{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IW24BJPEHTCORHQAD3ZPCQBRAI","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":"8e7afd0089d984882b5ddc3c98c2021132493026dd168fd3adb4366c5c66c558","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-04-28T07:11:02Z","title_canon_sha256":"51c2c699728a33a6ec6a74ec8fb0a8f4cc25745c436a74e87abf6464cffff917"},"schema_version":"1.0","source":{"id":"1604.08324","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08324","created_at":"2026-05-18T00:49:18Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08324v1","created_at":"2026-05-18T00:49:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08324","created_at":"2026-05-18T00:49:18Z"},{"alias_kind":"pith_short_12","alias_value":"IW24BJPEHTCO","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IW24BJPEHTCORHQA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IW24BJPE","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:1b00a3b2d08e4ebd77229d71b9f95d964ff305434ee064978e5a7f69abdde10a","target":"graph","created_at":"2026-05-18T00:49:18Z","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":"The so-called Whitham equation arises in the modeling of free surface water waves, and combines a generic nonlinear quadratic term with the exact linear dispersion relation for gravity waves on the free surface of a fluid with finite depth.\n  In this work, the effect of incorporating capillarity into the Whitham equation is in focus. The capillary Whitham equation is a nonlocal equation similar to the usual Whitham equation, but containing an additional term with a coefficient depending on the Bond number T which measures the relative strength of capillary and gravity effects on the wave motio","authors_text":"Filippo Remonato, Henrik Kalisch","cross_cats":["math.AP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-04-28T07:11:02Z","title":"Numerical Bifurcation for the Capillary Whitham Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08324","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":"sha256:7204f1bd72b93450e30a6e7dda76a419e831fa2336cfd1d0880e3888ca226354","target":"record","created_at":"2026-05-18T00:49:18Z","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":"8e7afd0089d984882b5ddc3c98c2021132493026dd168fd3adb4366c5c66c558","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-04-28T07:11:02Z","title_canon_sha256":"51c2c699728a33a6ec6a74ec8fb0a8f4cc25745c436a74e87abf6464cffff917"},"schema_version":"1.0","source":{"id":"1604.08324","kind":"arxiv","version":1}},"canonical_sha256":"45b5c0a5e43cc4e89e001ef2f140310209b51e7e6eb33254ab967ba447874c0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45b5c0a5e43cc4e89e001ef2f140310209b51e7e6eb33254ab967ba447874c0e","first_computed_at":"2026-05-18T00:49:18.782021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:18.782021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zU0KqUTpu5aYRK4SqjSgRDi/OsIUR0JDyV515UHFeCv/aTyPvu7+jjuGrIbWxQeGPHcaYt3r3vrlfCk5V74SCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:18.782494Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.08324","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7204f1bd72b93450e30a6e7dda76a419e831fa2336cfd1d0880e3888ca226354","sha256:1b00a3b2d08e4ebd77229d71b9f95d964ff305434ee064978e5a7f69abdde10a"],"state_sha256":"80325e3bc836de01e4ad8cb45d126154fc93002bd37b1e8481242f19a1f80e1d"}