{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XHT4CAVRF7T3PZF7IU63MPFZ45","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":"50083c3d845272f27295dbabdbe52ea439cdea2bdad9be3a8a354a9fc27b8e2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-27T15:46:16Z","title_canon_sha256":"b62bce49808c87d1c8e0bf419a30e09d617612b120d502ba5a1305d296659645"},"schema_version":"1.0","source":{"id":"1610.08848","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08848","created_at":"2026-05-18T01:01:07Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08848v1","created_at":"2026-05-18T01:01:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08848","created_at":"2026-05-18T01:01:07Z"},{"alias_kind":"pith_short_12","alias_value":"XHT4CAVRF7T3","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XHT4CAVRF7T3PZF7","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XHT4CAVR","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:f215ca3f118d0c92d8dca12c48a6a64869f18f4d162f43c2fb98856dd53f3fa6","target":"graph","created_at":"2026-05-18T01:01:07Z","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":"We consider the Cauchy problem for the continuity equation with a bounded nearly incompressible vector field $b\\colon (0,T) \\times \\mathbb R^d \\to \\mathbb R^d$, $T>0$. This class of vector fields arises in the context of hyperbolic conservation laws (in particular, the Keyfitz-Kranzer system).\n  It is well known that in the generic multi-dimensional case ($d\\ge 1$) near incompressibility is sufficient for existence of bounded weak solutions, but uniqueness may fail (even when the vector field is divergence-free), and hence further assumptions on the regularity of $b$ (e.g. Sobolev regularity) ","authors_text":"Nikolay A. Gusev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-27T15:46:16Z","title":"On the one-dimensional continuity equation with a nearly incompressible vector field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08848","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":"sha256:3f268f0c9a31fe0e7b076a4632d7a5b1e47e632df36f025bd0b62ddd4d68d136","target":"record","created_at":"2026-05-18T01:01:07Z","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":"50083c3d845272f27295dbabdbe52ea439cdea2bdad9be3a8a354a9fc27b8e2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-27T15:46:16Z","title_canon_sha256":"b62bce49808c87d1c8e0bf419a30e09d617612b120d502ba5a1305d296659645"},"schema_version":"1.0","source":{"id":"1610.08848","kind":"arxiv","version":1}},"canonical_sha256":"b9e7c102b12fe7b7e4bf453db63cb9e771f1aa0fd3e02d7f574c243e7372b0a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9e7c102b12fe7b7e4bf453db63cb9e771f1aa0fd3e02d7f574c243e7372b0a7","first_computed_at":"2026-05-18T01:01:07.108766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:07.108766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xr/Rnh6eWVCGqkXMmqRjVGyiOl5iVEjJKNpyjDbkr3rclMYJuykd0njMcV4EmgjIGcHNpZvD9r7+MiFIuNKjCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:07.109489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08848","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f268f0c9a31fe0e7b076a4632d7a5b1e47e632df36f025bd0b62ddd4d68d136","sha256:f215ca3f118d0c92d8dca12c48a6a64869f18f4d162f43c2fb98856dd53f3fa6"],"state_sha256":"3cb36f3a4022d480a86d6418defcb67c7e0c0ec549d9048514a1b5244f765089"}