{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:OMVTXH4U2S5SCVYNUMNGLMWEG2","short_pith_number":"pith:OMVTXH4U","canonical_record":{"source":{"id":"1104.5154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2011-02-23T16:35:01Z","cross_cats_sorted":[],"title_canon_sha256":"e84ba661d6c6fbcf151fd27a74eab44bfa501976d89522f358845b4e5af0e5f2","abstract_canon_sha256":"9b57fbb7e1508942a1f3885ab2825b37be271c042ab4c18db62b5269593b67f9"},"schema_version":"1.0"},"canonical_sha256":"732b3b9f94d4bb21570da31a65b2c436a34bb7f32ba468b6e13dbcd5e2309da2","source":{"kind":"arxiv","id":"1104.5154","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5154","created_at":"2026-05-18T04:23:22Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5154v1","created_at":"2026-05-18T04:23:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5154","created_at":"2026-05-18T04:23:22Z"},{"alias_kind":"pith_short_12","alias_value":"OMVTXH4U2S5S","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OMVTXH4U2S5SCVYN","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OMVTXH4U","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:OMVTXH4U2S5SCVYNUMNGLMWEG2","target":"record","payload":{"canonical_record":{"source":{"id":"1104.5154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2011-02-23T16:35:01Z","cross_cats_sorted":[],"title_canon_sha256":"e84ba661d6c6fbcf151fd27a74eab44bfa501976d89522f358845b4e5af0e5f2","abstract_canon_sha256":"9b57fbb7e1508942a1f3885ab2825b37be271c042ab4c18db62b5269593b67f9"},"schema_version":"1.0"},"canonical_sha256":"732b3b9f94d4bb21570da31a65b2c436a34bb7f32ba468b6e13dbcd5e2309da2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:22.506948Z","signature_b64":"2P/Taw+1yVBP1NCS+U1Q9wORPPeW6ArMyF2HOufsmRiQ3sZyqVVwOxWVCAVpH1YBcDeJhalOeuNksGXgEA4RAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"732b3b9f94d4bb21570da31a65b2c436a34bb7f32ba468b6e13dbcd5e2309da2","last_reissued_at":"2026-05-18T04:23:22.506482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:22.506482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.5154","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":"2026-05-18T04:23:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UpkdU8Gcp2nUzvBKO9S7i890L9vKJmPYSp+DJZ26gHUKh+roXLd4+ozWtsIEOwSMBceJEpBMUh6HpYplYUaxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:18:30.299622Z"},"content_sha256":"e6fb9afd70fed5e6006af643ef5223e1aeb3f0e7dede5aab4e7bd7aa68606d6b","schema_version":"1.0","event_id":"sha256:e6fb9afd70fed5e6006af643ef5223e1aeb3f0e7dede5aab4e7bd7aa68606d6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:OMVTXH4U2S5SCVYNUMNGLMWEG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Roll-waves in bi-layer flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Jean-Paul Vila (IMT), Marc Boutounet (INSA Toulouse), Pascal Noble (ICJ)","submitted_at":"2011-02-23T16:35:01Z","abstract_excerpt":"In this paper, we derive consistent shallow water equations for bi-layer flows of Newtonian fluids flowing down a ramp. We carry out a complete spectral analysis of steady flows in the low frequency regime and show the occurence of hydrodynamic instabilities, so called roll-waves, when steady flows are unstable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5154","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":"2026-05-18T04:23:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SJzNnqZVWWkua0f0ZQr3AFbWn+QbKz6yw6XS4zjMpCPEbLTkN7kNk91Z5xiidLaYB9p+xBbEmc3ltMAsqmWQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:18:30.299960Z"},"content_sha256":"cc1e4a764b9f4eb85006ce73a2b94988330569441d00bdc78553c2c4493e332d","schema_version":"1.0","event_id":"sha256:cc1e4a764b9f4eb85006ce73a2b94988330569441d00bdc78553c2c4493e332d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OMVTXH4U2S5SCVYNUMNGLMWEG2/bundle.json","state_url":"https://