{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:AQLVTKJE5A5FJP5BMQBWDEZ7JD","short_pith_number":"pith:AQLVTKJE","canonical_record":{"source":{"id":"1806.00652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-02T15:47:46Z","cross_cats_sorted":[],"title_canon_sha256":"b0701cb57d8261aa7602d2da20159b4985329651e411abd1c4354bbeda4e23b6","abstract_canon_sha256":"1cdb54f670e2b8f0688a8fb95a8fb6dae08adc5cc6761486c17d937922662d27"},"schema_version":"1.0"},"canonical_sha256":"041759a924e83a54bfa1640361933f48e096561ccf98026134deab0c6ac7cadb","source":{"kind":"arxiv","id":"1806.00652","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00652","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00652v1","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00652","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"AQLVTKJE5A5F","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AQLVTKJE5A5FJP5B","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AQLVTKJE","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:AQLVTKJE5A5FJP5BMQBWDEZ7JD","target":"record","payload":{"canonical_record":{"source":{"id":"1806.00652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-02T15:47:46Z","cross_cats_sorted":[],"title_canon_sha256":"b0701cb57d8261aa7602d2da20159b4985329651e411abd1c4354bbeda4e23b6","abstract_canon_sha256":"1cdb54f670e2b8f0688a8fb95a8fb6dae08adc5cc6761486c17d937922662d27"},"schema_version":"1.0"},"canonical_sha256":"041759a924e83a54bfa1640361933f48e096561ccf98026134deab0c6ac7cadb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:13.533587Z","signature_b64":"rRoXlMZFF5eu895nOPSu3zg/9suVg50EbrJ8FdEe0+qdngJZwOKsffL+NdIJy1fyaLXrwyicpKimvL8cg9zfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"041759a924e83a54bfa1640361933f48e096561ccf98026134deab0c6ac7cadb","last_reissued_at":"2026-05-17T23:50:13.532864Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:13.532864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.00652","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":"2026-05-17T23:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZgpMBSZjdDUq0Q3+lvblaS2HVZHeBhekcjh/Bk+qQqyhqbAiFN7qp6u7A5po9dZIW3Z3w+Yb5e45zlSyqvbpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:27:38.536426Z"},"content_sha256":"b2298d173b28802285e8eebf1d7677a18ef6a124c0f3f5843e9883d76f3dec37","schema_version":"1.0","event_id":"sha256:b2298d173b28802285e8eebf1d7677a18ef6a124c0f3f5843e9883d76f3dec37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:AQLVTKJE5A5FJP5BMQBWDEZ7JD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Viscous profiles in models of collective movements with negative diffusivities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Corli, Luisa Malaguti","submitted_at":"2018-06-02T15:47:46Z","abstract_excerpt":"In this paper we consider an advection-diffusion equation, in one space dimension, whose diffusivity can be negative. Such equations arise in particular in the modeling of vehicular traffic flows or crowds dynamics, where a negative diffusivity simulates aggregation phenomena. We focus on traveling-wave solutions that connect two states whose diffusivity has different signs; under some geometric conditions we prove the existence, uniqueness (in a suitable class of solutions avoiding plateaus) and sharpness of the corresponding profiles. Such results are then extended to the case of end states "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00652","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":"2026-05-17T23:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M3HkrOHfA6lo0i6V9RQ49b9TQVkOSdlZmREI0s11Yx5V8CqM2hCaR6mDlmgFe6S2VfWdXKdfD3nLCsYCB/JfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:27:38.536780Z"},"content_sha256":"7e65da2f8d310987867ee25f135fc3c76150efda2e0de36cca52040748300e79","schema_version":"1.0","event_id":"sha256:7e65da2f8d310987867ee25f135fc3c76150efda2e0de36cca52040748300e79"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQLVTKJE5A5FJP5BMQBWDEZ7JD/bundle.json","state_url":"https://pith.science/pith/AQLVTKJE5A5FJP5BMQBWDEZ7JD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQLVTKJE5A5FJP5BMQBWDEZ7JD/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":"2026-06-22T15:27:38Z","links":{"resolver":"https://pith.science/pith/AQLVTKJE5A5FJP5BMQBWDEZ7JD","bundle":"https://pith.science/pith/AQLVTKJE5A5FJP5BMQBWDEZ7JD/bundle.json","state":"https://pith.science/pith/AQLVTKJE5A5FJP5BMQBWDEZ7JD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQLVTKJE5A5FJP5BMQBWDEZ7JD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AQLVTKJE5A5FJP5BMQBWDEZ7JD","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":"1cdb54f670e2b8f0688a8fb95a8fb6dae08adc5cc6761486c17d937922662d27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-02T15:47:46Z","title_canon_sha256":"b0701cb57d8261aa7602d2da20159b4985329651e411abd1c4354bbeda4e23b6"},"schema_version":"1.0","source":{"id":"1806.00652","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00652","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00652v1","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00652","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"AQLVTKJE5A5F","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AQLVTKJE5A5FJP5B","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AQLVTKJE","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:7e65da2f8d310987867ee25f135fc3c76150efda2e0de36cca52040748300e79","target":"graph","created_at":"2026-05-17T23:50:13Z","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 an advection-diffusion equation, in one space dimension, whose diffusivity can be negative. Such equations arise in particular in the modeling of vehicular traffic flows or crowds dynamics, where a negative diffusivity simulates aggregation phenomena. We focus on traveling-wave solutions that connect two states whose diffusivity has different signs; under some geometric conditions we prove the existence, uniqueness (in a suitable class of solutions avoiding plateaus) and sharpness of the corresponding profiles. Such results are then extended to the case of end states ","authors_text":"Andrea Corli, Luisa Malaguti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-02T15:47:46Z","title":"Viscous profiles in models of collective movements with negative diffusivities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00652","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:b2298d173b28802285e8eebf1d7677a18ef6a124c0f3f5843e9883d76f3dec37","target":"record","created_at":"2026-05-17T23:50:13Z","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":"1cdb54f670e2b8f0688a8fb95a8fb6dae08adc5cc6761486c17d937922662d27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-02T15:47:46Z","title_canon_sha256":"b0701cb57d8261aa7602d2da20159b4985329651e411abd1c4354bbeda4e23b6"},"schema_version":"1.0","source":{"id":"1806.00652","kind":"arxiv","version":1}},"canonical_sha256":"041759a924e83a54bfa1640361933f48e096561ccf98026134deab0c6ac7cadb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"041759a924e83a54bfa1640361933f48e096561ccf98026134deab0c6ac7cadb","first_computed_at":"2026-05-17T23:50:13.532864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:13.532864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rRoXlMZFF5eu895nOPSu3zg/9suVg50EbrJ8FdEe0+qdngJZwOKsffL+NdIJy1fyaLXrwyicpKimvL8cg9zfAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:13.533587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.00652","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2298d173b28802285e8eebf1d7677a18ef6a124c0f3f5843e9883d76f3dec37","sha256:7e65da2f8d310987867ee25f135fc3c76150efda2e0de36cca52040748300e79"],"state_sha256":"2f73985c9c14d93e85a5a3340a1b3099b2d3c0cf44e9bb72a188fea4571a63a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LYFn7OXl9UIL7nRai2mtxuhhf7giJcdpP0Y7Bzm7W+2ukCZdHuZ1t7pUePu9EUuS0sQSe4lZ96WRZJdF8SNrDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T15:27:38.538714Z","bundle_sha256":"8a2f58f62a98a94b7452dd25cb4ad776b983a03802bb97912406fc672568c7fa"}}