{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:YMTXPBD2PASVHVGHGLKJFH6WU3","short_pith_number":"pith:YMTXPBD2","canonical_record":{"source":{"id":"1011.4236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-18T17:12:23Z","cross_cats_sorted":[],"title_canon_sha256":"54b2d7933d1789f0b910643ea4b2883e09b8a3fe22c9b0986be120ca83443910","abstract_canon_sha256":"f978f6bb40c42cd957f6e7188058b6637e8964637bd0ccde84ae1ef49ecf1890"},"schema_version":"1.0"},"canonical_sha256":"c32777847a782553d4c732d4929fd6a6fb5059dde58c26695e5882a38d776456","source":{"kind":"arxiv","id":"1011.4236","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4236","created_at":"2026-05-18T04:35:36Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4236v1","created_at":"2026-05-18T04:35:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4236","created_at":"2026-05-18T04:35:36Z"},{"alias_kind":"pith_short_12","alias_value":"YMTXPBD2PASV","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YMTXPBD2PASVHVGH","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YMTXPBD2","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:YMTXPBD2PASVHVGHGLKJFH6WU3","target":"record","payload":{"canonical_record":{"source":{"id":"1011.4236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-18T17:12:23Z","cross_cats_sorted":[],"title_canon_sha256":"54b2d7933d1789f0b910643ea4b2883e09b8a3fe22c9b0986be120ca83443910","abstract_canon_sha256":"f978f6bb40c42cd957f6e7188058b6637e8964637bd0ccde84ae1ef49ecf1890"},"schema_version":"1.0"},"canonical_sha256":"c32777847a782553d4c732d4929fd6a6fb5059dde58c26695e5882a38d776456","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:36.223659Z","signature_b64":"YPREs864A1Xio23o4fCMfjTLX0MlUe5ChYcTRM6tD8KPHV2ia+uIsV85VKuz2tHTKmFdGEdtz7nPCs4BO6aEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c32777847a782553d4c732d4929fd6a6fb5059dde58c26695e5882a38d776456","last_reissued_at":"2026-05-18T04:35:36.223031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:36.223031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.4236","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":"2026-05-18T04:35:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wunKP8anSS7A5wlce+fqPLvRmammCYTedsHoGdTYU7O0/PY8Po1zeuArGl511nezHw65Ztqj9dohKv1X5zsPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:47:09.219045Z"},"content_sha256":"4ea487b9dd49eb084ac3d30b5398ad2cc2a7233a9aec96dfe697e7782a47e9bc","schema_version":"1.0","event_id":"sha256:4ea487b9dd49eb084ac3d30b5398ad2cc2a7233a9aec96dfe697e7782a47e9bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:YMTXPBD2PASVHVGHGLKJFH6WU3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New entropy conditions for scalar conservation laws with discontinuous flux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Darko Mitrovic","submitted_at":"2010-11-18T17:12:23Z","abstract_excerpt":"We propose new Kruzhkov type entropy conditions for one dimensional scalar conservation law with a discontinuous flux. We prove existence and uniqueness of the entropy admissible weak solution to the corresponding Cauchy problem merely under assumptions on the flux which provide the maximum principle. In particular, we allow multiple flux crossings and we do not need any kind of genuine nonlinearity conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4236","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":"2026-05-18T04:35:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JXi5QPxOokaOUczEXVwskgHcmupmRrFOJnY5sJNKvcIspu4xvMn5qWn2KN9BoX2gGyQ13irCL6jmgfZ2GrsjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:47:09.219714Z"},"content_sha256":"92b6d4cc9975e8731fa52b85dd432976087b37d744bbae2aa8b484757f8b4bae","schema_version":"1.0","event_id":"sha256:92b6d4cc9975e8731fa52b85dd432976087b37d744bbae2aa8b484757f8b4bae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YMTXPBD2PASVHVGHGLKJFH6WU3/bundle.json","state_url":"https://pith.science/pith/YMTXPBD2PASVHVGHGLKJFH6WU3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YMTXPBD2PASVHVGHGLKJFH6WU3/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":"2026-06-07T18:47:09Z","links":{"resolver":"https://pith.science/pith/YMTXPBD2PASVHVGHGLKJFH6WU3","bundle":"https://pith.science/pith/YMTXPBD2PASVHVGHGLKJFH6WU3/bundle.json","state":"https://pith.science/pith/YMTXPBD2PASVHVGHGLKJFH6WU3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YMTXPBD2PASVHVGHGLKJFH6WU3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YMTXPBD2PASVHVGHGLKJFH6WU3","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":"f978f6bb40c42cd957f6e7188058b6637e8964637bd0ccde84ae1ef49ecf1890","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-18T17:12:23Z","title_canon_sha256":"54b2d7933d1789f0b910643ea4b2883e09b8a3fe22c9b0986be120ca83443910"},"schema_version":"1.0","source":{"id":"1011.4236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4236","created_at":"2026-05-18T04:35:36Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4236v1","created_at":"2026-05-18T04:35:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4236","created_at":"2026-05-18T04:35:36Z"},{"alias_kind":"pith_short_12","alias_value":"YMTXPBD2PASV","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YMTXPBD2PASVHVGH","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YMTXPBD2","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:92b6d4cc9975e8731fa52b85dd432976087b37d744bbae2aa8b484757f8b4bae","target":"graph","created_at":"2026-05-18T04:35:36Z","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 propose new Kruzhkov type entropy conditions for one dimensional scalar conservation law with a discontinuous flux. We prove existence and uniqueness of the entropy admissible weak solution to the corresponding Cauchy problem merely under assumptions on the flux which provide the maximum principle. In particular, we allow multiple flux crossings and we do not need any kind of genuine nonlinearity conditions.","authors_text":"Darko Mitrovic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-18T17:12:23Z","title":"New entropy conditions for scalar conservation laws with discontinuous flux"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4236","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":"sha256:4ea487b9dd49eb084ac3d30b5398ad2cc2a7233a9aec96dfe697e7782a47e9bc","target":"record","created_at":"2026-05-18T04:35:36Z","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":"f978f6bb40c42cd957f6e7188058b6637e8964637bd0ccde84ae1ef49ecf1890","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-18T17:12:23Z","title_canon_sha256":"54b2d7933d1789f0b910643ea4b2883e09b8a3fe22c9b0986be120ca83443910"},"schema_version":"1.0","source":{"id":"1011.4236","kind":"arxiv","version":1}},"canonical_sha256":"c32777847a782553d4c732d4929fd6a6fb5059dde58c26695e5882a38d776456","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c32777847a782553d4c732d4929fd6a6fb5059dde58c26695e5882a38d776456","first_computed_at":"2026-05-18T04:35:36.223031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:36.223031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YPREs864A1Xio23o4fCMfjTLX0MlUe5ChYcTRM6tD8KPHV2ia+uIsV85VKuz2tHTKmFdGEdtz7nPCs4BO6aEAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:36.223659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.4236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ea487b9dd49eb084ac3d30b5398ad2cc2a7233a9aec96dfe697e7782a47e9bc","sha256:92b6d4cc9975e8731fa52b85dd432976087b37d744bbae2aa8b484757f8b4bae"],"state_sha256":"697debfbde11944a6ff6222f1063f758f33d0357a573b738bf56c9ab6533a3e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v7qy1A+0dlU3fFqVzk90q5FOJV3ZJ14DXvRizuLbYX5xe/8Hib5NYiOtqu5LDtj4UcwRszxDQlxY/rwoDo5eDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:47:09.223376Z","bundle_sha256":"6eafae9eee8e9e0f4ce14803994e2b22918d134380d49bf5070305905a6da1b2"}}