{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PYT7RCDGJLCASJJ2MUGMV3B5JP","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":"6f73ebef98a6ddc5fa4560bcf0cf1a07944de31cdf48c2706f9ab73305eebc8e","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-07-07T09:13:09Z","title_canon_sha256":"3ad26fa14f7ae071cd610cebae2912ca31bd1cfa3003325672373a6e34dbb741"},"schema_version":"1.0","source":{"id":"2507.04794","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.04794","created_at":"2026-07-05T11:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"2507.04794v1","created_at":"2026-07-05T11:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.04794","created_at":"2026-07-05T11:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"PYT7RCDGJLCA","created_at":"2026-07-05T11:32:54Z"},{"alias_kind":"pith_short_16","alias_value":"PYT7RCDGJLCASJJ2","created_at":"2026-07-05T11:32:54Z"},{"alias_kind":"pith_short_8","alias_value":"PYT7RCDG","created_at":"2026-07-05T11:32:54Z"}],"graph_snapshots":[{"event_id":"sha256:56e2a755815f345af922fb2336fe74914cc4f721a76071be1153811f04c31def","target":"graph","created_at":"2026-07-05T11:32:54Z","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/2507.04794/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish minimax convergence rates for score-based generative models (SGMs) under the $1$-Wasserstein distance. Assuming the target density $p^\\star$ lies in a nonparametric $\\beta$-smooth H\\\"older class with either compact support or subGaussian tails on $\\mathbb{R}^d$, we prove that neural network-based score estimators trained via denoising score matching yield generative models achieving rate $n^{-(\\beta+1)/(2\\beta+d)}$ up to polylogarithmic factors. Our unified analysis handles arbitrary smoothness $\\beta > 0$, supports both deterministic and stochastic samplers, and leverages shape c","authors_text":"Arthur St\\'ephanovitch, Cl\\'ement Levrard, Eddie Aamari","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-07-07T09:13:09Z","title":"Generalization bounds for score-based generative models: a synthetic proof"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04794","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":"sha256:69d4c740d6b8ae8c50b716bc09bd59b86d0c0b3a29832ac33ac9b86506ad8d07","target":"record","created_at":"2026-07-05T11:32:54Z","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":"6f73ebef98a6ddc5fa4560bcf0cf1a07944de31cdf48c2706f9ab73305eebc8e","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-07-07T09:13:09Z","title_canon_sha256":"3ad26fa14f7ae071cd610cebae2912ca31bd1cfa3003325672373a6e34dbb741"},"schema_version":"1.0","source":{"id":"2507.04794","kind":"arxiv","version":1}},"canonical_sha256":"7e27f888664ac409253a650ccaec3d4bc0766521bf7357c64426b662599cf4f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e27f888664ac409253a650ccaec3d4bc0766521bf7357c64426b662599cf4f7","first_computed_at":"2026-07-05T11:32:54.293520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:32:54.293520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"itzPDg3FhlwCYxmfZKHh7O/GBTujBj+bRf+I5cQXCpsJXeFSn5AIqhS95gB52ljaIvamiCovFucZzmg9DYH0BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:32:54.294031Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.04794","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69d4c740d6b8ae8c50b716bc09bd59b86d0c0b3a29832ac33ac9b86506ad8d07","sha256:56e2a755815f345af922fb2336fe74914cc4f721a76071be1153811f04c31def"],"state_sha256":"6cd112ea9d11c3141d7fc51853fa157a0230dfc78b06beaa68c41177eb3da5d2"}