{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:OP6BPF7Z7LGXFUQHAG7FW4IAQF","short_pith_number":"pith:OP6BPF7Z","canonical_record":{"source":{"id":"2606.18071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-16T15:40:09Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"686a2293e3a0eb6243a9b1517a0777a109629f3fddab97f20c58ba5c92451525","abstract_canon_sha256":"73b6bbc09489636d883de500c343db1a253db5ef6ccf72892651ee6c0a110af5"},"schema_version":"1.0"},"canonical_sha256":"73fc1797f9facd72d20701be5b7100815acf48c2ed6366aad49250aea9786258","source":{"kind":"arxiv","id":"2606.18071","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18071","created_at":"2026-06-19T16:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18071v1","created_at":"2026-06-19T16:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18071","created_at":"2026-06-19T16:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"OP6BPF7Z7LGX","created_at":"2026-06-19T16:10:47Z"},{"alias_kind":"pith_short_16","alias_value":"OP6BPF7Z7LGXFUQH","created_at":"2026-06-19T16:10:47Z"},{"alias_kind":"pith_short_8","alias_value":"OP6BPF7Z","created_at":"2026-06-19T16:10:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:OP6BPF7Z7LGXFUQHAG7FW4IAQF","target":"record","payload":{"canonical_record":{"source":{"id":"2606.18071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-16T15:40:09Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"686a2293e3a0eb6243a9b1517a0777a109629f3fddab97f20c58ba5c92451525","abstract_canon_sha256":"73b6bbc09489636d883de500c343db1a253db5ef6ccf72892651ee6c0a110af5"},"schema_version":"1.0"},"canonical_sha256":"73fc1797f9facd72d20701be5b7100815acf48c2ed6366aad49250aea9786258","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:47.752571Z","signature_b64":"Am3ZwsKHOCaLf2+v1otvqWZaCiHFcH3IEnZVNQ/pMz4k2qIefnQq9yawIuW4JosvUsibk40VD1MG79adhHWFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73fc1797f9facd72d20701be5b7100815acf48c2ed6366aad49250aea9786258","last_reissued_at":"2026-06-19T16:10:47.752233Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:47.752233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.18071","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":"2026-06-19T16:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h5kXNnZGMfeDKcUE1uhV4bJ0cV0NV75IMQ7XTCz9vLwbn3xyGLJkURgfdjKeA1LmgdTBs2XX/Hjy2GdtHKbEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T03:29:38.022718Z"},"content_sha256":"7245645a9b4302799abb0399257d54a33cf47f7941c03f916328b7403f8a0f40","schema_version":"1.0","event_id":"sha256:7245645a9b4302799abb0399257d54a33cf47f7941c03f916328b7403f8a0f40"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:OP6BPF7Z7LGXFUQHAG7FW4IAQF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Volterra Generative Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Bingyan Han, Yusen Jia","submitted_at":"2026-06-16T15:40:09Z","abstract_excerpt":"Score-based diffusion models typically use Brownian perturbations, which provide tractable reverse-time dynamics but impose memoryless noising. We introduce Volterra generative models, a continuous-time score-based framework whose forward process injects path-dependent noise through fractional kernels. To handle the non-Markovian and non-semimartingale dynamics, we construct finite-dimensional Markovian lifts using Gaussian quadrature in both regimes and a hybrid finite-difference exponential approximation in the smooth regime. We prove squared error bounds, derive an augmented linear-Gaussian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18071","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/2606.18071/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":"2026-06-19T16:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ufZagGhN9iXtnx+JExU8lN0xSoFukmo9xRPrpX914x/dNFIYY/JQL3ksFE6XxWiu7S+VJDkz7Myyr1xc7xMzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T03:29:38.023085Z"},"content_sha256":"4f11be8574fa0c146b0fd7a693913975574f510c6eb0520c5bb885bb7bafb79a","schema_version":"1.0","event_id":"sha256:4f11be8574fa0c146b0fd7a693913975574f510c6eb0520c5bb885bb7bafb79a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OP6BPF7Z7LGXFUQHAG7FW4IAQF/bundle.json