{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7CFCLFS6OH47FHC2JNONLFAKAI","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":"b3e1ed4af3b958ba41abbf67f4621feabbb1c32e75624a03dba6ae86748595bb","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-15T10:20:05Z","title_canon_sha256":"08ba6475f997cac48340c296c79c570e394b12544fd5e6fb361be22ac448b8c3"},"schema_version":"1.0","source":{"id":"2605.15822","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.15822","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"arxiv_version","alias_value":"2605.15822v1","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15822","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"pith_short_12","alias_value":"7CFCLFS6OH47","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"pith_short_16","alias_value":"7CFCLFS6OH47FHC2","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"pith_short_8","alias_value":"7CFCLFS6","created_at":"2026-05-20T00:01:20Z"}],"graph_snapshots":[{"event_id":"sha256:b30a1a95efd2caaa54c08437e51e1b1c7a4726991333926a0757095f88ae61ad","target":"graph","created_at":"2026-05-20T00:01:20Z","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":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.724070Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.871203Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.15822/integrity.json","findings":[],"snapshot_sha256":"d97cbf7e95ab7794ab93601a619062b4da3b095317ee37d5962d1cfdcedc76ee","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Score-based generative models are trained in high-dimensional ambient spaces, yet many data distributions are supported on low-dimensional nonlinear structures. We prove that, for compact $d$-dimensional smooth manifolds $\\mathcal{M} \\subset [0,1]^D$ with $d > 2$ and $\\beta$-H\\\"older densities strictly positive on $\\mathcal{M}$, a variance-preserving SGM estimator attains the intrinsic Wasserstein--1 sample exponent $\\tilde{\\mathcal{O}}(D^{\\mathcal{O}_\\beta(d)}n^{-(\\beta+1)/(d+2\\beta)})$, up to logarithmic factors and explicit geometry and density factors. The full nonasymptotic bound explicit","authors_text":"Atsushi Nitanda, Guoji Fu, Taiji Suzuki, Wee Sun Lee","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-15T10:20:05Z","title":"Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.15822","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":"sha256:7f176cebb743eb98ab3d872b00b6fb61b70271aefed5df2c3aabbaa812177a90","target":"record","created_at":"2026-05-20T00:01:20Z","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":"b3e1ed4af3b958ba41abbf67f4621feabbb1c32e75624a03dba6ae86748595bb","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-15T10:20:05Z","title_canon_sha256":"08ba6475f997cac48340c296c79c570e394b12544fd5e6fb361be22ac448b8c3"},"schema_version":"1.0","source":{"id":"2605.15822","kind":"arxiv","version":1}},"canonical_sha256":"f88a25965e71f9f29c5a4b5cd5940a020b3a14b3e9a6ae3179bb1df167d3d0cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f88a25965e71f9f29c5a4b5cd5940a020b3a14b3e9a6ae3179bb1df167d3d0cf","first_computed_at":"2026-05-20T00:01:20.307256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:20.307256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hYQuh+kwFqhPGcv+Uu6qIJ+m7cfxeVA6f3k7zk1LhppDw7+JXuibumnlsI5riM9IUNW2WIQVhua1L/mZOJvfBA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:20.308162Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15822","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f176cebb743eb98ab3d872b00b6fb61b70271aefed5df2c3aabbaa812177a90","sha256:b30a1a95efd2caaa54c08437e51e1b1c7a4726991333926a0757095f88ae61ad"],"state_sha256":"6cd7015a97bc07c5980cb7b804eb2f0a9308198d2f31cceca2a15295238734d4"}