{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:63MKC4TLZWJWMVZP3LWXCVPUB5","short_pith_number":"pith:63MKC4TL","canonical_record":{"source":{"id":"2505.13463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-05-05T19:35:23Z","cross_cats_sorted":["physics.comp-ph","physics.flu-dyn"],"title_canon_sha256":"692d1cfee6a57a9ef4f3d402db7a1c18e8e2163d9463efd0e23ce251841d52a8","abstract_canon_sha256":"a605f96bd3bb0659c928a51220ccf694cc8b3c488d98eab484561c664e2c5e68"},"schema_version":"1.0"},"canonical_sha256":"f6d8a1726bcd9366572fdaed7155f40f60efa56f20568820abc98cf2b5261929","source":{"kind":"arxiv","id":"2505.13463","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.13463","created_at":"2026-07-05T11:06:13Z"},{"alias_kind":"arxiv_version","alias_value":"2505.13463v1","created_at":"2026-07-05T11:06:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13463","created_at":"2026-07-05T11:06:13Z"},{"alias_kind":"pith_short_12","alias_value":"63MKC4TLZWJW","created_at":"2026-07-05T11:06:13Z"},{"alias_kind":"pith_short_16","alias_value":"63MKC4TLZWJWMVZP","created_at":"2026-07-05T11:06:13Z"},{"alias_kind":"pith_short_8","alias_value":"63MKC4TL","created_at":"2026-07-05T11:06:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:63MKC4TLZWJWMVZP3LWXCVPUB5","target":"record","payload":{"canonical_record":{"source":{"id":"2505.13463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-05-05T19:35:23Z","cross_cats_sorted":["physics.comp-ph","physics.flu-dyn"],"title_canon_sha256":"692d1cfee6a57a9ef4f3d402db7a1c18e8e2163d9463efd0e23ce251841d52a8","abstract_canon_sha256":"a605f96bd3bb0659c928a51220ccf694cc8b3c488d98eab484561c664e2c5e68"},"schema_version":"1.0"},"canonical_sha256":"f6d8a1726bcd9366572fdaed7155f40f60efa56f20568820abc98cf2b5261929","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:06:13.675144Z","signature_b64":"gt6P2dOxrBZf/po0LIQ4lDjrJAyGaeYe6CKRvD36ovcVLQ2Ny3UUsm8nIpxO9iDeLuiudx2LLyWBESmHdanGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6d8a1726bcd9366572fdaed7155f40f60efa56f20568820abc98cf2b5261929","last_reissued_at":"2026-07-05T11:06:13.674620Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:06:13.674620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.13463","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":"2026-07-05T11:06:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UEJZtMntFgsRJovIpOyB9ZPa/Z7RVzkJa0BYivHx2UA02yNCeM6ESgO7T+lnIyp6ZsEQeRZlor+pEa+7Eh9MBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T09:09:32.799942Z"},"content_sha256":"65699a23d43cabb19bdcb1861308903a32b35a47672da98f2ebcfcdd564a8779","schema_version":"1.0","event_id":"sha256:65699a23d43cabb19bdcb1861308903a32b35a47672da98f2ebcfcdd564a8779"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:63MKC4TLZWJWMVZP3LWXCVPUB5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Predicting The Evolution of Interfaces with Fourier Neural Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph","physics.flu-dyn"],"primary_cat":"cs.LG","authors_text":"Paolo Guida, William L. Roberts","submitted_at":"2025-05-05T19:35:23Z","abstract_excerpt":"Recent progress in AI has established neural operators as powerful tools that can predict the evolution of partial differential equations, such as the Navier-Stokes equations. Some complex problems rely on sophisticated algorithms to deal with strong discontinuities in the computational domain. For example, liquid-vapour multiphase flows are a challenging problem in many configurations, particularly those involving large density gradients or phase change. The complexity mentioned above has not allowed for fine control of fast industrial processes or applications because computational fluid dyn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13463","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/2505.13463/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":"2026-07-05T11:06:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fkZVuLYu1nQxL6awnSuzp5ki4QYuXWgq825acjCUU/rzW9CeE5IL9nGIpH/IRlE8KubjnwfAS116Y7wOTPJSBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T09:09:32.800706Z"},"content_sha256":"73f028f84c4bad5e5dc6c2aef4f82a8e555767e7c5ff8e2336b01d111869a555","schema_version":"1.0","event_id":"sha256:73f028f84c4bad5e5dc6c2aef4f82a8e555767e7c5ff8e2336b01d111869a555"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63MKC4TLZWJWMVZP3LWXCVPUB5/bundle.json","state_url":"https://