{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:O3JQL4CBS5LIX4POZYBCEPWMRA","short_pith_number":"pith:O3JQL4CB","schema_version":"1.0","canonical_sha256":"76d305f04197568bf1eece02223ecc882041769806a1efbaad58fe6563c2bce9","source":{"kind":"arxiv","id":"1502.05158","version":1},"attestation_state":"computed","paper":{"title":"Singular solutions for a class of traveling wave equations arising in hydrodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS"],"primary_cat":"math.CA","authors_text":"Anna Geyer, V\\'ictor Ma\\~nosa","submitted_at":"2015-02-18T09:01:29Z","abstract_excerpt":"We give an exhaustive characterization of singular weak solutions for ordinary differential equations of the form $\\ddot{u}\\,u + \\frac{1}{2}\\dot{u}^2 + F'(u) =0$, where $F$ is an analytic function. Our motivation stems from the fact that in the context of hydrodynamics several prominent equations are reducible to an equation of this form upon passing to a moving frame. We construct peaked and cusped waves, fronts with finite-time decay and compact solitary waves. We prove that one cannot obtain peaked and compactly supported traveling waves for the same equation. In particular, a peaked travel"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1502.05158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-18T09:01:29Z","cross_cats_sorted":["math.AP","math.DS"],"title_canon_sha256":"14e13fc85c6a05a5ff7834ad4ae25b2eed81823a447e36ebf3ba2d2c1efa7a81","abstract_canon_sha256":"0fac623c040a51bcff859d4d5cb08aa183fcbea03064cd6946a29ff093424468"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:28.539601Z","signature_b64":"JE8E7HjNb5YJnJzE8uWdfcbMnaUb7nlWrUzrwPgkV4KyLQkXV5+WW2d1w31ZZvT0TbhrM6B8uTDA6EMaE5TJBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76d305f04197568bf1eece02223ecc882041769806a1efbaad58fe6563c2bce9","last_reissued_at":"2026-05-18T00:52:28.539085Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:28.539085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singular solutions for a class of traveling wave equations arising in hydrodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS"],"primary_cat":"math.CA","authors_text":"Anna Geyer, V\\'ictor Ma\\~nosa","submitted_at":"2015-02-18T09:01:29Z","abstract_excerpt":"We give an exhaustive characterization of singular weak solutions for ordinary differential equations of the form $\\ddot{u}\\,u + \\frac{1}{2}\\dot{u}^2 + F'(u) =0$, where $F$ is an analytic function. Our motivation stems from the fact that in the context of hydrodynamics several prominent equations are reducible to an equation of this form upon passing to a moving frame. We construct peaked and cusped waves, fronts with finite-time decay and compact solitary waves. We prove that one cannot obtain peaked and compactly supported traveling waves for the same equation. In particular, a peaked travel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05158","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.05158","created_at":"2026-05-18T00:52:28.539151+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.05158v1","created_at":"2026-05-18T00:52:28.539151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05158","created_at":"2026-05-18T00:52:28.539151+00:00"},{"alias_kind":"pith_short_12","alias_value":"O3JQL4CBS5LI","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"O3JQL4CBS5LIX4PO","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"O3JQL4CB","created_at":"2026-05-18T12:29:34.919912+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O3JQL4CBS5LIX4POZYBCEPWMRA","json":"https://pith.science/pith/O3JQL4CBS5LIX4POZYBCEPWMRA.json","graph_json":"https://pith.science/api/pith-number/O3JQL4CBS5LIX4POZYBCEPWMRA/graph.json","events_json":"https://pith.science/api/pith-number/O3JQL4CBS5LIX4POZYBCEPWMRA/events.json","paper":"https://pith.science/paper/O3JQL4CB"},"agent_actions":{"view_html":"https://pith.science/pith/O3JQL4CBS5LIX4POZYBCEPWMRA","download_json":"https://pith.science/pith/O3JQL4CBS5LIX4POZYBCEPWMRA.json","view_paper":"https://pith.science/paper/O3JQL4CB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.05158&json=true","fetch_graph":"https://pith.science/api/pith-number/O3JQL4CBS5LIX4POZYBCEPWMRA/graph.json","fetch_events":"https://pith.science/api/pith-number/O3JQL4CBS5LIX4POZYBCEPWMRA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O3JQL4CBS5LIX4POZYBCEPWMRA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O3JQL4CBS5LIX4POZYBCEPWMRA/action/storage_attestation","attest_author":"https://pith.science/pith/O3JQL4CBS5LIX4POZYBCEPWMRA/action/author_attestation","sign_citation":"https://pith.science/pith/O3JQL4CBS5LIX4POZYBCEPWMRA/action/citation_signature","submit_replication":"https://pith.science/pith/O3JQL4CBS5LIX4POZYBCEPWMRA/action/replication_record"}},"created_at":"2026-05-18T00:52:28.539151+00:00","updated_at":"2026-05-18T00:52:28.539151+00:00"}