{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DX3EKVVC53GYX6WJIVHKMHNEHT","short_pith_number":"pith:DX3EKVVC","canonical_record":{"source":{"id":"1602.03454","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-10T17:26:25Z","cross_cats_sorted":[],"title_canon_sha256":"b259daf06eb69bb36bece400577553c015e60a8c4779e368a1fba52d8979f3fb","abstract_canon_sha256":"0118e295459e683c76204363cddcb5b2568fa72e4be267d9eadc740a3e43b4b4"},"schema_version":"1.0"},"canonical_sha256":"1df64556a2eecd8bfac9454ea61da43cec411d746e75af82d89bb7e72d70216a","source":{"kind":"arxiv","id":"1602.03454","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03454","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03454v1","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03454","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"DX3EKVVC53GY","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DX3EKVVC53GYX6WJ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DX3EKVVC","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DX3EKVVC53GYX6WJIVHKMHNEHT","target":"record","payload":{"canonical_record":{"source":{"id":"1602.03454","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-10T17:26:25Z","cross_cats_sorted":[],"title_canon_sha256":"b259daf06eb69bb36bece400577553c015e60a8c4779e368a1fba52d8979f3fb","abstract_canon_sha256":"0118e295459e683c76204363cddcb5b2568fa72e4be267d9eadc740a3e43b4b4"},"schema_version":"1.0"},"canonical_sha256":"1df64556a2eecd8bfac9454ea61da43cec411d746e75af82d89bb7e72d70216a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:59.905775Z","signature_b64":"i7YWNkAO8puOJ9B/MUD3s9nM8aiKvn/no2gYFyiVJJRFFfLSc0N6RCkqyWja45Frsyss4P5pj9hD6MfO4LKEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1df64556a2eecd8bfac9454ea61da43cec411d746e75af82d89bb7e72d70216a","last_reissued_at":"2026-05-18T01:20:59.905196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:59.905196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.03454","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":"2026-05-18T01:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u/b93pD5nRWrvrA87KcjMiSXPF7HtwrACMv8oIIMImEWZJhuNcQ7SWH799MZRELtLTXUCsCaxLgGlzi4SJbuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:30:44.458782Z"},"content_sha256":"881000ab0d74b0fe5b25a2fe62ec0ea8a1d07c2153dd32bb5c1a4a87588a8716","schema_version":"1.0","event_id":"sha256:881000ab0d74b0fe5b25a2fe62ec0ea8a1d07c2153dd32bb5c1a4a87588a8716"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DX3EKVVC53GYX6WJIVHKMHNEHT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entropy solutions for a traffic model with phase transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Massimiliano Daniele Rosini, Mohamed Benyahia","submitted_at":"2016-02-10T17:26:25Z","abstract_excerpt":"In this paper, we consider the two phases macroscopic traffic model introduced in [P. Goatin, The Aw-Rascle vehicular traffic flow with phase transitions, Mathematical and Computer Modeling 44 (2006) 287-303]. We first apply the wave-front tracking method to prove existence and a priori bounds for weak solutions. Then, in the case the characteristic field corresponding to the free phase is linearly degenerate, we prove that the obtained weak solutions are in fact entropy solutions \\`a la Kruzhkov. The case of solutions attaining values at the vacuum is considered. We also present an explicit n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03454","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":"2026-05-18T01:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qq+bIdvmH0bjQpTT+KnSu36EF9oHc1iJPqbILdllYddCO10CJiqRYgPAK3OlqN6Z+3s34HvTilufNaJr8Yg2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:30:44.459131Z"},"content_sha256":"c014462fc34d8157758b6dad057af69f85206f4552b8b8c9cb87bebcf0ebf6c0","schema_version":"1.0","event_id":"sha256:c014462fc34d8157758b6dad057af69f85206f4552b8b8c9cb87bebcf0ebf6c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DX3EKVVC53GYX6WJIVHKMHNEHT/bundle.json","state_url":"https://pith