{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:F6WW2GPUXRRZJN5DANDEWD53HW","short_pith_number":"pith:F6WW2GPU","canonical_record":{"source":{"id":"2504.01093","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-01T18:10:46Z","cross_cats_sorted":["cs.AI","physics.comp-ph"],"title_canon_sha256":"61ec8561659cd1fe8155ed516b293ec89b2727c9f87393f9dbc3dd46bb40bf57","abstract_canon_sha256":"6f5bbed378e2ce5e5866aa2543ded00b82fddecd91d0dbfef36052f4e49fa73d"},"schema_version":"1.0"},"canonical_sha256":"2fad6d19f4bc6394b7a303464b0fbb3d8036ddb90ead8fc8a9cbd02fcf527939","source":{"kind":"arxiv","id":"2504.01093","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.01093","created_at":"2026-07-05T10:43:08Z"},{"alias_kind":"arxiv_version","alias_value":"2504.01093v1","created_at":"2026-07-05T10:43:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.01093","created_at":"2026-07-05T10:43:08Z"},{"alias_kind":"pith_short_12","alias_value":"F6WW2GPUXRRZ","created_at":"2026-07-05T10:43:08Z"},{"alias_kind":"pith_short_16","alias_value":"F6WW2GPUXRRZJN5D","created_at":"2026-07-05T10:43:08Z"},{"alias_kind":"pith_short_8","alias_value":"F6WW2GPU","created_at":"2026-07-05T10:43:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:F6WW2GPUXRRZJN5DANDEWD53HW","target":"record","payload":{"canonical_record":{"source":{"id":"2504.01093","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-01T18:10:46Z","cross_cats_sorted":["cs.AI","physics.comp-ph"],"title_canon_sha256":"61ec8561659cd1fe8155ed516b293ec89b2727c9f87393f9dbc3dd46bb40bf57","abstract_canon_sha256":"6f5bbed378e2ce5e5866aa2543ded00b82fddecd91d0dbfef36052f4e49fa73d"},"schema_version":"1.0"},"canonical_sha256":"2fad6d19f4bc6394b7a303464b0fbb3d8036ddb90ead8fc8a9cbd02fcf527939","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:43:08.966990Z","signature_b64":"zcThDmf4Nrx91WosNlvtOHQ98kaMaatkVqfRxwcN/T7CMKaqYmSKhaN7aIA3lngMQkVEY9cCJSZc1zZVhSDIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fad6d19f4bc6394b7a303464b0fbb3d8036ddb90ead8fc8a9cbd02fcf527939","last_reissued_at":"2026-07-05T10:43:08.966501Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:43:08.966501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.01093","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":"2026-07-05T10:43:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vl2T1XCoihIZbLlQNwXd2tpb+15KGtAd/W+3gzvaHUuB1uRvQdVHZLxOsIkEYv6q1mcA4T2SGSIDjEqO0CdrCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:37:10.099971Z"},"content_sha256":"f906baf141c8865a0ac29f28abbd4ca7c481a36041d142a46ac9b54b83176ae0","schema_version":"1.0","event_id":"sha256:f906baf141c8865a0ac29f28abbd4ca7c481a36041d142a46ac9b54b83176ae0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:F6WW2GPUXRRZJN5DANDEWD53HW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hard-constraining Neumann boundary conditions in physics-informed neural networks via Fourier feature embeddings","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.AI","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Andreas Rosskopf, Christopher Straub, Philipp Brendel, Vlad Medvedev","submitted_at":"2025-04-01T18:10:46Z","abstract_excerpt":"We present a novel approach to hard-constrain Neumann boundary conditions in physics-informed neural networks (PINNs) using Fourier feature embeddings. Neumann boundary conditions are used to described critical processes in various application, yet they are more challenging to hard-constrain in PINNs than Dirichlet conditions. Our method employs specific Fourier feature embeddings to directly incorporate Neumann boundary conditions into the neural network's architecture instead of learning them. The embedding can be naturally extended by high frequency modes to better capture high frequency ph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.01093","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/2504.01093/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":"2026-07-05T10:43:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Evm6zigLxgtjulqchCre+yIjrk1/kPhGffd+mHZZPqStLGhBTCdReQ8fZOYKlyVthm1dEVVrhIXnJsh/5fiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:37:10.101149Z"},"content_sha256":"78067646a66d97a29a65c713340d447807b0763f83455304f6a04cc252fad671","schema_version":"1.0","event_id":"sha256:78067646a66d97a29a65c713340d447807b0763f83455304f6a04cc252fad671"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F6WW2GPUXRRZJN5DANDEWD53HW/bundle.json","