{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GMRPA43MFG7FCJS63QGNN64SQV","short_pith_number":"pith:GMRPA43M","canonical_record":{"source":{"id":"2607.23226","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-25T14:24:38Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"087448b1bd6e15d9e43f3dd1ddb359443814d10a94d5747c1eb63de0f8390657","abstract_canon_sha256":"13c007a828d54e8edb362196b9e9e0847d0bfd4eba3564e7ef81e877267acda1"},"schema_version":"1.0"},"canonical_sha256":"3322f0736c29be51265edc0cd6fb92857eb1140c3865ec89861a0cd4515f2264","source":{"kind":"arxiv","id":"2607.23226","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23226","created_at":"2026-07-28T01:22:42Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23226v1","created_at":"2026-07-28T01:22:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23226","created_at":"2026-07-28T01:22:42Z"},{"alias_kind":"pith_short_12","alias_value":"GMRPA43MFG7F","created_at":"2026-07-28T01:22:42Z"},{"alias_kind":"pith_short_16","alias_value":"GMRPA43MFG7FCJS6","created_at":"2026-07-28T01:22:42Z"},{"alias_kind":"pith_short_8","alias_value":"GMRPA43M","created_at":"2026-07-28T01:22:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GMRPA43MFG7FCJS63QGNN64SQV","target":"record","payload":{"canonical_record":{"source":{"id":"2607.23226","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-25T14:24:38Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"087448b1bd6e15d9e43f3dd1ddb359443814d10a94d5747c1eb63de0f8390657","abstract_canon_sha256":"13c007a828d54e8edb362196b9e9e0847d0bfd4eba3564e7ef81e877267acda1"},"schema_version":"1.0"},"canonical_sha256":"3322f0736c29be51265edc0cd6fb92857eb1140c3865ec89861a0cd4515f2264","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T01:22:42.903298Z","signature_b64":"lLqfniiKjBSJu2yJaRw1RTWQCeONjIKvEzuYZH+87WgM23rca7LNJVeUU/vkEBYKwtgKicI4z5tk9LMP/xe7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3322f0736c29be51265edc0cd6fb92857eb1140c3865ec89861a0cd4515f2264","last_reissued_at":"2026-07-28T01:22:42.902521Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T01:22:42.902521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.23226","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-28T01:22:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L0PFyOavVDIo6SjN3vfrl4jZBwn5HTBP1AbI9gzDCmiGtSYeoom+9kuQGBHfIL+6hUH0uAVtz2nrJ+bIn3oLCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T15:46:20.290988Z"},"content_sha256":"41f3deb68918e4f74533324a4ac61a2500e953487d8258f4f21d0deb54aa8560","schema_version":"1.0","event_id":"sha256:41f3deb68918e4f74533324a4ac61a2500e953487d8258f4f21d0deb54aa8560"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GMRPA43MFG7FCJS63QGNN64SQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Chunlin Wu, Jinshu Huang, Yiming Jiang","submitted_at":"2026-07-25T14:24:38Z","abstract_excerpt":"Despite the empirical success of score-based diffusion models, a complete theoretical understanding of how finite-sample learning, network parameterization, and numerical discretization jointly dictate generative quality remains underdeveloped. Existing sampling analyses often evaluate the generative performance conditional on an oracle score or a pre-specified error threshold. In this work, we establish a unified convergence and generalization framework for score-based diffusion models parameterized by practical ResNet-type architectures. We analyze the generalization and convergence properti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23226","kind":"arxiv","version":1},"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/2607.23226/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":"2026-07-28T01:22:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Xgkct4/dqFR+a2RQK3kidmuDyqW42juokAiFlebIfdLOujg/guVB+EIOXb3UpH7DU+02bPZt4iWcu6ZLFBrAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T15:46:20.291370Z"},"content_sha256":"b1b2cdadf1ddb7b076010cc7ac61140c67d0468f46c403e63ecd75eeb8b26d40","schema_version":"1.0","event_id":"sha256:b1b2cdadf1ddb7b076010cc7ac61140c67d0468f46c403e63ecd75eeb8b26d40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GMRPA43MFG7FCJS63QGNN64SQV/bundle.json","state_url":"https://pith.science/pith/GMRPA43MFG7FCJS63QGNN64SQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GMRPA43MFG7FCJS63QGNN64SQV/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":"2026-08-01T15:46:20Z","links":{"resolver":"https://pith.science/pith/GMRPA43MFG7FCJS63QGNN64SQV","bundle":"https://pith.science/pith/GMRPA43MFG7FCJS63QGNN64SQV/bundle.json","state":"https://pith.science/pith/GMRPA43MFG7FCJS63QGNN64SQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GMRPA43MFG7FCJS63QGNN64SQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GMRPA43MFG7FCJS63QGNN64SQV","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":"13c007a828d54e8edb362196b9e9e0847d0bfd4eba3564e7ef81e877267acda1","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-25T14:24:38Z","title_canon_sha256":"087448b1bd6e15d9e43f3dd1ddb359443814d10a94d5747c1eb63de0f8390657"},"schema_version":"1.0","source":{"id":"2607.23226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23226","created_at":"2026-07-28T01:22:42Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23226v1","created_at":"2026-07-28T01:22:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23226","created_at":"2026-07-28T01:22:42Z"},{"alias_kind":"pith_short_12","alias_value":"GMRPA43MFG7F","created_at":"2026-07-28T01:22:42Z"},{"alias_kind":"pith_short_16","alias_value":"GMRPA43MFG7FCJS6","created_at":"2026-07-28T01:22:42Z"},{"alias_kind":"pith_short_8","alias_value":"GMRPA43M","created_at":"2026-07-28T01:22:42Z"}],"graph_snapshots":[{"event_id":"sha256:b1b2cdadf1ddb7b076010cc7ac61140c67d0468f46c403e63ecd75eeb8b26d40","target":"graph","created_at":"2026-07-28T01:22:42Z","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/2607.23226/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Despite the empirical success of score-based diffusion models, a complete theoretical understanding of how finite-sample learning, network parameterization, and numerical discretization jointly dictate generative quality remains underdeveloped. Existing sampling analyses often evaluate the generative performance conditional on an oracle score or a pre-specified error threshold. In this work, we establish a unified convergence and generalization framework for score-based diffusion models parameterized by practical ResNet-type architectures. We analyze the generalization and convergence properti","authors_text":"Chunlin Wu, Jinshu Huang, Yiming Jiang","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-25T14:24:38Z","title":"From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23226","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":"sha256:41f3deb68918e4f74533324a4ac61a2500e953487d8258f4f21d0deb54aa8560","target":"record","created_at":"2026-07-28T01:22:42Z","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":"13c007a828d54e8edb362196b9e9e0847d0bfd4eba3564e7ef81e877267acda1","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-25T14:24:38Z","title_canon_sha256":"087448b1bd6e15d9e43f3dd1ddb359443814d10a94d5747c1eb63de0f8390657"},"schema_version":"1.0","source":{"id":"2607.23226","kind":"arxiv","version":1}},"canonical_sha256":"3322f0736c29be51265edc0cd6fb92857eb1140c3865ec89861a0cd4515f2264","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3322f0736c29be51265edc0cd6fb92857eb1140c3865ec89861a0cd4515f2264","first_computed_at":"2026-07-28T01:22:42.902521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:22:42.902521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lLqfniiKjBSJu2yJaRw1RTWQCeONjIKvEzuYZH+87WgM23rca7LNJVeUU/vkEBYKwtgKicI4z5tk9LMP/xe7Bg==","signature_status":"signed_v1","signed_at":"2026-07-28T01:22:42.903298Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.23226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41f3deb68918e4f74533324a4ac61a2500e953487d8258f4f21d0deb54aa8560","sha256:b1b2cdadf1ddb7b076010cc7ac61140c67d0468f46c403e63ecd75eeb8b26d40"],"state_sha256":"21b131bbd881e045e6e6d36fa06ec78fe96534145195ca757efb4e0822d1bdb5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W/AQMArAZtvUvt1EpZb7CMhCFYOMqP4sptB5IqmHbbci6bX23+6vwQLmvPZcS0Mmg+uLcFWhb1C7ug4WuiClCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T15:46:20.293755Z","bundle_sha256":"486dd7efcb0f382f19bda55abd43b86b39f8ded5cc67ca031437851c28d6ab69"}}