{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5VZ2G2OWRG4MQDL6YEMMHLQ3QU","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":"ba067596f34ca9a364dcc90213d1ab0ecd5dce6403d9adb5a350ad84c54bd644","cross_cats_sorted":["physics.app-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-06-10T18:13:11Z","title_canon_sha256":"f66bbd01dd618af56e3f566a0c42024e5252ff0ef14c76f555f542d0d402f0ee"},"schema_version":"1.0","source":{"id":"1806.03697","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03697","created_at":"2026-05-18T00:06:39Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03697v2","created_at":"2026-05-18T00:06:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03697","created_at":"2026-05-18T00:06:39Z"},{"alias_kind":"pith_short_12","alias_value":"5VZ2G2OWRG4M","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5VZ2G2OWRG4MQDL6","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5VZ2G2OW","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:c0d4f1230d7a4e363e8ad67793ada9319810ea2bec517867ef758ca06027fb9c","target":"graph","created_at":"2026-05-18T00:06:39Z","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":"I present an approximation of Bessel function $J_0(r)$ of the first kind for small arguments near the origin. The approximation comprises a simple cosine function that is matched with $J_0(r)$ at $r=\\pi/\\textrm{e}$. A second matching is then carried out with the standard, but slightly modified, far-field approximation for $J_0(r)$, such that first and second derivatives are also considered. The approximation is practical when nonlinear dynamics come into play, in particular in the case of nonlinear interactions that involve second order differential equations as in acoustic--gravity wave theor","authors_text":"Usama Kadri","cross_cats":["physics.app-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-06-10T18:13:11Z","title":"Multiple-location matched approximation for Bessel function $J_0$ and its derivatives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03697","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":"sha256:9b1dd1869a4a6a779404b42928f358af334aa49175a048ed89154910e6bc6279","target":"record","created_at":"2026-05-18T00:06:39Z","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":"ba067596f34ca9a364dcc90213d1ab0ecd5dce6403d9adb5a350ad84c54bd644","cross_cats_sorted":["physics.app-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-06-10T18:13:11Z","title_canon_sha256":"f66bbd01dd618af56e3f566a0c42024e5252ff0ef14c76f555f542d0d402f0ee"},"schema_version":"1.0","source":{"id":"1806.03697","kind":"arxiv","version":2}},"canonical_sha256":"ed73a369d689b8c80d7ec118c3ae1b850b77616b11de1406f572c2dac9eb6a1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed73a369d689b8c80d7ec118c3ae1b850b77616b11de1406f572c2dac9eb6a1a","first_computed_at":"2026-05-18T00:06:39.507694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:39.507694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LN4j1xO4vvDYg0qDCRVjf8U4mf+Sg5CowMKJJLsbi53V+vzy+jwZEAbDBxs/nBKKu+kS3ZsANcAOtyH2V/EjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:39.508099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03697","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b1dd1869a4a6a779404b42928f358af334aa49175a048ed89154910e6bc6279","sha256:c0d4f1230d7a4e363e8ad67793ada9319810ea2bec517867ef758ca06027fb9c"],"state_sha256":"ec3aa8449be2513922cfe6338728cb410de65003ec1c8c3edc989292a23702fb"}