{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:W5ZZHAFGPNY6GOHNM2LUJZ6ZMH","short_pith_number":"pith:W5ZZHAFG","canonical_record":{"source":{"id":"1812.10279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T10:32:43Z","cross_cats_sorted":[],"title_canon_sha256":"45786ac2b7429c0b47a65b019f11328f8ea76a348488432ae0ea55aec23ba876","abstract_canon_sha256":"c9ceacf1cfdb9a03cbb3fb272203339799a6af74005204d3e6a72b86a0e4a467"},"schema_version":"1.0"},"canonical_sha256":"b7739380a67b71e338ed669744e7d961ffbdee7f5ff6636076b9bc793e8e4d4c","source":{"kind":"arxiv","id":"1812.10279","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10279","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10279v2","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10279","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"pith_short_12","alias_value":"W5ZZHAFGPNY6","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"W5ZZHAFGPNY6GOHN","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"W5ZZHAFG","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:W5ZZHAFGPNY6GOHNM2LUJZ6ZMH","target":"record","payload":{"canonical_record":{"source":{"id":"1812.10279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T10:32:43Z","cross_cats_sorted":[],"title_canon_sha256":"45786ac2b7429c0b47a65b019f11328f8ea76a348488432ae0ea55aec23ba876","abstract_canon_sha256":"c9ceacf1cfdb9a03cbb3fb272203339799a6af74005204d3e6a72b86a0e4a467"},"schema_version":"1.0"},"canonical_sha256":"b7739380a67b71e338ed669744e7d961ffbdee7f5ff6636076b9bc793e8e4d4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:58.707213Z","signature_b64":"MeAo2SDrRsTfia0Ip9TFOgem0+UfzwjRvzHHqDCpdcwvp7TsqXbtFy3q3/jcvvrJtfINFZ1nr+Afy0Jg5EtzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7739380a67b71e338ed669744e7d961ffbdee7f5ff6636076b9bc793e8e4d4c","last_reissued_at":"2026-05-17T23:47:58.706605Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:58.706605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.10279","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z4g92SnbN814DK6GYmttk8nane96EB6u7L590t4m++jft3OxfnytRGJUO9lOVHoP+lc/WNIIJ0Afr/QdSOPlAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:56:40.675975Z"},"content_sha256":"0367eed790a9f70dbbd4ba4a4bda5a10da39509f3fd8c08251d3ff4c46143195","schema_version":"1.0","event_id":"sha256:0367eed790a9f70dbbd4ba4a4bda5a10da39509f3fd8c08251d3ff4c46143195"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:W5ZZHAFGPNY6GOHNM2LUJZ6ZMH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dispersive shocks in Quantum Hydrodynamics with viscosity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Corrado Lattanzio, Delyan Zhelyazov, Pierangelo Marcati","submitted_at":"2018-12-26T10:32:43Z","abstract_excerpt":"In this paper we study existence and stability of shock profiles for a 1-D compressible Euler system in the context of Quantum Hydrodynamic models. The dispersive term is originated by the quantum effects described through the Bohm potential; moreover we introduce a (linear) viscosity to analyze its interplay with the former while proving existence, monotonicity and stability of travelling waves connecting a Lax shock for the underlying Euler system. The existence of monotone profiles is proved for sufficiently small shocks; while the case of large shocks leads to the (global) existence for an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10279","kind":"arxiv","version":2},"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":"2026-05-17T23:47:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yjWA0oy2F0WHv/zIPZODwODbLqQm+oRxcokZWqi59J/rn80KCwavRIHIYbvNRT/YofgX/8lnXBLLPRdNdykDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:56:40.676707Z"},"content_sha256":"b5c6a5e7e2dfb3dab1cbafa2bef50d5112a508c346d3ab17691c4d2e5f280b59","schema_version":"1.0","event_id":"sha256:b5c6a5e7e2dfb3dab1cbafa2bef50d5112a508c346d3ab17691c4d2e5f280b59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W5ZZHAFGPNY6GOHNM2LUJZ6ZMH/bundle.json","state_url":"https://pith.science/pith/W5ZZHAFGPNY6GOHNM2LUJZ6