{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:SFU5WVZH4QJ5BZ2CZHJ2CLYBV7","short_pith_number":"pith:SFU5WVZH","canonical_record":{"source":{"id":"1905.09041","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2019-05-22T09:50:10Z","cross_cats_sorted":[],"title_canon_sha256":"1c15b912b37b1e6badf5950fc8b907163a3411ca3e4bf231e0e848f7810e1839","abstract_canon_sha256":"e19fcfa7588f28ab6b6f1642deac0be3c355a3ed1820ac8348413e3e45e0e84b"},"schema_version":"1.0"},"canonical_sha256":"9169db5727e413d0e742c9d3a12f01afe4a4a7a1a5078265176651a70e4e7fc5","source":{"kind":"arxiv","id":"1905.09041","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.09041","created_at":"2026-05-17T23:45:22Z"},{"alias_kind":"arxiv_version","alias_value":"1905.09041v1","created_at":"2026-05-17T23:45:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.09041","created_at":"2026-05-17T23:45:22Z"},{"alias_kind":"pith_short_12","alias_value":"SFU5WVZH4QJ5","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SFU5WVZH4QJ5BZ2C","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SFU5WVZH","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:SFU5WVZH4QJ5BZ2CZHJ2CLYBV7","target":"record","payload":{"canonical_record":{"source":{"id":"1905.09041","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2019-05-22T09:50:10Z","cross_cats_sorted":[],"title_canon_sha256":"1c15b912b37b1e6badf5950fc8b907163a3411ca3e4bf231e0e848f7810e1839","abstract_canon_sha256":"e19fcfa7588f28ab6b6f1642deac0be3c355a3ed1820ac8348413e3e45e0e84b"},"schema_version":"1.0"},"canonical_sha256":"9169db5727e413d0e742c9d3a12f01afe4a4a7a1a5078265176651a70e4e7fc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:22.137385Z","signature_b64":"RBl345bPA+sBO4/NsV5HtrZONwza/H/P4Yka/pMXogNy1CxgqXG9a0LDg8+fxI9RSYjqkwq6c/XFbppKabuNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9169db5727e413d0e742c9d3a12f01afe4a4a7a1a5078265176651a70e4e7fc5","last_reissued_at":"2026-05-17T23:45:22.136950Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:22.136950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.09041","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gFaJoSC5RD2tZSWlQtr6qzVxuhD6RgFigmpyIO7Off74R8Zj9fEqSIc03xjGAuxc/3mn+1RtxditDdrIahYKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:22:11.930969Z"},"content_sha256":"c4437f9c544fe8c079759d279de216b7b3f1e9f60fbfa02be6a184c5e864a4d3","schema_version":"1.0","event_id":"sha256:c4437f9c544fe8c079759d279de216b7b3f1e9f60fbfa02be6a184c5e864a4d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:SFU5WVZH4QJ5BZ2CZHJ2CLYBV7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-posedness of the initial value problem for the Ostrovsky-Hunter equation with spatially dependent flux","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giuseppe Maria Coclite, Neelabja Chatterjee, Nils Henrik Risebro","submitted_at":"2019-05-22T09:50:10Z","abstract_excerpt":"In this paper we study the Ostrovsky-Hunter equation for the case where the flux function $f(x, u)$ may depend on the spatial variable with certain smoothness. Our main results are that if the flux function is smooth enough (specified later), then there exists a unique entropy solution. To show the existence, after proving some a priori estimates we have used the method of compensated compactness and to prove the uniqueness we have employed the method of doubling of variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09041","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V91OfN8uRTOJRYcOEaOK8zjIZ6dekTF/iA6SDSMCQDXnCTzDLsF9va70c6l2WUmuoxZPIxQGppNiHgIRJ1cCCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:22:11.931422Z"},"content_sha256":"faaabfb317c1f532e6c051f303403bb674cf15d149be8a19ca22fa5d39f86cf7","schema_version":"1.0","event_id":"sha256:faaabfb317c1f532e6c051f303403bb674cf15d149be8a19ca22fa5d39f86cf7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SFU5WVZH4QJ5BZ2CZHJ2CLYBV7/bundle.json","state_url":"https://pith.science/pith/SFU5WVZH4QJ5BZ2CZHJ2CLYBV7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