{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OH4UM5XZZRONQKNDJKQZFFGBT6","short_pith_number":"pith:OH4UM5XZ","canonical_record":{"source":{"id":"1404.2036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-08T08:17:48Z","cross_cats_sorted":[],"title_canon_sha256":"c1c983fd72dacfd20f38cc52963330940b277b6195e7dca78e0bc8f7324c9215","abstract_canon_sha256":"4e29b62011f5b9d3f59cb73fdfe838f7b2b53c02e85a540ee5d830211d2be063"},"schema_version":"1.0"},"canonical_sha256":"71f94676f9cc5cd829a34aa19294c19fa51677bcb1bbb277dd44ce0ce4fc88bc","source":{"kind":"arxiv","id":"1404.2036","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2036","created_at":"2026-05-18T02:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2036v1","created_at":"2026-05-18T02:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2036","created_at":"2026-05-18T02:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"OH4UM5XZZRON","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OH4UM5XZZRONQKND","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OH4UM5XZ","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OH4UM5XZZRONQKNDJKQZFFGBT6","target":"record","payload":{"canonical_record":{"source":{"id":"1404.2036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-08T08:17:48Z","cross_cats_sorted":[],"title_canon_sha256":"c1c983fd72dacfd20f38cc52963330940b277b6195e7dca78e0bc8f7324c9215","abstract_canon_sha256":"4e29b62011f5b9d3f59cb73fdfe838f7b2b53c02e85a540ee5d830211d2be063"},"schema_version":"1.0"},"canonical_sha256":"71f94676f9cc5cd829a34aa19294c19fa51677bcb1bbb277dd44ce0ce4fc88bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:38.697264Z","signature_b64":"aPZzfWwg3vJLL8LuwXPZokKIWr6uOP2oL/TV8tfgE231MLKectE/DSgJQ+2uj7xCFhydg9lbVqEOsi3ufcEbCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71f94676f9cc5cd829a34aa19294c19fa51677bcb1bbb277dd44ce0ce4fc88bc","last_reissued_at":"2026-05-18T02:54:38.696832Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:38.696832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.2036","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":"2026-05-18T02:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/LobV6GIrZR0Ys9B6/c2IPW8QIN/FRggmLT/VgumExVPeOKMFlJUJMjnfbtiZh4AJ1Zp0Qat2OJAK/KyJEmtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:54:11.622545Z"},"content_sha256":"629bd0cadc98df2a1a207197e9d2db1d59d9e59c2bec85945ea9f3f06d353985","schema_version":"1.0","event_id":"sha256:629bd0cadc98df2a1a207197e9d2db1d59d9e59c2bec85945ea9f3f06d353985"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OH4UM5XZZRONQKNDJKQZFFGBT6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-dimensional scalar balance laws with discontinuous flux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnieszka Swierczewska-Gwiazda, Aleksandra Zimmermann, Petra Wittbold, Piotr Gwiazda","submitted_at":"2014-04-08T08:17:48Z","abstract_excerpt":"We consider the problem of existence of entropy weak solutions to scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect both to the space variable x and the unknown quantity u. The problem is formulated in the framework of multi-valued mappings. We use the notion of entropy-measure valued solutions to prove the so-called contraction principle and comparison principle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2036","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":"2026-05-18T02:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bZRwFPmFS51Qek7Cj3jzVsepTi1dx8FLCZySirA9ODQq4X5Tyod71GdD0fSVzEU1iy0bEDKvnnc3WnAfF6/dAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:54:11.623385Z"},"content_sha256":"088ee310d20d8e751b09450c377a2768b1106d591e773b24bad04dbdd373cc08","schema_version":"1.0","event_id":"sha256:088ee310d20d8e751b09450c377a2768b1106d591e773b24bad04dbdd373cc08"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OH4UM5XZZRONQKNDJKQZFFGBT6/bundle.json","state_url":"https://pith.science/pith/OH4UM5XZZRONQKNDJKQZFFGBT6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OH4UM5XZZRONQKNDJKQZFFGBT6/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":"2026-05-30T15:54:11Z","links":{"resolver":"https://pith.science/pith/OH4UM5XZZRONQKNDJKQZFFGBT6","bundle":"https://pith.science/pith/OH4UM5XZZRONQKNDJKQZFFGBT6/bundle.json","state":"https://pith.science/pith/OH4UM5XZZRONQKNDJKQZFFGBT6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OH4UM5XZZRONQKNDJKQZFFGBT6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OH4UM5XZZRONQKNDJKQZFFGBT6","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":"4e29b62011f5b9d3f59cb73fdfe838f7b2b53c02e85a540ee5d830211d2be063","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-08T08:17:48Z","title_canon_sha256":"c1c983fd72dacfd20f38cc52963330940b277b6195e7dca78e0bc8f7324c9215"},"schema_version":"1.0","source":{"id":"1404.2036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2036","created_at":"2026-05-18T02:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2036v1","created_at":"2026-05-18T02:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2036","created_at":"2026-05-18T02:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"OH4UM5XZZRON","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OH4UM5XZZRONQKND","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OH4UM5XZ","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:088ee310d20d8e751b09450c377a2768b1106d591e773b24bad04dbdd373cc08","target":"graph","created_at":"2026-05-18T02:54:38Z","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 problem of existence of entropy weak solutions to scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect both to the space variable x and the unknown quantity u. The problem is formulated in the framework of multi-valued mappings. We use the notion of entropy-measure valued solutions to prove the so-called contraction principle and comparison principle.","authors_text":"Agnieszka Swierczewska-Gwiazda, Aleksandra Zimmermann, Petra Wittbold, Piotr Gwiazda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-08T08:17:48Z","title":"Multi-dimensional scalar balance laws with discontinuous flux"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2036","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":"sha256:629bd0cadc98df2a1a207197e9d2db1d59d9e59c2bec85945ea9f3f06d353985","target":"record","created_at":"2026-05-18T02:54:38Z","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":"4e29b62011f5b9d3f59cb73fdfe838f7b2b53c02e85a540ee5d830211d2be063","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-08T08:17:48Z","title_canon_sha256":"c1c983fd72dacfd20f38cc52963330940b277b6195e7dca78e0bc8f7324c9215"},"schema_version":"1.0","source":{"id":"1404.2036","kind":"arxiv","version":1}},"canonical_sha256":"71f94676f9cc5cd829a34aa19294c19fa51677bcb1bbb277dd44ce0ce4fc88bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71f94676f9cc5cd829a34aa19294c19fa51677bcb1bbb277dd44ce0ce4fc88bc","first_computed_at":"2026-05-18T02:54:38.696832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:38.696832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aPZzfWwg3vJLL8LuwXPZokKIWr6uOP2oL/TV8tfgE231MLKectE/DSgJQ+2uj7xCFhydg9lbVqEOsi3ufcEbCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:38.697264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:629bd0cadc98df2a1a207197e9d2db1d59d9e59c2bec85945ea9f3f06d353985","sha256:088ee310d20d8e751b09450c377a2768b1106d591e773b24bad04dbdd373cc08"],"state_sha256":"b93ff08b6bf901280f9d89cdcb5b745d66a0088b46c2d5f798f9d603bba9fdc1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I5QCzg/9BQ7wLQZjehamDb3E1T4qwTvS0lBq/pyPs/f8Znwq/zanf9RBg5VWn/jjjL6uOMnh3QL4VCUOMT9dDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:54:11.627955Z","bundle_sha256":"f458ed4429cc75427fddb8d9cf8c3f31468aae5fc77ab16e407502d3082bbbcc"}}