{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:3WOFAZWU32NPR4ULWWRDK7RGPZ","short_pith_number":"pith:3WOFAZWU","canonical_record":{"source":{"id":"2212.12827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-12-24T23:05:35Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"b5c738958fa2ab150f45d796230316004faeb746bc89fcc6b764ec10ce2d9db0","abstract_canon_sha256":"9ebe110ac214ad6e86b2b18bf820a6c73532254a084ef324dc770f70b9cc12f0"},"schema_version":"1.0"},"canonical_sha256":"dd9c5066d4de9af8f28bb5a2357e267e6c17dd754a96df667e32434aab8de8c3","source":{"kind":"arxiv","id":"2212.12827","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.12827","created_at":"2026-07-05T11:45:26Z"},{"alias_kind":"arxiv_version","alias_value":"2212.12827v2","created_at":"2026-07-05T11:45:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.12827","created_at":"2026-07-05T11:45:26Z"},{"alias_kind":"pith_short_12","alias_value":"3WOFAZWU32NP","created_at":"2026-07-05T11:45:26Z"},{"alias_kind":"pith_short_16","alias_value":"3WOFAZWU32NPR4UL","created_at":"2026-07-05T11:45:26Z"},{"alias_kind":"pith_short_8","alias_value":"3WOFAZWU","created_at":"2026-07-05T11:45:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:3WOFAZWU32NPR4ULWWRDK7RGPZ","target":"record","payload":{"canonical_record":{"source":{"id":"2212.12827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-12-24T23:05:35Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"b5c738958fa2ab150f45d796230316004faeb746bc89fcc6b764ec10ce2d9db0","abstract_canon_sha256":"9ebe110ac214ad6e86b2b18bf820a6c73532254a084ef324dc770f70b9cc12f0"},"schema_version":"1.0"},"canonical_sha256":"dd9c5066d4de9af8f28bb5a2357e267e6c17dd754a96df667e32434aab8de8c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:45:26.402547Z","signature_b64":"TkqPyGjDIvO9Obicb7SceNPLQDDcj+PombS9ELHrruR3bHhveJaXzEExFDWZaB1DUlZ4bjFo/w8FkAP/D5n1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd9c5066d4de9af8f28bb5a2357e267e6c17dd754a96df667e32434aab8de8c3","last_reissued_at":"2026-07-05T11:45:26.402118Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:45:26.402118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.12827","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":"2026-07-05T11:45:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u+NX39P97Exi0phPhFyKFDNv4Z1ARdNcQAzofeycG87uSKfCpxIdygYWs5vJ9vBaeGNyJwDDsz6tmiLdUEEACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:47:27.252235Z"},"content_sha256":"084c6152038aacc348921b0fbe84045f8cf4ab577ec940041b1ed43be0e30c99","schema_version":"1.0","event_id":"sha256:084c6152038aacc348921b0fbe84045f8cf4ab577ec940041b1ed43be0e30c99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:3WOFAZWU32NPR4ULWWRDK7RGPZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the stability of symmetric flows in a two-dimensional channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Bernard Helffer, Yaniv Almog","submitted_at":"2022-12-24T23:05:35Z","abstract_excerpt":"We consider the stability of symmetric flows in a two-dimensional\n  channel (including the Poiseuille flow). In 2015 Grenier, Guo, and\n  Nguyen have established instability of these flows in a particular\n  region of the parameter space, affirming formal asymptotics results\n  from the 1940's. We prove that these flows are stable outside this\n  region in parameter space. More precisely we show that the\n  Orr-Sommerfeld operator\n  $$ {\\mathcal B} =\\Big(-\\frac{d^2}{dx^2}+i\\beta(U+i\\lambda)\\Big)\\Big(\\frac{d^2}{dx^2}-\\alpha^2\\Big) -i\\beta U^{\\prime\\prime}\\,, $$\n  which is defined on $$\n  