.science/pith/DX3EKVVC53GYX6WJIVHKMHNEHT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DX3EKVVC53GYX6WJIVHKMHNEHT/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":"2026-05-28T01:30:44Z","links":{"resolver":"https://pith.science/pith/DX3EKVVC53GYX6WJIVHKMHNEHT","bundle":"https://pith.science/pith/DX3EKVVC53GYX6WJIVHKMHNEHT/bundle.json","state":"https://pith.science/pith/DX3EKVVC53GYX6WJIVHKMHNEHT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DX3EKVVC53GYX6WJIVHKMHNEHT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DX3EKVVC53GYX6WJIVHKMHNEHT","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":"0118e295459e683c76204363cddcb5b2568fa72e4be267d9eadc740a3e43b4b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-10T17:26:25Z","title_canon_sha256":"b259daf06eb69bb36bece400577553c015e60a8c4779e368a1fba52d8979f3fb"},"schema_version":"1.0","source":{"id":"1602.03454","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03454","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03454v1","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03454","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"DX3EKVVC53GY","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DX3EKVVC53GYX6WJ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DX3EKVVC","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:c014462fc34d8157758b6dad057af69f85206f4552b8b8c9cb87bebcf0ebf6c0","target":"graph","created_at":"2026-05-18T01:20:59Z","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 consider the two phases macroscopic traffic model introduced in [P. Goatin, The Aw-Rascle vehicular traffic flow with phase transitions, Mathematical and Computer Modeling 44 (2006) 287-303]. We first apply the wave-front tracking method to prove existence and a priori bounds for weak solutions. Then, in the case the characteristic field corresponding to the free phase is linearly degenerate, we prove that the obtained weak solutions are in fact entropy solutions \\`a la Kruzhkov. The case of solutions attaining values at the vacuum is considered. We also present an explicit n","authors_text":"Massimiliano Daniele Rosini, Mohamed Benyahia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-10T17:26:25Z","title":"Entropy solutions for a traffic model with phase transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03454","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":"sha256:881000ab0d74b0fe5b25a2fe62ec0ea8a1d07c2153dd32bb5c1a4a87588a8716","target":"record","created_at":"2026-05-18T01:20:59Z","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":"0118e295459e683c76204363cddcb5b2568fa72e4be267d9eadc740a3e43b4b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-10T17:26:25Z","title_canon_sha256":"b259daf06eb69bb36bece400577553c015e60a8c4779e368a1fba52d8979f3fb"},"schema_version":"1.0","source":{"id":"1602.03454","kind":"arxiv","version":1}},"canonical_sha256":"1df64556a2eecd8bfac9454ea61da43cec411d746e75af82d89bb7e72d70216a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1df64556a2eecd8bfac9454ea61da43cec411d746e75af82d89bb7e72d70216a","first_computed_at":"2026-05-18T01:20:59.905196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:59.905196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i7YWNkAO8puOJ9B/MUD3s9nM8aiKvn/no2gYFyiVJJRFFfLSc0N6RCkqyWja45Frsyss4P5pj9hD6MfO4LKEBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:59.905775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.03454","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:881000ab0d74b0fe5b25a2fe62ec0ea8a1d07c2153dd32bb5c1a4a87588a8716","sha256:c014462fc34d8157758b6dad057af69f85206f4552b8b8c9cb87bebcf0ebf6c0"],"state_sha256":"5181dc37ad59f42a439a1c0be7c21204667075be0cba49dd1b3f738a4d78b27e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6xyqKWceF6a/nQR4Kp+DIKt9zCNkvjdCMUO2NB+2TEm7Qywua4aFFpmTc48Pf/UEay/A8kR6bN0QurGyas/7Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:30:44.461129Z","bundle_sha256":"e3a31aa76f2d43d00b499d51482cdc7a8300d6c3be06f3888e2b00585f9cecd0"}}