{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VVBE5MR2TMA5ZAOD2XJKVPOEWY","short_pith_number":"pith:VVBE5MR2","canonical_record":{"source":{"id":"1507.07286","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-07-27T03:12:21Z","cross_cats_sorted":["astro-ph.SR"],"title_canon_sha256":"fbb796d55681ada041b8fca3f793b039a386cb9fa7b357089fe6d9826349ed51","abstract_canon_sha256":"080b8942c3dc50972a5ad8effb4cfae8883ddd24e08c4c63f54668211e1f5dbf"},"schema_version":"1.0"},"canonical_sha256":"ad424eb23a9b01dc81c3d5d2aabdc4b63f0b1cd39e5264eb1ce62920215a77f3","source":{"kind":"arxiv","id":"1507.07286","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07286","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07286v1","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07286","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"VVBE5MR2TMA5","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VVBE5MR2TMA5ZAOD","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VVBE5MR2","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VVBE5MR2TMA5ZAOD2XJKVPOEWY","target":"record","payload":{"canonical_record":{"source":{"id":"1507.07286","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-07-27T03:12:21Z","cross_cats_sorted":["astro-ph.SR"],"title_canon_sha256":"fbb796d55681ada041b8fca3f793b039a386cb9fa7b357089fe6d9826349ed51","abstract_canon_sha256":"080b8942c3dc50972a5ad8effb4cfae8883ddd24e08c4c63f54668211e1f5dbf"},"schema_version":"1.0"},"canonical_sha256":"ad424eb23a9b01dc81c3d5d2aabdc4b63f0b1cd39e5264eb1ce62920215a77f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:15.247796Z","signature_b64":"L/xbgQV0yTOvQgOfr3+MqWvSzfAc/MfP8hBKLY+/+7aP6wL1bL2wH11wHsNMJu1c58fry0RRwC9iabx+eZX+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad424eb23a9b01dc81c3d5d2aabdc4b63f0b1cd39e5264eb1ce62920215a77f3","last_reissued_at":"2026-05-18T01:34:15.247162Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:15.247162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.07286","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":"2026-05-18T01:34:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5zfYvdDVqnmZ/gHha0KjHzmJ84OSMgvWcbB3C7CAHRFvCGmRl3LqhGxlCugNmMDiEQ5KmpJfa0POjBWN/kBtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:05:25.660232Z"},"content_sha256":"5f0077b7b25611d3547aa224d21d8f8e320779b86c36b0f07df1d3defbe551af","schema_version":"1.0","event_id":"sha256:5f0077b7b25611d3547aa224d21d8f8e320779b86c36b0f07df1d3defbe551af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VVBE5MR2TMA5ZAOD2XJKVPOEWY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The stability of stratified spatially periodic shear flows at low P\\'eclet number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.SR"],"primary_cat":"physics.flu-dyn","authors_text":"Basile Gallet, Pascale Garaud, Tobias Bischoff","submitted_at":"2015-07-27T03:12:21Z","abstract_excerpt":"This work addresses the question of the stability of stratified, spatially periodic shear flows at low P\\'eclet number but high Reynolds number. This little-studied limit is motivated by astrophysical systems, where the Prandtl number is often very small. Furthermore, it can be studied using a reduced set of \"low-P\\'eclet-number equations\" proposed by Lignieres [Astronomy & Astrophysics, 348, 933-939, 1999]. Through a linear stability analysis, we first determine the conditions for instability to infinitesimal perturbations. We formally extend Squire's theorem to the low-P\\'eclet-number equati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07286","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":"2026-05-18T01:34:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vNODdYXxIHRQ7r6NC1tdLXyErxcxnhQ9cGb7+EzVTfyvz94IF/WrnPK5VZvjBzv+/kWK5Tppdbf0UCz/vKF5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:05:25.660747Z"},"content_sha256":"1e807f059e9f202278e00cb870800a4b1c79d42e13b2ce2065c10fc682118287","schema_version":"1.0","event_id":"sha256:1e807f059e9f202278e00cb870800a4b1c79d42e13b2ce2065c10fc682118287"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VVBE5MR2TMA5ZAOD2XJKVPOEWY/bundle.json","state_url":"https://pith.science/pith/VVBE5MR2TMA5ZAOD2XJKVPOEWY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VVBE5MR2TMA5ZAOD2XJKVPOEWY/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":"2026-06-05T20:05:25Z","links":{"resolver":"https://pith.science/pith/VVBE5MR2TMA5ZAOD2XJKVPOEWY","bundle":"https://pith.science/pith/VVBE5MR2TMA5ZAOD2XJKVPOEWY/bundle.json","state":"https://pith.science/pith/VVBE5MR2TMA5ZAOD2XJKVPOEWY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VVBE5MR2TMA5ZAOD2XJKVPOEWY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VVBE5MR2TMA5ZAOD2XJKVPOEWY","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":"080b8942c3dc50972a5ad8effb4cfae8883ddd24e08c4c63f54668211e1f5dbf","cross_cats_sorted":["astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-07-27T03:12:21Z","title_canon_sha256":"fbb796d55681ada041b8fca3f793b039a386cb9fa7b357089fe6d9826349ed51"},"schema_version":"1.0","source":{"id":"1507.07286","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07286","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07286v1","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07286","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"VVBE5MR2TMA5","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VVBE5MR2TMA5ZAOD","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VVBE5MR2","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:1e807f059e9f202278e00cb870800a4b1c79d42e13b2ce2065c10fc682118287","target":"graph","created_at":"2026-05-18T01:34:15Z","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":"This work addresses the question of the stability of stratified, spatially periodic shear flows at low P\\'eclet number but high Reynolds number. This little-studied limit is motivated by astrophysical systems, where the Prandtl number is often very small. Furthermore, it can be studied using a reduced set of \"low-P\\'eclet-number equations\" proposed by Lignieres [Astronomy & Astrophysics, 348, 933-939, 1999]. Through a linear stability analysis, we first determine the conditions for instability to infinitesimal perturbations. We formally extend Squire's theorem to the low-P\\'eclet-number equati","authors_text":"Basile Gallet, Pascale Garaud, Tobias Bischoff","cross_cats":["astro-ph.SR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-07-27T03:12:21Z","title":"The stability of stratified spatially periodic shear flows at low P\\'eclet number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07286","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":"sha256:5f0077b7b25611d3547aa224d21d8f8e320779b86c36b0f07df1d3defbe551af","target":"record","created_at":"2026-05-18T01:34:15Z","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":"080b8942c3dc50972a5ad8effb4cfae8883ddd24e08c4c63f54668211e1f5dbf","cross_cats_sorted":["astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-07-27T03:12:21Z","title_canon_sha256":"fbb796d55681ada041b8fca3f793b039a386cb9fa7b357089fe6d9826349ed51"},"schema_version":"1.0","source":{"id":"1507.07286","kind":"arxiv","version":1}},"canonical_sha256":"ad424eb23a9b01dc81c3d5d2aabdc4b63f0b1cd39e5264eb1ce62920215a77f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad424eb23a9b01dc81c3d5d2aabdc4b63f0b1cd39e5264eb1ce62920215a77f3","first_computed_at":"2026-05-18T01:34:15.247162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:15.247162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L/xbgQV0yTOvQgOfr3+MqWvSzfAc/MfP8hBKLY+/+7aP6wL1bL2wH11wHsNMJu1c58fry0RRwC9iabx+eZX+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:15.247796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.07286","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f0077b7b25611d3547aa224d21d8f8e320779b86c36b0f07df1d3defbe551af","sha256:1e807f059e9f202278e00cb870800a4b1c79d42e13b2ce2065c10fc682118287"],"state_sha256":"e4e576390a9de40ba4a363f3523713827e78db0e96846c99158dff7e0c71ece5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QoEz6WuZsu1W4mSuxium+d9YJ/TuQW/z70oafN6FlC8SbYmDl+JUM0GgYelpVHR+wO5nntlYtGwz/Rb1viHcCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:05:25.664744Z","bundle_sha256":"6a84e02b545ea9687cdcacc16d37888d95142ab86ca7df28456983cd262f667a"}}