pith.science/pith/OMVTXH4U2S5SCVYNUMNGLMWEG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OMVTXH4U2S5SCVYNUMNGLMWEG2/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":"2026-06-26T00:18:30Z","links":{"resolver":"https://pith.science/pith/OMVTXH4U2S5SCVYNUMNGLMWEG2","bundle":"https://pith.science/pith/OMVTXH4U2S5SCVYNUMNGLMWEG2/bundle.json","state":"https://pith.science/pith/OMVTXH4U2S5SCVYNUMNGLMWEG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OMVTXH4U2S5SCVYNUMNGLMWEG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OMVTXH4U2S5SCVYNUMNGLMWEG2","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":"9b57fbb7e1508942a1f3885ab2825b37be271c042ab4c18db62b5269593b67f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2011-02-23T16:35:01Z","title_canon_sha256":"e84ba661d6c6fbcf151fd27a74eab44bfa501976d89522f358845b4e5af0e5f2"},"schema_version":"1.0","source":{"id":"1104.5154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5154","created_at":"2026-05-18T04:23:22Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5154v1","created_at":"2026-05-18T04:23:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5154","created_at":"2026-05-18T04:23:22Z"},{"alias_kind":"pith_short_12","alias_value":"OMVTXH4U2S5S","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OMVTXH4U2S5SCVYN","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OMVTXH4U","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:cc1e4a764b9f4eb85006ce73a2b94988330569441d00bdc78553c2c4493e332d","target":"graph","created_at":"2026-05-18T04:23:22Z","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 derive consistent shallow water equations for bi-layer flows of Newtonian fluids flowing down a ramp. We carry out a complete spectral analysis of steady flows in the low frequency regime and show the occurence of hydrodynamic instabilities, so called roll-waves, when steady flows are unstable.","authors_text":"Jean-Paul Vila (IMT), Marc Boutounet (INSA Toulouse), Pascal Noble (ICJ)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2011-02-23T16:35:01Z","title":"Roll-waves in bi-layer flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5154","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:e6fb9afd70fed5e6006af643ef5223e1aeb3f0e7dede5aab4e7bd7aa68606d6b","target":"record","created_at":"2026-05-18T04:23:22Z","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":"9b57fbb7e1508942a1f3885ab2825b37be271c042ab4c18db62b5269593b67f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2011-02-23T16:35:01Z","title_canon_sha256":"e84ba661d6c6fbcf151fd27a74eab44bfa501976d89522f358845b4e5af0e5f2"},"schema_version":"1.0","source":{"id":"1104.5154","kind":"arxiv","version":1}},"canonical_sha256":"732b3b9f94d4bb21570da31a65b2c436a34bb7f32ba468b6e13dbcd5e2309da2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"732b3b9f94d4bb21570da31a65b2c436a34bb7f32ba468b6e13dbcd5e2309da2","first_computed_at":"2026-05-18T04:23:22.506482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:22.506482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2P/Taw+1yVBP1NCS+U1Q9wORPPeW6ArMyF2HOufsmRiQ3sZyqVVwOxWVCAVpH1YBcDeJhalOeuNksGXgEA4RAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:22.506948Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.5154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6fb9afd70fed5e6006af643ef5223e1aeb3f0e7dede5aab4e7bd7aa68606d6b","sha256:cc1e4a764b9f4eb85006ce73a2b94988330569441d00bdc78553c2c4493e332d"],"state_sha256":"fd4b1ae663ce04f8b807cd155b1ed98775c4cf39e4d93e6ae425cddc30111096"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7y5JKBN9s8qSHeedyuJ8eRxxPTxGC6L9Fc7o3OckYLbDLVuwb3WKCSV7n3giOduItJU+KUL6cwp7XvrsvEU+Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:18:30.301794Z","bundle_sha256":"6d7eb5a2e889fbf9fc230a881c6335c16f10e5476ff36a00c8f5b895d78531a3"}}