{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EUXIWHXLVGSEEIW6LNPOB32DWL","short_pith_number":"pith:EUXIWHXL","canonical_record":{"source":{"id":"2503.10771","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-13T18:05:43Z","cross_cats_sorted":["cs.NA","math.AP"],"title_canon_sha256":"8dd9afaf6a486c7d8950d5ddc68483dc53e0969a769de4e4b47f446da1663932","abstract_canon_sha256":"de24b49d7ef71463773fcc66802e314d35ddb32b9f9b83f4136107f8cc6fc686"},"schema_version":"1.0"},"canonical_sha256":"252e8b1eeba9a44222de5b5ee0ef43b2e0d40b96d483e36d29ae7ddbeb7abb22","source":{"kind":"arxiv","id":"2503.10771","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.10771","created_at":"2026-05-27T01:05:33Z"},{"alias_kind":"arxiv_version","alias_value":"2503.10771v3","created_at":"2026-05-27T01:05:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.10771","created_at":"2026-05-27T01:05:33Z"},{"alias_kind":"pith_short_12","alias_value":"EUXIWHXLVGSE","created_at":"2026-05-27T01:05:33Z"},{"alias_kind":"pith_short_16","alias_value":"EUXIWHXLVGSEEIW6","created_at":"2026-05-27T01:05:33Z"},{"alias_kind":"pith_short_8","alias_value":"EUXIWHXL","created_at":"2026-05-27T01:05:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EUXIWHXLVGSEEIW6LNPOB32DWL","target":"record","payload":{"canonical_record":{"source":{"id":"2503.10771","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-13T18:05:43Z","cross_cats_sorted":["cs.NA","math.AP"],"title_canon_sha256":"8dd9afaf6a486c7d8950d5ddc68483dc53e0969a769de4e4b47f446da1663932","abstract_canon_sha256":"de24b49d7ef71463773fcc66802e314d35ddb32b9f9b83f4136107f8cc6fc686"},"schema_version":"1.0"},"canonical_sha256":"252e8b1eeba9a44222de5b5ee0ef43b2e0d40b96d483e36d29ae7ddbeb7abb22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T01:05:33.606961Z","signature_b64":"YMLN59BGyP4dsIgJWuz2yBhNZBMT7PWQYpfOit5hKURHAKLLnTy/fLvUVMYFRdRwGnSSqUo4stL346V85SaBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"252e8b1eeba9a44222de5b5ee0ef43b2e0d40b96d483e36d29ae7ddbeb7abb22","last_reissued_at":"2026-05-27T01:05:33.606070Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T01:05:33.606070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.10771","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-27T01:05:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YWe1GOuqDCeUXSlND9vWzpLrgL59CvPb6wzMxgWVeDbKKj0Vs4zBIUqzF92bgvjTLFWZ2ftLiiuNVqQs3w/MAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:33:06.406213Z"},"content_sha256":"2a9f057a0b3a339409721591723943e94e45815a6b3ca29cb4942762786e61b9","schema_version":"1.0","event_id":"sha256:2a9f057a0b3a339409721591723943e94e45815a6b3ca29cb4942762786e61b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EUXIWHXLVGSEEIW6LNPOB32DWL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis and numerical analysis of the Helmholtz-Korteweg equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Patrick E. Farrell, Tim van Beeck, Umberto Zerbinati","submitted_at":"2025-03-13T18:05:43Z","abstract_excerpt":"We analyse the nematic Helmholtz-Korteweg equation, a variant of the classical Helmholtz equation that describes time-harmonic wave propagation in calamitic fluids in the presence of nematic order. A prominent example is given by nematic liquid crystals, which can be modeled as nematic Korteweg fluids - that is, fluids whose stress tensor depends on density gradients and on a nematic director describing the orientation of the anisotropic molecules. These materials exhibit anisotropic acoustic properties that can be tuned by external electromagnetic fields, making them attractive for potential "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.10771","kind":"arxiv","version":3},"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/2503.10771/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":"2026-05-27T01:05:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bkOXIbTHwiP4GFZ1oZ3QZAcXYbv8kf6x6OM08FPBzCy/1zFo4Y7Rymt4Cxc4Xzg0En58EATZSDWjbZMwEZ4gCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:33:06.406622Z"},"content_sha256":"dcb45db0727ba055b4c08fd140ce581bff3bbc7a5e71b73a96b105515f1651b2","schema_version":"1.0","event_id":"sha256:dcb45db0727ba055b4c08fd140ce581bff3bbc7a5e71b73a96b105515f1651b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EUXIWHXLVGSEEIW6LNPOB32DWL/bundle.json","state_url":"https://pith.science/pith/EUXIWHXLVGSEEIW6LNPOB32DWL