{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:OLUG6QUEIHEJYJ4T5ULMMB47TL","short_pith_number":"pith:OLUG6QUE","canonical_record":{"source":{"id":"2602.09708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T12:11:07Z","cross_cats_sorted":["cs.AI","cs.CV","cs.NA","math.NA"],"title_canon_sha256":"a66d0c2d7ef02a13e1124b2d72d16152c995e9e800a48d86de6e11203aef40ef","abstract_canon_sha256":"020871b2c8f7cbf70f5d7188f9a0556050f7d1853005260436606f330f81dbc8"},"schema_version":"1.0"},"canonical_sha256":"72e86f428441c89c2793ed16c6079f9af206b10db8264f0bef9a2b6cd96444fa","source":{"kind":"arxiv","id":"2602.09708","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.09708","created_at":"2026-06-03T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"2602.09708v2","created_at":"2026-06-03T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.09708","created_at":"2026-06-03T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"OLUG6QUEIHEJ","created_at":"2026-06-03T01:05:48Z"},{"alias_kind":"pith_short_16","alias_value":"OLUG6QUEIHEJYJ4T","created_at":"2026-06-03T01:05:48Z"},{"alias_kind":"pith_short_8","alias_value":"OLUG6QUE","created_at":"2026-06-03T01:05:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:OLUG6QUEIHEJYJ4T5ULMMB47TL","target":"record","payload":{"canonical_record":{"source":{"id":"2602.09708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T12:11:07Z","cross_cats_sorted":["cs.AI","cs.CV","cs.NA","math.NA"],"title_canon_sha256":"a66d0c2d7ef02a13e1124b2d72d16152c995e9e800a48d86de6e11203aef40ef","abstract_canon_sha256":"020871b2c8f7cbf70f5d7188f9a0556050f7d1853005260436606f330f81dbc8"},"schema_version":"1.0"},"canonical_sha256":"72e86f428441c89c2793ed16c6079f9af206b10db8264f0bef9a2b6cd96444fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:48.793211Z","signature_b64":"Lx4h1us4uAR7F+GzGePaltO8VPwhNJ0Ol0L8CU3sn3MD3s/VPzLSJ7CtHd2THP2DJE4YAr0i6p6oagw9l2eKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72e86f428441c89c2793ed16c6079f9af206b10db8264f0bef9a2b6cd96444fa","last_reissued_at":"2026-06-03T01:05:48.792710Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:48.792710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.09708","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T01:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FEg212hyX/kgh8tLwtgr94U91W+LThPjkK717QlkYDTBvSLu9yjk5Stpa9Zyxj6Ae1X3W8FUb9Yef/eiDLE9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:50:27.068425Z"},"content_sha256":"3807e108c82ebe12218a046158cb82bc61ca4e9536cda6627cb9c681bbb56125","schema_version":"1.0","event_id":"sha256:3807e108c82ebe12218a046158cb82bc61ca4e9536cda6627cb9c681bbb56125"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:OLUG6QUEIHEJYJ4T5ULMMB47TL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Physics-informed diffusion models in spectral space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CV","cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Arnulf Jentzen, Davide Gallon, Patrick Cheridito, Philippe von Wurstemberger","submitted_at":"2026-02-10T12:11:07Z","abstract_excerpt":"We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems. We learn the joint distribution of PDE parameters and solutions via a diffusion process in a latent space of scaled spectral representations, where Gaussian noise corresponds to functions with controlled regularity. This spectral formulation enables significant dimensionality r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.09708","kind":"arxiv","version":2},"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/2602.09708/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":"2026-06-03T01:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yjlaAHdCVreHb4fhUbieJgxa0c5ve/bLs3NrmkiUGk5idSQz9TnxYFNeL57B3L5sSD7Rq60SUn+BA/WzXj3LCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:50:27.068802Z"},"content_sha256":"cf74f4868405e6cf0bd11e5b50c5460bdeeb64d79ffc264b01fa87bf1912ef87","schema_version":"1.0","event_id":"sha256:cf74f4868405e6cf0bd11e5b50c5460bdeeb64d79ffc264b01fa87bf1912ef87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OLUG6QUEIHEJYJ4T5ULMMB47TL/bundle.json","state