ZMH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W5ZZHAFGPNY6GOHNM2LUJZ6ZMH/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":"2026-06-06T18:56:40Z","links":{"resolver":"https://pith.science/pith/W5ZZHAFGPNY6GOHNM2LUJZ6ZMH","bundle":"https://pith.science/pith/W5ZZHAFGPNY6GOHNM2LUJZ6ZMH/bundle.json","state":"https://pith.science/pith/W5ZZHAFGPNY6GOHNM2LUJZ6ZMH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W5ZZHAFGPNY6GOHNM2LUJZ6ZMH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:W5ZZHAFGPNY6GOHNM2LUJZ6ZMH","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":"c9ceacf1cfdb9a03cbb3fb272203339799a6af74005204d3e6a72b86a0e4a467","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T10:32:43Z","title_canon_sha256":"45786ac2b7429c0b47a65b019f11328f8ea76a348488432ae0ea55aec23ba876"},"schema_version":"1.0","source":{"id":"1812.10279","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10279","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10279v2","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10279","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"pith_short_12","alias_value":"W5ZZHAFGPNY6","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"W5ZZHAFGPNY6GOHN","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"W5ZZHAFG","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:b5c6a5e7e2dfb3dab1cbafa2bef50d5112a508c346d3ab17691c4d2e5f280b59","target":"graph","created_at":"2026-05-17T23:47:58Z","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 existence and stability of shock profiles for a 1-D compressible Euler system in the context of Quantum Hydrodynamic models. The dispersive term is originated by the quantum effects described through the Bohm potential; moreover we introduce a (linear) viscosity to analyze its interplay with the former while proving existence, monotonicity and stability of travelling waves connecting a Lax shock for the underlying Euler system. The existence of monotone profiles is proved for sufficiently small shocks; while the case of large shocks leads to the (global) existence for an","authors_text":"Corrado Lattanzio, Delyan Zhelyazov, Pierangelo Marcati","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T10:32:43Z","title":"Dispersive shocks in Quantum Hydrodynamics with viscosity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10279","kind":"arxiv","version":2},"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":"sha256:0367eed790a9f70dbbd4ba4a4bda5a10da39509f3fd8c08251d3ff4c46143195","target":"record","created_at":"2026-05-17T23:47:58Z","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":"c9ceacf1cfdb9a03cbb3fb272203339799a6af74005204d3e6a72b86a0e4a467","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T10:32:43Z","title_canon_sha256":"45786ac2b7429c0b47a65b019f11328f8ea76a348488432ae0ea55aec23ba876"},"schema_version":"1.0","source":{"id":"1812.10279","kind":"arxiv","version":2}},"canonical_sha256":"b7739380a67b71e338ed669744e7d961ffbdee7f5ff6636076b9bc793e8e4d4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7739380a67b71e338ed669744e7d961ffbdee7f5ff6636076b9bc793e8e4d4c","first_computed_at":"2026-05-17T23:47:58.706605Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:58.706605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MeAo2SDrRsTfia0Ip9TFOgem0+UfzwjRvzHHqDCpdcwvp7TsqXbtFy3q3/jcvvrJtfINFZ1nr+Afy0Jg5EtzDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:58.707213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.10279","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0367eed790a9f70dbbd4ba4a4bda5a10da39509f3fd8c08251d3ff4c46143195","sha256:b5c6a5e7e2dfb3dab1cbafa2bef50d5112a508c346d3ab17691c4d2e5f280b59"],"state_sha256":"3a22baf0732cf1a361dd4d6766fa7c75b12ebf68fab1932b5ca685d69fe4a027"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c5ijLDfaMHBKDLTd+BQs9OprxmkdRK4PwnU8NqlmINHBa0Ude0BKcC10MysUQ6LRtsRleDl8Fb9w2nMykeJRCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:56:40.681225Z","bundle_sha256":"1e07ee9bf99bcfe69a81e74d879ea27379e0ce7be193a83a02b7856d497b1de7"}}