{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:GSN7CGJ7FPXWIICBZFP4ODELFE","short_pith_number":"pith:GSN7CGJ7","canonical_record":{"source":{"id":"2303.10155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2023-03-17T17:43:48Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"969d0c2d64b9d92f6d32da3dbb2be441acaca15f5b28c3ab80187335a0c8714a","abstract_canon_sha256":"eeea419cd722e759bd6b3e51eb25836aa72b08210476b0b42f52df1e4e17f859"},"schema_version":"1.0"},"canonical_sha256":"349bf1193f2bef642041c95fc70c8b291717dad42f591fd8536b8e3b9bf9cc38","source":{"kind":"arxiv","id":"2303.10155","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.10155","created_at":"2026-07-05T08:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"2303.10155v3","created_at":"2026-07-05T08:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.10155","created_at":"2026-07-05T08:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"GSN7CGJ7FPXW","created_at":"2026-07-05T08:20:49Z"},{"alias_kind":"pith_short_16","alias_value":"GSN7CGJ7FPXWIICB","created_at":"2026-07-05T08:20:49Z"},{"alias_kind":"pith_short_8","alias_value":"GSN7CGJ7","created_at":"2026-07-05T08:20:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:GSN7CGJ7FPXWIICBZFP4ODELFE","target":"record","payload":{"canonical_record":{"source":{"id":"2303.10155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2023-03-17T17:43:48Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"969d0c2d64b9d92f6d32da3dbb2be441acaca15f5b28c3ab80187335a0c8714a","abstract_canon_sha256":"eeea419cd722e759bd6b3e51eb25836aa72b08210476b0b42f52df1e4e17f859"},"schema_version":"1.0"},"canonical_sha256":"349bf1193f2bef642041c95fc70c8b291717dad42f591fd8536b8e3b9bf9cc38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:20:49.682500Z","signature_b64":"CUUmQhuo3t3F/V1eDcmPpaqOcyNXHh8HU1cCSNNIHPcQNoN8Squxo5lLYtb303vPXAtJNav/FZ+1BMCWvrmzBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"349bf1193f2bef642041c95fc70c8b291717dad42f591fd8536b8e3b9bf9cc38","last_reissued_at":"2026-07-05T08:20:49.681903Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:20:49.681903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.10155","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":"2026-07-05T08:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2mK2dPlZxKdRdA4a67RvaSSTeklNcAu7UDbBSjhaH6FZqh7LZQp3E6fszAocVgDgRMXrIkXSTpVHE37WlIZFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:45:19.952946Z"},"content_sha256":"c2897a7442c2f3164368d695349def2ae6a86d8f87fa81f10ee3d5772fa6391c","schema_version":"1.0","event_id":"sha256:c2897a7442c2f3164368d695349def2ae6a86d8f87fa81f10ee3d5772fa6391c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:GSN7CGJ7FPXWIICBZFP4ODELFE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability and statistical inference for semidiscrete optimal transport maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Kengo Kato, Ritwik Sadhu, Ziv Goldfeld","submitted_at":"2023-03-17T17:43:48Z","abstract_excerpt":"We study statistical inference for the optimal transport (OT) map (also known as the Brenier map) from a known absolutely continuous reference distribution onto an unknown finitely discrete target distribution. We derive limit distributions for the $L^p$-error with arbitrary $p \\in [1,\\infty)$ and for linear functionals of the empirical OT map, together with their moment convergence. The former has a non-Gaussian limit, whose explicit density is derived, while the latter attains asymptotic normality. For both cases, we also establish consistency of the nonparametric bootstrap. The derivation o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.10155","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.10155/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":"2026-07-05T08:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x5EOPAEldawkWTYjglIRP0akz+aosdwew6K9WRfdTuVjZCFg7DQ8jDDaG6iuKZHU9BrjvtP3M7m3XnBpnm5cCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:45:19.953350Z"},"content_sha256":"7e3cad90aa7c6c7fa2259bb9978e1a8c11ae0bd2508767df4167a3fa1eba72c1","schema_version":"1.0","event_id":"sha256:7e3cad90aa7c6c7fa2259bb9978e1a8c11ae0bd2508767df4167a3fa1eba72c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GSN7CGJ7FPXWIICBZFP4ODELFE/bundle.json","state_url":"https://pith.science