state_url":"https://pith.science/pith/F6WW2GPUXRRZJN5DANDEWD53HW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F6WW2GPUXRRZJN5DANDEWD53HW/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":"2026-08-14T17:37:10Z","links":{"resolver":"https://pith.science/pith/F6WW2GPUXRRZJN5DANDEWD53HW","bundle":"https://pith.science/pith/F6WW2GPUXRRZJN5DANDEWD53HW/bundle.json","state":"https://pith.science/pith/F6WW2GPUXRRZJN5DANDEWD53HW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F6WW2GPUXRRZJN5DANDEWD53HW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:F6WW2GPUXRRZJN5DANDEWD53HW","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":"6f5bbed378e2ce5e5866aa2543ded00b82fddecd91d0dbfef36052f4e49fa73d","cross_cats_sorted":["cs.AI","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-01T18:10:46Z","title_canon_sha256":"61ec8561659cd1fe8155ed516b293ec89b2727c9f87393f9dbc3dd46bb40bf57"},"schema_version":"1.0","source":{"id":"2504.01093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.01093","created_at":"2026-07-05T10:43:08Z"},{"alias_kind":"arxiv_version","alias_value":"2504.01093v1","created_at":"2026-07-05T10:43:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.01093","created_at":"2026-07-05T10:43:08Z"},{"alias_kind":"pith_short_12","alias_value":"F6WW2GPUXRRZ","created_at":"2026-07-05T10:43:08Z"},{"alias_kind":"pith_short_16","alias_value":"F6WW2GPUXRRZJN5D","created_at":"2026-07-05T10:43:08Z"},{"alias_kind":"pith_short_8","alias_value":"F6WW2GPU","created_at":"2026-07-05T10:43:08Z"}],"graph_snapshots":[{"event_id":"sha256:78067646a66d97a29a65c713340d447807b0763f83455304f6a04cc252fad671","target":"graph","created_at":"2026-07-05T10:43:08Z","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/2504.01093/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a novel approach to hard-constrain Neumann boundary conditions in physics-informed neural networks (PINNs) using Fourier feature embeddings. Neumann boundary conditions are used to described critical processes in various application, yet they are more challenging to hard-constrain in PINNs than Dirichlet conditions. Our method employs specific Fourier feature embeddings to directly incorporate Neumann boundary conditions into the neural network's architecture instead of learning them. The embedding can be naturally extended by high frequency modes to better capture high frequency ph","authors_text":"Andreas Rosskopf, Christopher Straub, Philipp Brendel, Vlad Medvedev","cross_cats":["cs.AI","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-01T18:10:46Z","title":"Hard-constraining Neumann boundary conditions in physics-informed neural networks via Fourier feature embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.01093","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:f906baf141c8865a0ac29f28abbd4ca7c481a36041d142a46ac9b54b83176ae0","target":"record","created_at":"2026-07-05T10:43:08Z","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":"6f5bbed378e2ce5e5866aa2543ded00b82fddecd91d0dbfef36052f4e49fa73d","cross_cats_sorted":["cs.AI","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-01T18:10:46Z","title_canon_sha256":"61ec8561659cd1fe8155ed516b293ec89b2727c9f87393f9dbc3dd46bb40bf57"},"schema_version":"1.0","source":{"id":"2504.01093","kind":"arxiv","version":1}},"canonical_sha256":"2fad6d19f4bc6394b7a303464b0fbb3d8036ddb90ead8fc8a9cbd02fcf527939","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fad6d19f4bc6394b7a303464b0fbb3d8036ddb90ead8fc8a9cbd02fcf527939","first_computed_at":"2026-07-05T10:43:08.966501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:43:08.966501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zcThDmf4Nrx91WosNlvtOHQ98kaMaatkVqfRxwcN/T7CMKaqYmSKhaN7aIA3lngMQkVEY9cCJSZc1zZVhSDIAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:43:08.966990Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.01093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f906baf141c8865a0ac29f28abbd4ca7c481a36041d142a46ac9b54b83176ae0","sha256:78067646a66d97a29a65c713340d447807b0763f83455304f6a04cc252fad671"],"state_sha256":"471beea4f1de8ac0fa594aaa1d528baeee5730882f68cd51fba03e65f453bce3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kkEnBw+AZJy6byDoDP8Dqhzq7zJP59Iv7B2ltYymyI8U0RPZLY6zY8VZkxNstejhHvIhuIVM40CgRvDr0pn3Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T17:37:10.121840Z","bundle_sha256":"067a5c1579141a61e8967c8891d3479ac5e2ccdcb4d6d6968d6f71c8551cd8e3"}}