{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:CXLDOCYWXQBWRZYLTAK2ZDEZJ5","short_pith_number":"pith:CXLDOCYW","schema_version":"1.0","canonical_sha256":"15d6370b16bc0368e70b9815ac8c994f58f2c06d7b7e7b934d74320f91a1815b","source":{"kind":"arxiv","id":"2302.01289","version":1},"attestation_state":"computed","paper":{"title":"A characteristics approach to shock formation in 2D Euler with azimuthal symmetry and entropy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Isaac Neal, Steve Shkoller, Vlad Vicol","submitted_at":"2023-02-02T18:19:37Z","abstract_excerpt":"We provide a detailed analysis of the shock formation process for the non-isentropic 2d Euler equations in azimuthal symmetry. We prove that from an open set of smooth and generic initial data, solutions of Euler form a first singularity or gradient blow-up or shock. This first singularity is termed a H\\\"{o}lder $C^{\\frac{1}{3}}$ pre-shock, and our analysis provides the first detailed description of this cusp solution. The novelty of this work relative to [Buckmaster-Drivas-Shkoller-Vicol, 2022] is that we herein consider a much larger class of initial data, allow for a non-constant initial en"},"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":"2302.01289","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-02-02T18:19:37Z","cross_cats_sorted":[],"title_canon_sha256":"a91c51996e6e44736ec940652eecdf438b398926259f769f3ea7360c10edc8f6","abstract_canon_sha256":"7226246af82d37ae4240a6735760989a9e8d910eb2c776c7de2f227a366025ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:38:24.638555Z","signature_b64":"T21yw53Sp75I42Y5mjPDMh32nDo68NC3hNhgJ2uGu9wpDAbEWJanYYZNzFnLVWe1D1rfVuHOtqI85EXpRN37DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15d6370b16bc0368e70b9815ac8c994f58f2c06d7b7e7b934d74320f91a1815b","last_reissued_at":"2026-07-05T05:38:24.638195Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:38:24.638195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A characteristics approach to shock formation in 2D Euler with azimuthal symmetry and entropy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Isaac Neal, Steve Shkoller, Vlad Vicol","submitted_at":"2023-02-02T18:19:37Z","abstract_excerpt":"We provide a detailed analysis of the shock formation process for the non-isentropic 2d Euler equations in azimuthal symmetry. We prove that from an open set of smooth and generic initial data, solutions of Euler form a first singularity or gradient blow-up or shock. This first singularity is termed a H\\\"{o}lder $C^{\\frac{1}{3}}$ pre-shock, and our analysis provides the first detailed description of this cusp solution. The novelty of this work relative to [Buckmaster-Drivas-Shkoller-Vicol, 2022] is that we herein consider a much larger class of initial data, allow for a non-constant initial en"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.01289","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.01289/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2302.01289","created_at":"2026-07-05T05:38:24.638257+00:00"},{"alias_kind":"arxiv_version","alias_value":"2302.01289v1","created_at":"2026-07-05T05:38:24.638257+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.01289","created_at":"2026-07-05T05:38:24.638257+00:00"},{"alias_kind":"pith_short_12","alias_value":"CXLDOCYWXQBW","created_at":"2026-07-05T05:38:24.638257+00:00"},{"alias_kind":"pith_short_16","alias_value":"CXLDOCYWXQBWRZYL","created_at":"2026-07-05T05:38:24.638257+00:00"},{"alias_kind":"pith_short_8","alias_value":"CXLDOCYW","created_at":"2026-07-05T05:38:24.638257+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.21040","citing_title":"Gradient catastrophes and an infinite hierarchy of H\\\"older cusp-singularities for 1D Euler","ref_index":39,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CXLDOCYWXQBWRZYLTAK2ZDEZJ5","json":"https://pith.science/pith/CXLDOCYWXQBWRZYLTAK2ZDEZJ5.json","graph_json":"https://pith.science/api/pith-number/CXLDOCYWXQBWRZYLTAK2ZDEZJ5/graph.json","events_json":"https://pith.science/api/pith-number/CXLDOCYWXQBWRZYLTAK2ZDEZJ5/events.json","paper":"https://pith.science/paper/CXLDOCYW"},"agent_actions":{"view_html":"https://pith.science/pith/CXLDOCYWXQBWRZYLTAK2ZDEZJ5","download_json":"https://pith.science/pith/CXLDOCYWXQBWRZYLTAK2ZDEZJ5.json","view_paper":"https://pith.science/paper/CXLDOCYW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2302.01289&json=true","fetch_graph":"https://pith.science/api/pith-number/CXLDOCYWXQBWRZYLTAK2ZDEZJ5/graph.json","fetch_events":"https://pith.science/api/pith-number/CXLDOCYWXQBWRZYLTAK2ZDEZJ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CXLDOCYWXQBWRZYLTAK2ZDEZJ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CXLDOCYWXQBWRZYLTAK2ZDEZJ5/action/storage_attestation","attest_author":"https://pith.science/pith/CXLDOCYWXQBWRZYLTAK2ZDEZJ5/action/author_attestation","sign_citation":"https://pith.science/pith/CXLDOCYWXQBWRZYLTAK2ZDEZJ5/action/citation_signature","submit_replication":"https://pith.science/pith/CXLDOCYWXQBWRZYLTAK2ZDEZJ5/action/replication_record"}},"created_at":"2026-07-05T05:38:24.638257+00:00","updated_at":"2026-07-05T05:38:24.638257+00:00"}