{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:42YWC3PISHYYIAD2MOUGHYUVZ5","short_pith_number":"pith:42YWC3PI","canonical_record":{"source":{"id":"1601.05581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-21T10:40:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3a959edc4ded423a47a918a4e94728f0daa960da1683420caf8536f9f2580a1b","abstract_canon_sha256":"b83d1da750a32907b7c2ab241a0fa8505badb5f7a6543d0a7034ee0c37e1917b"},"schema_version":"1.0"},"canonical_sha256":"e6b1616de891f184007a63a863e295cf66924f2aff32d1665669a504d5e8efa5","source":{"kind":"arxiv","id":"1601.05581","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05581","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05581v1","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05581","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"42YWC3PISHYY","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"42YWC3PISHYYIAD2","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"42YWC3PI","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:42YWC3PISHYYIAD2MOUGHYUVZ5","target":"record","payload":{"canonical_record":{"source":{"id":"1601.05581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-21T10:40:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3a959edc4ded423a47a918a4e94728f0daa960da1683420caf8536f9f2580a1b","abstract_canon_sha256":"b83d1da750a32907b7c2ab241a0fa8505badb5f7a6543d0a7034ee0c37e1917b"},"schema_version":"1.0"},"canonical_sha256":"e6b1616de891f184007a63a863e295cf66924f2aff32d1665669a504d5e8efa5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:13.450834Z","signature_b64":"1ehiPnuZ/h4mX5QfpSyC/iYeHYcFgtdlV0SO7jBH+9UWdQISZksz489dWF4JKLqficH6zHqrJPCrY/JNde0qBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6b1616de891f184007a63a863e295cf66924f2aff32d1665669a504d5e8efa5","last_reissued_at":"2026-05-18T01:22:13.450195Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:13.450195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.05581","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":"2026-05-18T01:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TaoajUOkNOs0eTKB795Zo4VDVDN7qi23K3QAkr94gy6/EARDFXzvFIA5Wgw8rQq+FnCG3KciZwquErC8FnxWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:04:47.502529Z"},"content_sha256":"c0f0d17c0b9ac319154f7369cf1237dd7b369944d6203db0206086b404189da9","schema_version":"1.0","event_id":"sha256:c0f0d17c0b9ac319154f7369cf1237dd7b369944d6203db0206086b404189da9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:42YWC3PISHYYIAD2MOUGHYUVZ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation of a compressible Navier-Stokes system by non-linear acoustical models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Anna Rozanova-Pierrat (MAS)","submitted_at":"2016-01-21T10:40:31Z","abstract_excerpt":"We analyse the existing derivation of the models of non-linear acoustics such as the Kuznetsov equation, the NPE equation and the KZK equation. The technique of introducing a corrector in the derivation ansatz allows to consider the solutions of these equations as approximations of the solution of the initial system (a com-pressible Navier-Stokes/Euler system). The validation of the approximation ansatz is given for the KZK equation case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05581","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":""},"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":"2026-05-18T01:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"THy+tDxk0tLNuGwmSBhK3yg/JaSLV8Lq1EzQPpN1GcGZdXN7zjDmOeT0pRLBWci2dIvhk/MO7b1/kWpoRVMvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:04:47.503229Z"},"content_sha256":"233f44fcda236a87fd8f7dcedfcc4394d5a51796431143f669d054301805cf88","schema_version":"1.0","event_id":"sha256:233f44fcda236a87fd8f7dcedfcc4394d5a51796431143f669d054301805cf88"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/42YWC3PISHYYIAD2MOUGHYUVZ5/bundle.json","state_url":"https://pith.science/pith/42YWC3PISHYYIAD2MOUGHYUVZ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/42YWC3PISHYYIAD2MOUGHYUVZ5/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":"2026-06-09T21:04:47Z","links":{"resolver":"https://pith.science/pith/42YWC3PISHYYIAD2MOUGHYUVZ5","bundle":"https://pith.science/pith/42YWC3PISHYYIAD2MOUGHYUVZ5/bundle.json","state":"https://pith.science/pith/42YWC3PISHYYIAD2MOUGHYUVZ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/42YWC3PISHYYIAD2MOUGHYUVZ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:42YWC3PISHYYIAD2MOUGHYUVZ5","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":"b83d1da750a32907b7c2ab241a0fa8505badb5f7a6543d0a7034ee0c37e1917b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-21T10:40:31Z","title_canon_sha256":"3a959edc4ded423a47a918a4e94728f0daa960da1683420caf8536f9f2580a1b"},"schema_version":"1.0","source":{"id":"1601.05581","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05581","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05581v1","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05581","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"42YWC3PISHYY","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"42YWC3PISHYYIAD2","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"42YWC3PI","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:233f44fcda236a87fd8f7dcedfcc4394d5a51796431143f669d054301805cf88","target":"graph","created_at":"2026-05-18T01:22:13Z","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"},"paper":{"abstract_excerpt":"We analyse the existing derivation of the models of non-linear acoustics such as the Kuznetsov equation, the NPE equation and the KZK equation. The technique of introducing a corrector in the derivation ansatz allows to consider the solutions of these equations as approximations of the solution of the initial system (a com-pressible Navier-Stokes/Euler system). The validation of the approximation ansatz is given for the KZK equation case.","authors_text":"Anna Rozanova-Pierrat (MAS)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-21T10:40:31Z","title":"Approximation of a compressible Navier-Stokes system by non-linear acoustical models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05581","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:c0f0d17c0b9ac319154f7369cf1237dd7b369944d6203db0206086b404189da9","target":"record","created_at":"2026-05-18T01:22:13Z","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":"b83d1da750a32907b7c2ab241a0fa8505badb5f7a6543d0a7034ee0c37e1917b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-21T10:40:31Z","title_canon_sha256":"3a959edc4ded423a47a918a4e94728f0daa960da1683420caf8536f9f2580a1b"},"schema_version":"1.0","source":{"id":"1601.05581","kind":"arxiv","version":1}},"canonical_sha256":"e6b1616de891f184007a63a863e295cf66924f2aff32d1665669a504d5e8efa5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6b1616de891f184007a63a863e295cf66924f2aff32d1665669a504d5e8efa5","first_computed_at":"2026-05-18T01:22:13.450195Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:13.450195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ehiPnuZ/h4mX5QfpSyC/iYeHYcFgtdlV0SO7jBH+9UWdQISZksz489dWF4JKLqficH6zHqrJPCrY/JNde0qBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:13.450834Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05581","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0f0d17c0b9ac319154f7369cf1237dd7b369944d6203db0206086b404189da9","sha256:233f44fcda236a87fd8f7dcedfcc4394d5a51796431143f669d054301805cf88"],"state_sha256":"4be7177dd13538bc14ee23e4ea448f421fe87052439e0f776a06586f203fe046"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DASklhZsAacQHFaalitlA5G09onyaltkKM650II6qSPIdIhqH9poEi3MkiXauvJN3Ai5B1iAJ8e384JYqmGUBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T21:04:47.507169Z","bundle_sha256":"70db2b3f04cebd416d3386c003576470caaae27caefb253a4a00bd5781352c54"}}