{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EUFTFIKKQNHT44B3JSZBK6CHSH","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":"e89f1a93c46d5edf76aa3ac014870b27213d9c85ca4df5cff94d9e6e27881de8","cross_cats_sorted":["cs.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-08-03T15:49:08Z","title_canon_sha256":"a14f35bb6631dda39b8866653c074ffa87c199436da926c1ebb77413d3c75d1c"},"schema_version":"1.0","source":{"id":"2608.02406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.02406","created_at":"2026-08-04T02:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"2608.02406v1","created_at":"2026-08-04T02:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.02406","created_at":"2026-08-04T02:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"EUFTFIKKQNHT","created_at":"2026-08-04T02:12:09Z"},{"alias_kind":"pith_short_16","alias_value":"EUFTFIKKQNHT44B3","created_at":"2026-08-04T02:12:09Z"},{"alias_kind":"pith_short_8","alias_value":"EUFTFIKK","created_at":"2026-08-04T02:12:09Z"}],"graph_snapshots":[{"event_id":"sha256:1f8553d849ed0abc20c7a0a8e153c62565e6d0bdc07f26e9bc115b86b29fee6f","target":"graph","created_at":"2026-08-04T02:12:09Z","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/2608.02406/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a unified framework for the error analysis of generative models based on the entropy production rate of the forward-reverse diffusion process pair. For a pair of continuity equation flows, the rate admits a closed velocity form identity whose time integral decomposes the terminal Kullback--Leibler (KL) divergence into the sum of an initialization error, a score approximation error, and a time-discretization error. By analyzing the entropy production at the level of marginal distributions, rather than in path space, our framework yields a sharp convergence rate of $\\mathcal{O}(h^2)","authors_text":"Han Wu, Zhiwen Zhang","cross_cats":["cs.NA","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-08-03T15:49:08Z","title":"A Unified Kullback--Leibler Divergence Analysis of Generative Diffusion Models via Entropy Production Rate"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02406","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:b3dd157f54cf72f81c3068b5ba12345b08e991e70fde572aa27e49b67d9d9ea2","target":"record","created_at":"2026-08-04T02:12:09Z","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":"e89f1a93c46d5edf76aa3ac014870b27213d9c85ca4df5cff94d9e6e27881de8","cross_cats_sorted":["cs.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-08-03T15:49:08Z","title_canon_sha256":"a14f35bb6631dda39b8866653c074ffa87c199436da926c1ebb77413d3c75d1c"},"schema_version":"1.0","source":{"id":"2608.02406","kind":"arxiv","version":1}},"canonical_sha256":"250b32a14a834f3e703b4cb215784791f12dd51073852d58753bf72af6c3a4ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"250b32a14a834f3e703b4cb215784791f12dd51073852d58753bf72af6c3a4ac","first_computed_at":"2026-08-04T02:12:09.295355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T02:12:09.295355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UN6onzW53atqcg8ZNHwvOkF8G5FVr0eLh3TjxiAYJKdSbD0rqYrgt9flDwFKYGs32KZtBwAjYn51AWWz0jTpDg==","signature_status":"signed_v1","signed_at":"2026-08-04T02:12:09.296898Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.02406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3dd157f54cf72f81c3068b5ba12345b08e991e70fde572aa27e49b67d9d9ea2","sha256:1f8553d849ed0abc20c7a0a8e153c62565e6d0bdc07f26e9bc115b86b29fee6f"],"state_sha256":"155bbabae6a7703a34a14a9aaa78b74079022d263eb9dade83fb802beffa589a"}