{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DGX5PKJ5HHWYCNOSW65CVF4U2R","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":"b520b3ddcc9c33e06b82dc12ac0a9ad138e32794f80ec58d0041eab9efad82f8","cross_cats_sorted":["math.FA","math.PR"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.MG","submitted_at":"2026-05-25T05:58:49Z","title_canon_sha256":"fb3c5df885e16d0d2ebb001fa6204f148daf078520e8db0a526def62fcda4356"},"schema_version":"1.0","source":{"id":"2605.25448","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25448","created_at":"2026-05-26T02:04:36Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25448v1","created_at":"2026-05-26T02:04:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25448","created_at":"2026-05-26T02:04:36Z"},{"alias_kind":"pith_short_12","alias_value":"DGX5PKJ5HHWY","created_at":"2026-05-26T02:04:36Z"},{"alias_kind":"pith_short_16","alias_value":"DGX5PKJ5HHWYCNOS","created_at":"2026-05-26T02:04:36Z"},{"alias_kind":"pith_short_8","alias_value":"DGX5PKJ5","created_at":"2026-05-26T02:04:36Z"}],"graph_snapshots":[{"event_id":"sha256:e91dc27af77a58a992d6be16ddc013dc596a71bd8f83b2ec75e89edb3fe541b6","target":"graph","created_at":"2026-05-26T02:04:36Z","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/2605.25448/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove quantitative stability estimates for Wasserstein barycenters on Alexandrov spaces with curvature bounded from below. The proof combines the variational strategy of Carlier--Delalande--M\\'erigot with heat-kernel regularization, which supplies the regularity needed for dual convexity arguments in this non-smooth curved setting. The main result is an explicit strong-convexity modulus for the barycentric variance functional. As a consequence, barycenters depend H\\\"older-continuously on the underlying distributions with respect to the $1$-Wasserstein distance on the space of probability me","authors_text":"Bang-Xian Han, Zhuo-Nan Zhu","cross_cats":["math.FA","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.MG","submitted_at":"2026-05-25T05:58:49Z","title":"Quantitative Stability of Wasserstein Barycenters over Alexandrov Spaces with Lower Curvature Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25448","kind":"arxiv","version":1},"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:d44f5f41be183052f68939c2b8143e1b7aeae9975a94af7a1d4ae487b202bf8f","target":"record","created_at":"2026-05-26T02:04:36Z","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":"b520b3ddcc9c33e06b82dc12ac0a9ad138e32794f80ec58d0041eab9efad82f8","cross_cats_sorted":["math.FA","math.PR"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.MG","submitted_at":"2026-05-25T05:58:49Z","title_canon_sha256":"fb3c5df885e16d0d2ebb001fa6204f148daf078520e8db0a526def62fcda4356"},"schema_version":"1.0","source":{"id":"2605.25448","kind":"arxiv","version":1}},"canonical_sha256":"19afd7a93d39ed8135d2b7ba2a9794d457203ee183b8e3a9cc0e273632901d79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19afd7a93d39ed8135d2b7ba2a9794d457203ee183b8e3a9cc0e273632901d79","first_computed_at":"2026-05-26T02:04:36.012233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:36.012233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eNLPjXxQ0UniMKpyXXFsRYo3U4hBtR4bBD2icSIAhW2yvVc8oskdiyyRBIPkVRaylKFwx/T9njvm7N2Yb4nzCw==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:36.013065Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25448","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d44f5f41be183052f68939c2b8143e1b7aeae9975a94af7a1d4ae487b202bf8f","sha256:e91dc27af77a58a992d6be16ddc013dc596a71bd8f83b2ec75e89edb3fe541b6"],"state_sha256":"00ab24baa8d5598aae938479a405c1e6bb8b9affc26e1a0e2d3ab7f30d79c8c5"}