","state_url":"https://pith.science/pith/OP6BPF7Z7LGXFUQHAG7FW4IAQF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OP6BPF7Z7LGXFUQHAG7FW4IAQF/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":"2026-07-04T03:29:38Z","links":{"resolver":"https://pith.science/pith/OP6BPF7Z7LGXFUQHAG7FW4IAQF","bundle":"https://pith.science/pith/OP6BPF7Z7LGXFUQHAG7FW4IAQF/bundle.json","state":"https://pith.science/pith/OP6BPF7Z7LGXFUQHAG7FW4IAQF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OP6BPF7Z7LGXFUQHAG7FW4IAQF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OP6BPF7Z7LGXFUQHAG7FW4IAQF","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":"73b6bbc09489636d883de500c343db1a253db5ef6ccf72892651ee6c0a110af5","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-16T15:40:09Z","title_canon_sha256":"686a2293e3a0eb6243a9b1517a0777a109629f3fddab97f20c58ba5c92451525"},"schema_version":"1.0","source":{"id":"2606.18071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18071","created_at":"2026-06-19T16:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18071v1","created_at":"2026-06-19T16:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18071","created_at":"2026-06-19T16:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"OP6BPF7Z7LGX","created_at":"2026-06-19T16:10:47Z"},{"alias_kind":"pith_short_16","alias_value":"OP6BPF7Z7LGXFUQH","created_at":"2026-06-19T16:10:47Z"},{"alias_kind":"pith_short_8","alias_value":"OP6BPF7Z","created_at":"2026-06-19T16:10:47Z"}],"graph_snapshots":[{"event_id":"sha256:4f11be8574fa0c146b0fd7a693913975574f510c6eb0520c5bb885bb7bafb79a","target":"graph","created_at":"2026-06-19T16:10:47Z","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/2606.18071/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Score-based diffusion models typically use Brownian perturbations, which provide tractable reverse-time dynamics but impose memoryless noising. We introduce Volterra generative models, a continuous-time score-based framework whose forward process injects path-dependent noise through fractional kernels. To handle the non-Markovian and non-semimartingale dynamics, we construct finite-dimensional Markovian lifts using Gaussian quadrature in both regimes and a hybrid finite-difference exponential approximation in the smooth regime. We prove squared error bounds, derive an augmented linear-Gaussian","authors_text":"Bingyan Han, Yusen Jia","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-16T15:40:09Z","title":"Volterra Generative Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18071","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":"sha256:7245645a9b4302799abb0399257d54a33cf47f7941c03f916328b7403f8a0f40","target":"record","created_at":"2026-06-19T16:10:47Z","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":"73b6bbc09489636d883de500c343db1a253db5ef6ccf72892651ee6c0a110af5","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-16T15:40:09Z","title_canon_sha256":"686a2293e3a0eb6243a9b1517a0777a109629f3fddab97f20c58ba5c92451525"},"schema_version":"1.0","source":{"id":"2606.18071","kind":"arxiv","version":1}},"canonical_sha256":"73fc1797f9facd72d20701be5b7100815acf48c2ed6366aad49250aea9786258","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73fc1797f9facd72d20701be5b7100815acf48c2ed6366aad49250aea9786258","first_computed_at":"2026-06-19T16:10:47.752233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:47.752233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Am3ZwsKHOCaLf2+v1otvqWZaCiHFcH3IEnZVNQ/pMz4k2qIefnQq9yawIuW4JosvUsibk40VD1MG79adhHWFDA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:47.752571Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7245645a9b4302799abb0399257d54a33cf47f7941c03f916328b7403f8a0f40","sha256:4f11be8574fa0c146b0fd7a693913975574f510c6eb0520c5bb885bb7bafb79a"],"state_sha256":"d4239d313e23c60dbe454074c0ca9ed0cea5fb165897031b85d7b1a9fda9a9a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6vSJbA5VxS7SVgWVEJP8N4UIOgMrgKWEvGTmscPX18XWWeWdN8AT525dffrT64ZvQh4MTAB0vMIW8MP0R6OOBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T03:29:38.025248Z","bundle_sha256":"5988702dad83f53aa7bec587a6715df3fd1de47aa5f8018bf250082cf5e29908"}}