{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L7RV2XMSOQRSPYO2XO5TSCNKY4","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":"161477f90fc1541a07bc6af68bdfd6d3095677404a925e79caabf918492cb930","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-20T10:25:44Z","title_canon_sha256":"c939a88089d179ac268745e7757df456d0046b95568be068a8febd145222c7fa"},"schema_version":"1.0","source":{"id":"1812.08463","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08463","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08463v1","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08463","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"pith_short_12","alias_value":"L7RV2XMSOQRS","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L7RV2XMSOQRSPYO2","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L7RV2XMS","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:60d08b127344b29239a45543abdc323ed627022d47df28577f311c358cb48a45","target":"graph","created_at":"2026-05-17T23:57:49Z","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 study the periodic Ostrovsky-Hunter equation in the case where the flux function may depend on the spatial variable. Our main results are that if the flux function is twice differentiable, then there exists a unique entropy solution. This entropy solution may be constructed as a limit of approximate solutions generated by a finite volume scheme, and the finite volume approximations converge to the entropy solution at a rate 1/2.","authors_text":"Neelabja Chatterjee, Nils Henrik Risebro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-20T10:25:44Z","title":"The Ostrovsky Hunter equation with a space dependent flux function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08463","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":"sha256:2467cea6d6b6b18183ac610a42cf12da0c712739146d879397a64088f36ca619","target":"record","created_at":"2026-05-17T23:57:49Z","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":"161477f90fc1541a07bc6af68bdfd6d3095677404a925e79caabf918492cb930","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-20T10:25:44Z","title_canon_sha256":"c939a88089d179ac268745e7757df456d0046b95568be068a8febd145222c7fa"},"schema_version":"1.0","source":{"id":"1812.08463","kind":"arxiv","version":1}},"canonical_sha256":"5fe35d5d92742327e1dabbbb3909aac7364cbd7466f2ec7765cd34ca8ae9e1c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fe35d5d92742327e1dabbbb3909aac7364cbd7466f2ec7765cd34ca8ae9e1c1","first_computed_at":"2026-05-17T23:57:49.912742Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:49.912742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7jMEQqsbm11ASBdte/nLoTbEbbZmv/iIJcdk6KmW1mUvZuJp/1QZ27xqOt2ZiIJWrt3LNMTLnwh6RN9JiBqEBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:49.913382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.08463","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2467cea6d6b6b18183ac610a42cf12da0c712739146d879397a64088f36ca619","sha256:60d08b127344b29239a45543abdc323ed627022d47df28577f311c358cb48a45"],"state_sha256":"db14d6818200732167fa9707d21e1b6f162a4ea4b95a0b53b82de96b80eb971c"}