{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:B5NJJWHNJ4J6BUSJGY6OEOQL3B","short_pith_number":"pith:B5NJJWHN","canonical_record":{"source":{"id":"2606.12710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-10T21:55:55Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"7da5da0d284efb8194928b17bea60a0fb2b301605e991673ddf0fd25560e22b6","abstract_canon_sha256":"79ad25525c25af9fa59c74d21a9ce5521a831a19cf8089bb2b3b2536b93cdf50"},"schema_version":"1.0"},"canonical_sha256":"0f5a94d8ed4f13e0d249363ce23a0bd85b0ef5e9d9a3c8bf361e974081fc2cce","source":{"kind":"arxiv","id":"2606.12710","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.12710","created_at":"2026-06-12T01:08:46Z"},{"alias_kind":"arxiv_version","alias_value":"2606.12710v1","created_at":"2026-06-12T01:08:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.12710","created_at":"2026-06-12T01:08:46Z"},{"alias_kind":"pith_short_12","alias_value":"B5NJJWHNJ4J6","created_at":"2026-06-12T01:08:46Z"},{"alias_kind":"pith_short_16","alias_value":"B5NJJWHNJ4J6BUSJ","created_at":"2026-06-12T01:08:46Z"},{"alias_kind":"pith_short_8","alias_value":"B5NJJWHN","created_at":"2026-06-12T01:08:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:B5NJJWHNJ4J6BUSJGY6OEOQL3B","target":"record","payload":{"canonical_record":{"source":{"id":"2606.12710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-10T21:55:55Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"7da5da0d284efb8194928b17bea60a0fb2b301605e991673ddf0fd25560e22b6","abstract_canon_sha256":"79ad25525c25af9fa59c74d21a9ce5521a831a19cf8089bb2b3b2536b93cdf50"},"schema_version":"1.0"},"canonical_sha256":"0f5a94d8ed4f13e0d249363ce23a0bd85b0ef5e9d9a3c8bf361e974081fc2cce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:08:46.788357Z","signature_b64":"4Kg3AJdnzgrSJg7f5RygbrV3AK7WW0zNFMmy7LPQUIFhLqOIg/oGbLoreljrVXDUeYXRYo98FhqgZ8L/Hsv1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f5a94d8ed4f13e0d249363ce23a0bd85b0ef5e9d9a3c8bf361e974081fc2cce","last_reissued_at":"2026-06-12T01:08:46.787555Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:08:46.787555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.12710","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":"2026-06-12T01:08:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sKJLr6vEyWZJ4EG8OdNllq3HHRd9hnASRVydc9Xjjds3BAb7oHehB9oz9oaz+TVPCbAeWe/AcFKTf05Ydpm7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:53:51.963114Z"},"content_sha256":"3a557fe60b7140f58af6bd674b2620cfac84117ab463ecc1e05f6511e6328aa4","schema_version":"1.0","event_id":"sha256:3a557fe60b7140f58af6bd674b2620cfac84117ab463ecc1e05f6511e6328aa4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:B5NJJWHNJ4J6BUSJGY6OEOQL3B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Stabilized Path-Space Approach to Diffusion-Based Posterior Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Evan Scope Crafts, Hassan Mansour, Saviz Mowlavi, Umberto Villa, Wael H. Ali, Yanting Ma","submitted_at":"2026-06-10T21:55:55Z","abstract_excerpt":"Diffusion models provide expressive data-driven priors for Bayesian inverse problems, but many diffusion posterior samplers rely on heuristic guidance approximations that can fail for nonlinear operators and multimodal posteriors. In this work, we develop a stabilized path-space framework for diffusion-based posterior sampling. Starting from a base diffusion process whose terminal marginal represents the prior, we define a likelihood-weighted target measure on trajectories and cast posterior sampling as learning a controlled stochastic process whose path measure matches this target. This formu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12710","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/2606.12710/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":"2026-06-12T01:08:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5xPgMo3qvSbbsPekjCEBSqdSLX8Sd6vLi6Cr6LldNf8nr4MkphZUAtIM6OWLw0+Wor0wloUUbbQFw7UycDZoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:53:51.963506Z"},"content_sha256":"73b8674036dfe1df595cb92d4885b66e33fdd0442e6db3d74e37c09069a0ad63","schema_version":"1.0","event_id":"sha256:73b8674036dfe1df595cb92d4885b66e33fdd0442e6db3d74e37c09069a0ad63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B5NJJWHNJ4J6BUSJGY6OEOQL3B/bundle.json","state_url":"https://pith.science/pith