/pith/GSN7CGJ7FPXWIICBZFP4ODELFE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GSN7CGJ7FPXWIICBZFP4ODELFE/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":"2026-07-07T05:45:19Z","links":{"resolver":"https://pith.science/pith/GSN7CGJ7FPXWIICBZFP4ODELFE","bundle":"https://pith.science/pith/GSN7CGJ7FPXWIICBZFP4ODELFE/bundle.json","state":"https://pith.science/pith/GSN7CGJ7FPXWIICBZFP4ODELFE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GSN7CGJ7FPXWIICBZFP4ODELFE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:GSN7CGJ7FPXWIICBZFP4ODELFE","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":"eeea419cd722e759bd6b3e51eb25836aa72b08210476b0b42f52df1e4e17f859","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2023-03-17T17:43:48Z","title_canon_sha256":"969d0c2d64b9d92f6d32da3dbb2be441acaca15f5b28c3ab80187335a0c8714a"},"schema_version":"1.0","source":{"id":"2303.10155","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.10155","created_at":"2026-07-05T08:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"2303.10155v3","created_at":"2026-07-05T08:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.10155","created_at":"2026-07-05T08:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"GSN7CGJ7FPXW","created_at":"2026-07-05T08:20:49Z"},{"alias_kind":"pith_short_16","alias_value":"GSN7CGJ7FPXWIICB","created_at":"2026-07-05T08:20:49Z"},{"alias_kind":"pith_short_8","alias_value":"GSN7CGJ7","created_at":"2026-07-05T08:20:49Z"}],"graph_snapshots":[{"event_id":"sha256:7e3cad90aa7c6c7fa2259bb9978e1a8c11ae0bd2508767df4167a3fa1eba72c1","target":"graph","created_at":"2026-07-05T08:20:49Z","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/2303.10155/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study statistical inference for the optimal transport (OT) map (also known as the Brenier map) from a known absolutely continuous reference distribution onto an unknown finitely discrete target distribution. We derive limit distributions for the $L^p$-error with arbitrary $p \\in [1,\\infty)$ and for linear functionals of the empirical OT map, together with their moment convergence. The former has a non-Gaussian limit, whose explicit density is derived, while the latter attains asymptotic normality. For both cases, we also establish consistency of the nonparametric bootstrap. The derivation o","authors_text":"Kengo Kato, Ritwik Sadhu, Ziv Goldfeld","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2023-03-17T17:43:48Z","title":"Stability and statistical inference for semidiscrete optimal transport maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.10155","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:c2897a7442c2f3164368d695349def2ae6a86d8f87fa81f10ee3d5772fa6391c","target":"record","created_at":"2026-07-05T08:20:49Z","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":"eeea419cd722e759bd6b3e51eb25836aa72b08210476b0b42f52df1e4e17f859","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2023-03-17T17:43:48Z","title_canon_sha256":"969d0c2d64b9d92f6d32da3dbb2be441acaca15f5b28c3ab80187335a0c8714a"},"schema_version":"1.0","source":{"id":"2303.10155","kind":"arxiv","version":3}},"canonical_sha256":"349bf1193f2bef642041c95fc70c8b291717dad42f591fd8536b8e3b9bf9cc38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"349bf1193f2bef642041c95fc70c8b291717dad42f591fd8536b8e3b9bf9cc38","first_computed_at":"2026-07-05T08:20:49.681903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:20:49.681903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CUUmQhuo3t3F/V1eDcmPpaqOcyNXHh8HU1cCSNNIHPcQNoN8Squxo5lLYtb303vPXAtJNav/FZ+1BMCWvrmzBw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:20:49.682500Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.10155","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2897a7442c2f3164368d695349def2ae6a86d8f87fa81f10ee3d5772fa6391c","sha256:7e3cad90aa7c6c7fa2259bb9978e1a8c11ae0bd2508767df4167a3fa1eba72c1"],"state_sha256":"95b3a5964bbea802cdae20d0903a7b7200e36e450254408885b663174c4ec63e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PbigZ/PSsNpVhTvn+HwFq7hw/d+nT80XX8mw3TRed32DmIsnJm2+68ADvuUnnKjiVFMtTGDKgh2drr1j7Xi8Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T05:45:19.955467Z","bundle_sha256":"3383e6de0c46655d32e96744db073d2227ac6e9c61742d0c08be5f99c4e5f607"}}