07-05T02:17:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.06379","created_at":"2026-07-05T02:17:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZYX52KOQVVAR","created_at":"2026-07-05T02:17:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZYX52KOQVVAR5VFH","created_at":"2026-07-05T02:17:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZYX52KOQ","created_at":"2026-07-05T02:17:50Z"}],"graph_snapshots":[{"event_id":"sha256:22f35f4cb3c0544ee3b97724816a02af32158893dc9ad0ec39efd1dfff0781a9","target":"graph","created_at":"2026-07-05T02:17:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.06379/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of optimal transportation with general cost between a empirical measure and a general target probability on R d , with d $\\ge$ 1. We extend results in [19] and prove asymptotic stability of both optimal transport maps and potentials for a large class of costs in R d. We derive a central limit theorem (CLT) towards a Gaussian distribution for the empirical transportation cost under minimal assumptions, with a new proof based on the Efron-Stein inequality and on the sequential compactness of the closed unit ball in L 2 (P) for the weak topology. We provide also CLTs for e","authors_text":"Alberto Gonz\\'alez-Sanz (IMT, Eustasio del Barrio (IMUVA), IMUVA), Jean-Michel Loubes (IMT)","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-02-12T07:53:22Z","title":"Central Limit Theorems for General Transportation Costs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.06379","kind":"arxiv","version":2},"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:f73e161a37534a2b58dc6229a7f47086aceb20ab46029aacd4c119093ef707cc","target":"record","created_at":"2026-07-05T02:17:50Z","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":"6331228b620ef67d51f299375bb166cc82b05beaa59f121239b03052a39467b6","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-02-12T07:53:22Z","title_canon_sha256":"3b3edf247cd8f1f84dc01369a83a298ff289475568286cc634301cd39589da1d"},"schema_version":"1.0","source":{"id":"2102.06379","kind":"arxiv","version":2}},"canonical_sha256":"ce2fdd29d0ad411ed4a7e6dd0a08f2605dbd7665b7902acb1a7eb81ba0770235","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce2fdd29d0ad411ed4a7e6dd0a08f2605dbd7665b7902acb1a7eb81ba0770235","first_computed_at":"2026-07-05T02:17:50.831973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:17:50.831973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aaVr3p9dXuAd+v3A6OsxBxHS8gbkR9ZlnN6M0/RkiZbSfIxJdNtv9OjeDsi1zFoEkINwe9duV9cyrrIUtffaCg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:17:50.832461Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.06379","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f73e161a37534a2b58dc6229a7f47086aceb20ab46029aacd4c119093ef707cc","sha256:22f35f4cb3c0544ee3b97724816a02af32158893dc9ad0ec39efd1dfff0781a9"],"state_sha256":"beea8835ebbb78e5817dcb13dfff39cde2ae9805011ed0883d7e61bb7b32d21a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vIWvkQhdvy0Ms3a0rcGxXHofRYxwh3eanRP9VH+2hMIgtUZRY4kJjrbMa6QuYaAwAPGwU5MMO/bAlorRYS8GDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T20:56:29.600943Z","bundle_sha256":"3a7339fd28f108d659c64bb14bd3b8a2ff834a3be88a3bad9cde537b3c1e9c4b"}}