/B5NJJWHNJ4J6BUSJGY6OEOQL3B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B5NJJWHNJ4J6BUSJGY6OEOQL3B/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":"2026-06-20T06:53:51Z","links":{"resolver":"https://pith.science/pith/B5NJJWHNJ4J6BUSJGY6OEOQL3B","bundle":"https://pith.science/pith/B5NJJWHNJ4J6BUSJGY6OEOQL3B/bundle.json","state":"https://pith.science/pith/B5NJJWHNJ4J6BUSJGY6OEOQL3B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B5NJJWHNJ4J6BUSJGY6OEOQL3B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:B5NJJWHNJ4J6BUSJGY6OEOQL3B","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":"79ad25525c25af9fa59c74d21a9ce5521a831a19cf8089bb2b3b2536b93cdf50","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-10T21:55:55Z","title_canon_sha256":"7da5da0d284efb8194928b17bea60a0fb2b301605e991673ddf0fd25560e22b6"},"schema_version":"1.0","source":{"id":"2606.12710","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.12710","created_at":"2026-06-12T01:08:46Z"},{"alias_kind":"arxiv_version","alias_value":"2606.12710v1","created_at":"2026-06-12T01:08:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.12710","created_at":"2026-06-12T01:08:46Z"},{"alias_kind":"pith_short_12","alias_value":"B5NJJWHNJ4J6","created_at":"2026-06-12T01:08:46Z"},{"alias_kind":"pith_short_16","alias_value":"B5NJJWHNJ4J6BUSJ","created_at":"2026-06-12T01:08:46Z"},{"alias_kind":"pith_short_8","alias_value":"B5NJJWHN","created_at":"2026-06-12T01:08:46Z"}],"graph_snapshots":[{"event_id":"sha256:73b8674036dfe1df595cb92d4885b66e33fdd0442e6db3d74e37c09069a0ad63","target":"graph","created_at":"2026-06-12T01:08:46Z","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/2606.12710/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Diffusion models provide expressive data-driven priors for Bayesian inverse problems, but many diffusion posterior samplers rely on heuristic guidance approximations that can fail for nonlinear operators and multimodal posteriors. In this work, we develop a stabilized path-space framework for diffusion-based posterior sampling. Starting from a base diffusion process whose terminal marginal represents the prior, we define a likelihood-weighted target measure on trajectories and cast posterior sampling as learning a controlled stochastic process whose path measure matches this target. This formu","authors_text":"Evan Scope Crafts, Hassan Mansour, Saviz Mowlavi, Umberto Villa, Wael H. Ali, Yanting Ma","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-10T21:55:55Z","title":"A Stabilized Path-Space Approach to Diffusion-Based Posterior Sampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12710","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":"sha256:3a557fe60b7140f58af6bd674b2620cfac84117ab463ecc1e05f6511e6328aa4","target":"record","created_at":"2026-06-12T01:08:46Z","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":"79ad25525c25af9fa59c74d21a9ce5521a831a19cf8089bb2b3b2536b93cdf50","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-10T21:55:55Z","title_canon_sha256":"7da5da0d284efb8194928b17bea60a0fb2b301605e991673ddf0fd25560e22b6"},"schema_version":"1.0","source":{"id":"2606.12710","kind":"arxiv","version":1}},"canonical_sha256":"0f5a94d8ed4f13e0d249363ce23a0bd85b0ef5e9d9a3c8bf361e974081fc2cce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f5a94d8ed4f13e0d249363ce23a0bd85b0ef5e9d9a3c8bf361e974081fc2cce","first_computed_at":"2026-06-12T01:08:46.787555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:08:46.787555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Kg3AJdnzgrSJg7f5RygbrV3AK7WW0zNFMmy7LPQUIFhLqOIg/oGbLoreljrVXDUeYXRYo98FhqgZ8L/Hsv1Cg==","signature_status":"signed_v1","signed_at":"2026-06-12T01:08:46.788357Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.12710","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a557fe60b7140f58af6bd674b2620cfac84117ab463ecc1e05f6511e6328aa4","sha256:73b8674036dfe1df595cb92d4885b66e33fdd0442e6db3d74e37c09069a0ad63"],"state_sha256":"fa72497f3e3f01b35482537d7061482486d9dba3fd9963a82b34a0c4a046f542"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"18Kfv7GudKn6tYXzDzjhllhMe/1yXWtQTLN/I+OGbhEfp2BFsylH5FJt/M6Q0BXojeFz3ACj7yebfXxAUZ7SDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:53:51.965589Z","bundle_sha256":"bdb320a537b3bb39160838d536e2bbe5dbfb09656d3752ed46fd74c290314c5f"}}