{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:I5NNE2TL5SDSDEOONNQWFXL7N5","short_pith_number":"pith:I5NNE2TL","canonical_record":{"source":{"id":"2506.04948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-05T12:21:44Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"fc9c3bbcd959095d79cf9a9472d178d6b605785d592b1bc76b671d0cdf6c4b6f","abstract_canon_sha256":"8c4575f7a16e7ca38c4beb49e95249519a18c0439f71404047dce0fc116f4ad7"},"schema_version":"1.0"},"canonical_sha256":"475ad26a6bec872191ce6b6162dd7f6f560ef9eacf36330eda723d1dabbb0826","source":{"kind":"arxiv","id":"2506.04948","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04948","created_at":"2026-05-28T01:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04948v2","created_at":"2026-05-28T01:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04948","created_at":"2026-05-28T01:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"I5NNE2TL5SDS","created_at":"2026-05-28T01:04:28Z"},{"alias_kind":"pith_short_16","alias_value":"I5NNE2TL5SDSDEOO","created_at":"2026-05-28T01:04:28Z"},{"alias_kind":"pith_short_8","alias_value":"I5NNE2TL","created_at":"2026-05-28T01:04:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:I5NNE2TL5SDSDEOONNQWFXL7N5","target":"record","payload":{"canonical_record":{"source":{"id":"2506.04948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-05T12:21:44Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"fc9c3bbcd959095d79cf9a9472d178d6b605785d592b1bc76b671d0cdf6c4b6f","abstract_canon_sha256":"8c4575f7a16e7ca38c4beb49e95249519a18c0439f71404047dce0fc116f4ad7"},"schema_version":"1.0"},"canonical_sha256":"475ad26a6bec872191ce6b6162dd7f6f560ef9eacf36330eda723d1dabbb0826","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T01:04:28.512860Z","signature_b64":"uuIltDcCfdBbK/A0orySKDDnBLk/robTXPvyZdvOoCudOui+5CffSxZhB75LepL6ylhhonzWY5JqaKpdD8/cAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"475ad26a6bec872191ce6b6162dd7f6f560ef9eacf36330eda723d1dabbb0826","last_reissued_at":"2026-05-28T01:04:28.512113Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T01:04:28.512113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.04948","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":"2026-05-28T01:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kZ228+dx2GdGhrwWrKIfvoTjLY1iwSeWEdCD46WVgax5WfuRwgAb4fbZZP38yT5L+0oUbe4uQ8j1ZGOBJlRNAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T00:21:19.936669Z"},"content_sha256":"28f74f7c36dc5794b79b3a7d8a6ef35f17b12c22bb57487564b63a8f49041ff5","schema_version":"1.0","event_id":"sha256:28f74f7c36dc5794b79b3a7d8a6ef35f17b12c22bb57487564b63a8f49041ff5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:I5NNE2TL5SDSDEOONNQWFXL7N5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unregularized limit of stochastic gradient method for Wasserstein distributionally robust optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.OC","authors_text":"Tam Le (LPSM (UMR\\_8001), UPCit\\'e)","submitted_at":"2025-06-05T12:21:44Z","abstract_excerpt":"Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a sampled approximation of the original objective. We establish convergence of the approximate gradients to subgradients of the unregularized objective as the regularization parameter vanishes, enabling convergence guarantees for stochastic gradient methods. We obtain qualitative convergence results under general assumptions, then we provide convergence rates"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04948","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/2506.04948/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":"2026-05-28T01:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k4uI7oCgPRrTrKCgf/Dzuvh5n4ZqljUCRHogFjUOmGIAcGdYQzgFE1g9qvYGLRE6XuxjaAd0YJ/vtyVC0YD7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T00:21:19.937036Z"},"content_sha256":"420e12dee056ade5824c1af47284992b4814601dc9a2e3e4eceec25931e3f5f8","schema_version":"1.0","event_id":"sha256:420e12dee056ade5824c1af47284992b4814601dc9a2e3e4eceec25931e3f5f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I5NNE2TL5SDSDEOONNQWFXL7N5/bundle.json","state_url":"https://pith.science/pith/I5NNE2TL5SDSDEOONNQWFXL7N5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I5NNE2TL5SDSDEOONNQWFXL7N5/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":"2026-06-30T00:21:19Z","links":{"resolver":"https://pith.science/pith/I5NNE2TL5SDSDEOONNQWFXL7N5","bundle":"https://pith.science/pith/I5NNE2TL5SDSDEOONNQWFXL7N5/bundle.json","state":"https://pith.science/pith/I5NNE2TL5SDSDEOONNQWFXL7N5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I5NNE2TL5SDSDEOONNQWFXL7N5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:I5NNE2TL5SDSDEOONNQWFXL7N5","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":"8c4575f7a16e7ca38c4beb49e95249519a18c0439f71404047dce0fc116f4ad7","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-05T12:21:44Z","title_canon_sha256":"fc9c3bbcd959095d79cf9a9472d178d6b605785d592b1bc76b671d0cdf6c4b6f"},"schema_version":"1.0","source":{"id":"2506.04948","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04948","created_at":"2026-05-28T01:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04948v2","created_at":"2026-05-28T01:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04948","created_at":"2026-05-28T01:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"I5NNE2TL5SDS","created_at":"2026-05-28T01:04:28Z"},{"alias_kind":"pith_short_16","alias_value":"I5NNE2TL5SDSDEOO","created_at":"2026-05-28T01:04:28Z"},{"alias_kind":"pith_short_8","alias_value":"I5NNE2TL","created_at":"2026-05-28T01:04:28Z"}],"graph_snapshots":[{"event_id":"sha256:420e12dee056ade5824c1af47284992b4814601dc9a2e3e4eceec25931e3f5f8","target":"graph","created_at":"2026-05-28T01:04:28Z","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/2506.04948/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a sampled approximation of the original objective. We establish convergence of the approximate gradients to subgradients of the unregularized objective as the regularization parameter vanishes, enabling convergence guarantees for stochastic gradient methods. We obtain qualitative convergence results under general assumptions, then we provide convergence rates","authors_text":"Tam Le (LPSM (UMR\\_8001), UPCit\\'e)","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-05T12:21:44Z","title":"Unregularized limit of stochastic gradient method for Wasserstein distributionally robust optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04948","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":"sha256:28f74f7c36dc5794b79b3a7d8a6ef35f17b12c22bb57487564b63a8f49041ff5","target":"record","created_at":"2026-05-28T01:04:28Z","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":"8c4575f7a16e7ca38c4beb49e95249519a18c0439f71404047dce0fc116f4ad7","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-05T12:21:44Z","title_canon_sha256":"fc9c3bbcd959095d79cf9a9472d178d6b605785d592b1bc76b671d0cdf6c4b6f"},"schema_version":"1.0","source":{"id":"2506.04948","kind":"arxiv","version":2}},"canonical_sha256":"475ad26a6bec872191ce6b6162dd7f6f560ef9eacf36330eda723d1dabbb0826","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"475ad26a6bec872191ce6b6162dd7f6f560ef9eacf36330eda723d1dabbb0826","first_computed_at":"2026-05-28T01:04:28.512113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:28.512113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uuIltDcCfdBbK/A0orySKDDnBLk/robTXPvyZdvOoCudOui+5CffSxZhB75LepL6ylhhonzWY5JqaKpdD8/cAA==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:28.512860Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.04948","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28f74f7c36dc5794b79b3a7d8a6ef35f17b12c22bb57487564b63a8f49041ff5","sha256:420e12dee056ade5824c1af47284992b4814601dc9a2e3e4eceec25931e3f5f8"],"state_sha256":"116eb8044dc87af95c22a3cf9cbe2f5c0b0b1d76b11e2e961f8c52f21c8e0281"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GZA7WMXvUIM5MCP04j2Qmqs1FmwC6YeFhYlxEHn6RV8Bp76z6leAxJ0Sis44M4A3jLNF/sBy4Zg0uWoX31HhBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T00:21:19.938964Z","bundle_sha256":"405f883c8eeb9f68ddc0f03c548dfc7ff22fce2c08c80e112a4baa0d806435c8"}}