_url":"https://pith.science/pith/OLUG6QUEIHEJYJ4T5ULMMB47TL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OLUG6QUEIHEJYJ4T5ULMMB47TL/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":"2026-06-26T00:50:27Z","links":{"resolver":"https://pith.science/pith/OLUG6QUEIHEJYJ4T5ULMMB47TL","bundle":"https://pith.science/pith/OLUG6QUEIHEJYJ4T5ULMMB47TL/bundle.json","state":"https://pith.science/pith/OLUG6QUEIHEJYJ4T5ULMMB47TL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OLUG6QUEIHEJYJ4T5ULMMB47TL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OLUG6QUEIHEJYJ4T5ULMMB47TL","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":"020871b2c8f7cbf70f5d7188f9a0556050f7d1853005260436606f330f81dbc8","cross_cats_sorted":["cs.AI","cs.CV","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T12:11:07Z","title_canon_sha256":"a66d0c2d7ef02a13e1124b2d72d16152c995e9e800a48d86de6e11203aef40ef"},"schema_version":"1.0","source":{"id":"2602.09708","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.09708","created_at":"2026-06-03T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"2602.09708v2","created_at":"2026-06-03T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.09708","created_at":"2026-06-03T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"OLUG6QUEIHEJ","created_at":"2026-06-03T01:05:48Z"},{"alias_kind":"pith_short_16","alias_value":"OLUG6QUEIHEJYJ4T","created_at":"2026-06-03T01:05:48Z"},{"alias_kind":"pith_short_8","alias_value":"OLUG6QUE","created_at":"2026-06-03T01:05:48Z"}],"graph_snapshots":[{"event_id":"sha256:cf74f4868405e6cf0bd11e5b50c5460bdeeb64d79ffc264b01fa87bf1912ef87","target":"graph","created_at":"2026-06-03T01:05:48Z","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/2602.09708/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems. We learn the joint distribution of PDE parameters and solutions via a diffusion process in a latent space of scaled spectral representations, where Gaussian noise corresponds to functions with controlled regularity. This spectral formulation enables significant dimensionality r","authors_text":"Arnulf Jentzen, Davide Gallon, Patrick Cheridito, Philippe von Wurstemberger","cross_cats":["cs.AI","cs.CV","cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T12:11:07Z","title":"Physics-informed diffusion models in spectral space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.09708","kind":"arxiv","version":2},"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":"sha256:3807e108c82ebe12218a046158cb82bc61ca4e9536cda6627cb9c681bbb56125","target":"record","created_at":"2026-06-03T01:05:48Z","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":"020871b2c8f7cbf70f5d7188f9a0556050f7d1853005260436606f330f81dbc8","cross_cats_sorted":["cs.AI","cs.CV","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T12:11:07Z","title_canon_sha256":"a66d0c2d7ef02a13e1124b2d72d16152c995e9e800a48d86de6e11203aef40ef"},"schema_version":"1.0","source":{"id":"2602.09708","kind":"arxiv","version":2}},"canonical_sha256":"72e86f428441c89c2793ed16c6079f9af206b10db8264f0bef9a2b6cd96444fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72e86f428441c89c2793ed16c6079f9af206b10db8264f0bef9a2b6cd96444fa","first_computed_at":"2026-06-03T01:05:48.792710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:48.792710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lx4h1us4uAR7F+GzGePaltO8VPwhNJ0Ol0L8CU3sn3MD3s/VPzLSJ7CtHd2THP2DJE4YAr0i6p6oagw9l2eKBA==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:48.793211Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.09708","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3807e108c82ebe12218a046158cb82bc61ca4e9536cda6627cb9c681bbb56125","sha256:cf74f4868405e6cf0bd11e5b50c5460bdeeb64d79ffc264b01fa87bf1912ef87"],"state_sha256":"baa385235cc8018ada31ff0263c0845688a206c6c22ae903b214915802b8b2b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mYTVOwjQo8ZvMb6Cm28M89SIAPWhVhA79F+JzpnVVKxkBVOhs3WO+kSPOu66ZKxGOBsJzeqYmeghDPEvdfwoAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:50:27.070806Z","bundle_sha256":"bdbc70db6d263b2023a948e56e6d6789a1ecd7743d0ed130cf3cfb1cdf394327"}}