{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:KQO74OVG4EIY2SSFET7VNVSC3Y","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":"291c941848b5b9468e9f430993b03cede5331b740b0b95bb2cc1925e557445dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-09-20T18:39:46Z","title_canon_sha256":"881a084e5a76534c55acfd4565b2d3bdc1f4a14aef9dfbd276bb68243bc7d10d"},"schema_version":"1.0","source":{"id":"2009.09494","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.09494","created_at":"2026-07-05T03:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"2009.09494v2","created_at":"2026-07-05T03:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.09494","created_at":"2026-07-05T03:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"KQO74OVG4EIY","created_at":"2026-07-05T03:09:15Z"},{"alias_kind":"pith_short_16","alias_value":"KQO74OVG4EIY2SSF","created_at":"2026-07-05T03:09:15Z"},{"alias_kind":"pith_short_8","alias_value":"KQO74OVG","created_at":"2026-07-05T03:09:15Z"}],"graph_snapshots":[{"event_id":"sha256:90de8b88aed028ad5565a1d3c64bcb8a08dc295193b1605268ba72d408444673","target":"graph","created_at":"2026-07-05T03:09:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2009.09494/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we numerically study a class of solutions with spiraling singularities in vorticity for two-dimensional, inviscid, compressible Euler systems, where the initial data have an algebraic singularity in vorticity at the origin. These are different from the multi-dimensional Riemann problems widely studied in the literature. Our computations provide numerical evidence of the existence of initial value problems with multiple solutions, thus revealing a fundamental obstruction toward the well-posedness of the governing equations. The compressible Euler equations are solved using the po","authors_text":"Alberto Bressan, Hailiang Liu, Yi Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-09-20T18:39:46Z","title":"Numerical Study of Non-uniqueness for 2D Compressible Isentropic Euler Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.09494","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:f8afa44f779a98288b3299f7e1922ee2bbfd4f31ac950f1046c479e1b1be0802","target":"record","created_at":"2026-07-05T03:09:15Z","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":"291c941848b5b9468e9f430993b03cede5331b740b0b95bb2cc1925e557445dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-09-20T18:39:46Z","title_canon_sha256":"881a084e5a76534c55acfd4565b2d3bdc1f4a14aef9dfbd276bb68243bc7d10d"},"schema_version":"1.0","source":{"id":"2009.09494","kind":"arxiv","version":2}},"canonical_sha256":"541dfe3aa6e1118d4a4524ff56d642de25f128ef9f2337a757eaa7bf8494b17a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"541dfe3aa6e1118d4a4524ff56d642de25f128ef9f2337a757eaa7bf8494b17a","first_computed_at":"2026-07-05T03:09:15.886762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:09:15.886762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kMiNg7MU/MGeCwiU51+L/HgNnMC3U4QLYEZj8ahvstQ9+Plf9qf4YZZdWCSOJDUungDD9uVvKLNdd0g02oTmAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:09:15.887249Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.09494","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8afa44f779a98288b3299f7e1922ee2bbfd4f31ac950f1046c479e1b1be0802","sha256:90de8b88aed028ad5565a1d3c64bcb8a08dc295193b1605268ba72d408444673"],"state_sha256":"5183cbee74fe4177b4d4313daf08e6b7bc2b0adb3cf5c6e4366e54d9b01987b2"}