{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:LD4MQ57MEGG5Y3MWHM44VUTL3I","short_pith_number":"pith:LD4MQ57M","schema_version":"1.0","canonical_sha256":"58f8c877ec218ddc6d963b39cad26bda063312248ddca01233588e79a8f430be","source":{"kind":"arxiv","id":"physics/0604009","version":1},"attestation_state":"computed","paper":{"title":"The critical Reynolds number of a laminar mixing layer","license":"","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"M. P. Manoharan, Pinaki Bhattacharya, Rama Govindarajan, R. Narasimha","submitted_at":"2006-04-03T10:30:32Z","abstract_excerpt":"It has hitherto been widely considered that a mixing layer is unstable at all Reynolds numbers. However this is untenable from energy considerations, which demand that there must exist a non-zero Reynolds number below which disturbances cannot extract energy from the mean flow. It is shown here that a linear stability analysis of similarity solutions of the plane mixing layer, including the effects of flow non-parallelism, using the minimal composite theory and the properties of adjoints following Govindarajan & Narasimha (2005), resolves the issue by yielding non-zero critical Reynolds number"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"physics/0604009","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"physics.flu-dyn","submitted_at":"2006-04-03T10:30:32Z","cross_cats_sorted":[],"title_canon_sha256":"e67377912c5cbf19a2d8c49028100a5dd00d6725e7ee234cd380c04943571b7c","abstract_canon_sha256":"8916d8ed5481b0805d6bd4baa6aa285c7af37b85e604559309d67e8876eaa440"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:54:40.065554Z","signature_b64":"ZbYkMEW3EsMOXP99KtPTy7AkaJCh+DVOP7DiOZ5Qdav7YlGCsnOcspIRCtB2dYSdr+0X7vYNVZKrh1t/ml90BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58f8c877ec218ddc6d963b39cad26bda063312248ddca01233588e79a8f430be","last_reissued_at":"2026-07-04T14:54:40.065183Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:54:40.065183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The critical Reynolds number of a laminar mixing layer","license":"","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"M. P. Manoharan, Pinaki Bhattacharya, Rama Govindarajan, R. Narasimha","submitted_at":"2006-04-03T10:30:32Z","abstract_excerpt":"It has hitherto been widely considered that a mixing layer is unstable at all Reynolds numbers. However this is untenable from energy considerations, which demand that there must exist a non-zero Reynolds number below which disturbances cannot extract energy from the mean flow. It is shown here that a linear stability analysis of similarity solutions of the plane mixing layer, including the effects of flow non-parallelism, using the minimal composite theory and the properties of adjoints following Govindarajan & Narasimha (2005), resolves the issue by yielding non-zero critical Reynolds number"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0604009","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/physics/0604009/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"physics/0604009","created_at":"2026-07-04T14:54:40.065242+00:00"},{"alias_kind":"arxiv_version","alias_value":"physics/0604009v1","created_at":"2026-07-04T14:54:40.065242+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0604009","created_at":"2026-07-04T14:54:40.065242+00:00"},{"alias_kind":"pith_short_12","alias_value":"LD4MQ57MEGG5","created_at":"2026-07-04T14:54:40.065242+00:00"},{"alias_kind":"pith_short_16","alias_value":"LD4MQ57MEGG5Y3MW","created_at":"2026-07-04T14:54:40.065242+00:00"},{"alias_kind":"pith_short_8","alias_value":"LD4MQ57M","created_at":"2026-07-04T14:54:40.065242+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LD4MQ57MEGG5Y3MWHM44VUTL3I","json":"https://pith.science/pith/LD4MQ57MEGG5Y3MWHM44VUTL3I.json","graph_json":"https://pith.science/api/pith-number/LD4MQ57MEGG5Y3MWHM44VUTL3I/graph.json","events_json":"https://pith.science/api/pith-number/LD4MQ57MEGG5Y3MWHM44VUTL3I/events.json","paper":"https://pith.science/paper/LD4MQ57M"},"agent_actions":{"view_html":"https://pith.science/pith/LD4MQ57MEGG5Y3MWHM44VUTL3I","download_json":"https://pith.science/pith/LD4MQ57MEGG5Y3MWHM44VUTL3I.json","view_paper":"https://pith.science/paper/LD4MQ57M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=physics/0604009&json=true","fetch_graph":"https://pith.science/api/pith-number/LD4MQ57MEGG5Y3MWHM44VUTL3I/graph.json","fetch_events":"https://pith.science/api/pith-number/LD4MQ57MEGG5Y3MWHM44VUTL3I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LD4MQ57MEGG5Y3MWHM44VUTL3I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LD4MQ57MEGG5Y3MWHM44VUTL3I/action/storage_attestation","attest_author":"https://pith.science/pith/LD4MQ57MEGG5Y3MWHM44VUTL3I/action/author_attestation","sign_citation":"https://pith.science/pith/LD4MQ57MEGG5Y3MWHM44VUTL3I/action/citation_signature","submit_replication":"https://pith.science/pith/LD4MQ57MEGG5Y3MWHM44VUTL3I/action/replication_record"}},"created_at":"2026-07-04T14:54:40.065242+00:00","updated_at":"2026-07-04T14:54:40.065242+00:00"}