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EUXIWHXLVGSEEIW6LNPOB32DWL/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":"2026-05-28T22:33:06Z","links":{"resolver":"https://pith.science/pith/EUXIWHXLVGSEEIW6LNPOB32DWL","bundle":"https://pith.science/pith/EUXIWHXLVGSEEIW6LNPOB32DWL/bundle.json","state":"https://pith.science/pith/EUXIWHXLVGSEEIW6LNPOB32DWL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EUXIWHXLVGSEEIW6LNPOB32DWL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EUXIWHXLVGSEEIW6LNPOB32DWL","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":"de24b49d7ef71463773fcc66802e314d35ddb32b9f9b83f4136107f8cc6fc686","cross_cats_sorted":["cs.NA","math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-13T18:05:43Z","title_canon_sha256":"8dd9afaf6a486c7d8950d5ddc68483dc53e0969a769de4e4b47f446da1663932"},"schema_version":"1.0","source":{"id":"2503.10771","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.10771","created_at":"2026-05-27T01:05:33Z"},{"alias_kind":"arxiv_version","alias_value":"2503.10771v3","created_at":"2026-05-27T01:05:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.10771","created_at":"2026-05-27T01:05:33Z"},{"alias_kind":"pith_short_12","alias_value":"EUXIWHXLVGSE","created_at":"2026-05-27T01:05:33Z"},{"alias_kind":"pith_short_16","alias_value":"EUXIWHXLVGSEEIW6","created_at":"2026-05-27T01:05:33Z"},{"alias_kind":"pith_short_8","alias_value":"EUXIWHXL","created_at":"2026-05-27T01:05:33Z"}],"graph_snapshots":[{"event_id":"sha256:dcb45db0727ba055b4c08fd140ce581bff3bbc7a5e71b73a96b105515f1651b2","target":"graph","created_at":"2026-05-27T01:05:33Z","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/2503.10771/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyse the nematic Helmholtz-Korteweg equation, a variant of the classical Helmholtz equation that describes time-harmonic wave propagation in calamitic fluids in the presence of nematic order. A prominent example is given by nematic liquid crystals, which can be modeled as nematic Korteweg fluids - that is, fluids whose stress tensor depends on density gradients and on a nematic director describing the orientation of the anisotropic molecules. These materials exhibit anisotropic acoustic properties that can be tuned by external electromagnetic fields, making them attractive for potential ","authors_text":"Patrick E. Farrell, Tim van Beeck, Umberto Zerbinati","cross_cats":["cs.NA","math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-13T18:05:43Z","title":"Analysis and numerical analysis of the Helmholtz-Korteweg equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.10771","kind":"arxiv","version":3},"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":"sha256:2a9f057a0b3a339409721591723943e94e45815a6b3ca29cb4942762786e61b9","target":"record","created_at":"2026-05-27T01:05:33Z","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":"de24b49d7ef71463773fcc66802e314d35ddb32b9f9b83f4136107f8cc6fc686","cross_cats_sorted":["cs.NA","math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-13T18:05:43Z","title_canon_sha256":"8dd9afaf6a486c7d8950d5ddc68483dc53e0969a769de4e4b47f446da1663932"},"schema_version":"1.0","source":{"id":"2503.10771","kind":"arxiv","version":3}},"canonical_sha256":"252e8b1eeba9a44222de5b5ee0ef43b2e0d40b96d483e36d29ae7ddbeb7abb22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"252e8b1eeba9a44222de5b5ee0ef43b2e0d40b96d483e36d29ae7ddbeb7abb22","first_computed_at":"2026-05-27T01:05:33.606070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T01:05:33.606070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YMLN59BGyP4dsIgJWuz2yBhNZBMT7PWQYpfOit5hKURHAKLLnTy/fLvUVMYFRdRwGnSSqUo4stL346V85SaBCA==","signature_status":"signed_v1","signed_at":"2026-05-27T01:05:33.606961Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.10771","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a9f057a0b3a339409721591723943e94e45815a6b3ca29cb4942762786e61b9","sha256:dcb45db0727ba055b4c08fd140ce581bff3bbc7a5e71b73a96b105515f1651b2"],"state_sha256":"dd93d4d68efe2e16d224d80e3020485a008ce6e39b685bce0d76d05109d42302"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LW53lVNgq52Vw1vg147UxRbZFoIp0kxTagdBefVVgyb1qDqlJpHaVBVIPJx6qxu0aIdal66Zx0F67So7o0FfDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:33:06.409472Z","bundle_sha256":"45b77994ac3b222ef48de6ae78c5fc4e32405209c8730c89b1a46966dde2b141"}}