SFU5WVZH4QJ5BZ2CZHJ2CLYBV7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T00:22:11Z","links":{"resolver":"https://pith.science/pith/SFU5WVZH4QJ5BZ2CZHJ2CLYBV7","bundle":"https://pith.science/pith/SFU5WVZH4QJ5BZ2CZHJ2CLYBV7/bundle.json","state":"https://pith.science/pith/SFU5WVZH4QJ5BZ2CZHJ2CLYBV7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SFU5WVZH4QJ5BZ2CZHJ2CLYBV7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SFU5WVZH4QJ5BZ2CZHJ2CLYBV7","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":"e19fcfa7588f28ab6b6f1642deac0be3c355a3ed1820ac8348413e3e45e0e84b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2019-05-22T09:50:10Z","title_canon_sha256":"1c15b912b37b1e6badf5950fc8b907163a3411ca3e4bf231e0e848f7810e1839"},"schema_version":"1.0","source":{"id":"1905.09041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.09041","created_at":"2026-05-17T23:45:22Z"},{"alias_kind":"arxiv_version","alias_value":"1905.09041v1","created_at":"2026-05-17T23:45:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.09041","created_at":"2026-05-17T23:45:22Z"},{"alias_kind":"pith_short_12","alias_value":"SFU5WVZH4QJ5","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SFU5WVZH4QJ5BZ2C","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SFU5WVZH","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:faaabfb317c1f532e6c051f303403bb674cf15d149be8a19ca22fa5d39f86cf7","target":"graph","created_at":"2026-05-17T23:45:22Z","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":"In this paper we study the Ostrovsky-Hunter equation for the case where the flux function $f(x, u)$ may depend on the spatial variable with certain smoothness. Our main results are that if the flux function is smooth enough (specified later), then there exists a unique entropy solution. To show the existence, after proving some a priori estimates we have used the method of compensated compactness and to prove the uniqueness we have employed the method of doubling of variables.","authors_text":"Giuseppe Maria Coclite, Neelabja Chatterjee, Nils Henrik Risebro","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2019-05-22T09:50:10Z","title":"Well-posedness of the initial value problem for the Ostrovsky-Hunter equation with spatially dependent flux"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09041","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:c4437f9c544fe8c079759d279de216b7b3f1e9f60fbfa02be6a184c5e864a4d3","target":"record","created_at":"2026-05-17T23:45:22Z","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":"e19fcfa7588f28ab6b6f1642deac0be3c355a3ed1820ac8348413e3e45e0e84b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2019-05-22T09:50:10Z","title_canon_sha256":"1c15b912b37b1e6badf5950fc8b907163a3411ca3e4bf231e0e848f7810e1839"},"schema_version":"1.0","source":{"id":"1905.09041","kind":"arxiv","version":1}},"canonical_sha256":"9169db5727e413d0e742c9d3a12f01afe4a4a7a1a5078265176651a70e4e7fc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9169db5727e413d0e742c9d3a12f01afe4a4a7a1a5078265176651a70e4e7fc5","first_computed_at":"2026-05-17T23:45:22.136950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:22.136950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RBl345bPA+sBO4/NsV5HtrZONwza/H/P4Yka/pMXogNy1CxgqXG9a0LDg8+fxI9RSYjqkwq6c/XFbppKabuNAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:22.137385Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.09041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4437f9c544fe8c079759d279de216b7b3f1e9f60fbfa02be6a184c5e864a4d3","sha256:faaabfb317c1f532e6c051f303403bb674cf15d149be8a19ca22fa5d39f86cf7"],"state_sha256":"161e53cc1cbba12a0183e656967d439da67e068e713b593661a744d882df6127"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gWnn1d9y2hp+V7EwiBp+cO8qdm8odNk2Vq18tcMhmgZ1mMzeVZxeqr8ceT8oSvlmYmL/Dckxr0VLC5MO2Th3Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:22:11.934881Z","bundle_sha256":"81ad07f8ac6d2378556f8a1fa8da76aac9bce553cb4081967a64cb20517de08f"}}