pith.science/pith/63MKC4TLZWJWMVZP3LWXCVPUB5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63MKC4TLZWJWMVZP3LWXCVPUB5/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":"2026-08-18T09:09:32Z","links":{"resolver":"https://pith.science/pith/63MKC4TLZWJWMVZP3LWXCVPUB5","bundle":"https://pith.science/pith/63MKC4TLZWJWMVZP3LWXCVPUB5/bundle.json","state":"https://pith.science/pith/63MKC4TLZWJWMVZP3LWXCVPUB5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63MKC4TLZWJWMVZP3LWXCVPUB5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:63MKC4TLZWJWMVZP3LWXCVPUB5","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":"a605f96bd3bb0659c928a51220ccf694cc8b3c488d98eab484561c664e2c5e68","cross_cats_sorted":["physics.comp-ph","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-05-05T19:35:23Z","title_canon_sha256":"692d1cfee6a57a9ef4f3d402db7a1c18e8e2163d9463efd0e23ce251841d52a8"},"schema_version":"1.0","source":{"id":"2505.13463","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.13463","created_at":"2026-07-05T11:06:13Z"},{"alias_kind":"arxiv_version","alias_value":"2505.13463v1","created_at":"2026-07-05T11:06:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13463","created_at":"2026-07-05T11:06:13Z"},{"alias_kind":"pith_short_12","alias_value":"63MKC4TLZWJW","created_at":"2026-07-05T11:06:13Z"},{"alias_kind":"pith_short_16","alias_value":"63MKC4TLZWJWMVZP","created_at":"2026-07-05T11:06:13Z"},{"alias_kind":"pith_short_8","alias_value":"63MKC4TL","created_at":"2026-07-05T11:06:13Z"}],"graph_snapshots":[{"event_id":"sha256:73f028f84c4bad5e5dc6c2aef4f82a8e555767e7c5ff8e2336b01d111869a555","target":"graph","created_at":"2026-07-05T11:06:13Z","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/2505.13463/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent progress in AI has established neural operators as powerful tools that can predict the evolution of partial differential equations, such as the Navier-Stokes equations. Some complex problems rely on sophisticated algorithms to deal with strong discontinuities in the computational domain. For example, liquid-vapour multiphase flows are a challenging problem in many configurations, particularly those involving large density gradients or phase change. The complexity mentioned above has not allowed for fine control of fast industrial processes or applications because computational fluid dyn","authors_text":"Paolo Guida, William L. Roberts","cross_cats":["physics.comp-ph","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-05-05T19:35:23Z","title":"Predicting The Evolution of Interfaces with Fourier Neural Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13463","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":"sha256:65699a23d43cabb19bdcb1861308903a32b35a47672da98f2ebcfcdd564a8779","target":"record","created_at":"2026-07-05T11:06:13Z","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":"a605f96bd3bb0659c928a51220ccf694cc8b3c488d98eab484561c664e2c5e68","cross_cats_sorted":["physics.comp-ph","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-05-05T19:35:23Z","title_canon_sha256":"692d1cfee6a57a9ef4f3d402db7a1c18e8e2163d9463efd0e23ce251841d52a8"},"schema_version":"1.0","source":{"id":"2505.13463","kind":"arxiv","version":1}},"canonical_sha256":"f6d8a1726bcd9366572fdaed7155f40f60efa56f20568820abc98cf2b5261929","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6d8a1726bcd9366572fdaed7155f40f60efa56f20568820abc98cf2b5261929","first_computed_at":"2026-07-05T11:06:13.674620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:06:13.674620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gt6P2dOxrBZf/po0LIQ4lDjrJAyGaeYe6CKRvD36ovcVLQ2Ny3UUsm8nIpxO9iDeLuiudx2LLyWBESmHdanGAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:06:13.675144Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.13463","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65699a23d43cabb19bdcb1861308903a32b35a47672da98f2ebcfcdd564a8779","sha256:73f028f84c4bad5e5dc6c2aef4f82a8e555767e7c5ff8e2336b01d111869a555"],"state_sha256":"72570985e4572ff45ac42b446da19fce136b54c5cde0b066aef6dde22ddce84a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LZ+y05zzbbfxxtAuFono7ioOX5fm7+CKZVwuFYUwKCndbBa1ggJSOnN862oXXik3nIRhidqNvUKbc59kiCx9Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T09:09:32.807821Z","bundle_sha256":"410c74a50dd1d8493a06e535af87b00b29d4b80ed818e6a384725e2dbccc9ac9"}}