D({\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.12827","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.12827/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:45:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yK4YXHWnOXgfpXOPoMn5uXM+RVAVtCzRQv5XPLXWo0s1RvJ9BDNPL90kNVtgUFgzxnlzuFQzPxfwBrl2+5/OCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:47:27.253164Z"},"content_sha256":"b4592ed7af2548e98bb25e064e6b961970d06d8d20b86066b3f268312cc6d98c","schema_version":"1.0","event_id":"sha256:b4592ed7af2548e98bb25e064e6b961970d06d8d20b86066b3f268312cc6d98c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3WOFAZWU32NPR4ULWWRDK7RGPZ/bundle.json","state_url":"https://pith.science/pith/3WOFAZWU32NPR4ULWWRDK7RGPZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3WOFAZWU32NPR4ULWWRDK7RGPZ/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":"2026-08-12T07:47:27Z","links":{"resolver":"https://pith.science/pith/3WOFAZWU32NPR4ULWWRDK7RGPZ","bundle":"https://pith.science/pith/3WOFAZWU32NPR4ULWWRDK7RGPZ/bundle.json","state":"https://pith.science/pith/3WOFAZWU32NPR4ULWWRDK7RGPZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3WOFAZWU32NPR4ULWWRDK7RGPZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:3WOFAZWU32NPR4ULWWRDK7RGPZ","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":"9ebe110ac214ad6e86b2b18bf820a6c73532254a084ef324dc770f70b9cc12f0","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-12-24T23:05:35Z","title_canon_sha256":"b5c738958fa2ab150f45d796230316004faeb746bc89fcc6b764ec10ce2d9db0"},"schema_version":"1.0","source":{"id":"2212.12827","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.12827","created_at":"2026-07-05T11:45:26Z"},{"alias_kind":"arxiv_version","alias_value":"2212.12827v2","created_at":"2026-07-05T11:45:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.12827","created_at":"2026-07-05T11:45:26Z"},{"alias_kind":"pith_short_12","alias_value":"3WOFAZWU32NP","created_at":"2026-07-05T11:45:26Z"},{"alias_kind":"pith_short_16","alias_value":"3WOFAZWU32NPR4UL","created_at":"2026-07-05T11:45:26Z"},{"alias_kind":"pith_short_8","alias_value":"3WOFAZWU","created_at":"2026-07-05T11:45:26Z"}],"graph_snapshots":[{"event_id":"sha256:b4592ed7af2548e98bb25e064e6b961970d06d8d20b86066b3f268312cc6d98c","target":"graph","created_at":"2026-07-05T11:45:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2212.12827/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the stability of symmetric flows in a two-dimensional\n  channel (including the Poiseuille flow). In 2015 Grenier, Guo, and\n  Nguyen have established instability of these flows in a particular\n  region of the parameter space, affirming formal asymptotics results\n  from the 1940's. We prove that these flows are stable outside this\n  region in parameter space. More precisely we show that the\n  Orr-Sommerfeld operator\n  $$ {\\mathcal B} =\\Big(-\\frac{d^2}{dx^2}+i\\beta(U+i\\lambda)\\Big)\\Big(\\frac{d^2}{dx^2}-\\alpha^2\\Big) -i\\beta U^{\\prime\\prime}\\,, $$\n  which is defined on $$\n  D({\\mathcal","authors_text":"Bernard Helffer, Yaniv Almog","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-12-24T23:05:35Z","title":"On the stability of symmetric flows in a two-dimensional channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.12827","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":"sha256:084c6152038aacc348921b0fbe84045f8cf4ab577ec940041b1ed43be0e30c99","target":"record","created_at":"2026-07-05T11:45:26Z","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":"9ebe110ac214ad6e86b2b18bf820a6c73532254a084ef324dc770f70b9cc12f0","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-12-24T23:05:35Z","title_canon_sha256":"b5c738958fa2ab150f45d796230316004faeb746bc89fcc6b764ec10ce2d9db0"},"schema_version":"1.0","source":{"id":"2212.12827","kind":"arxiv","version":2}},"canonical_sha256":"dd9c5066d4de9af8f28bb5a2357e267e6c17dd754a96df667e32434aab8de8c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd9c5066d4de9af8f28bb5a2357e267e6c17dd754a96df667e32434aab8de8c3","first_computed_at":"2026-07-05T11:45:26.402118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:45:26.402118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TkqPyGjDIvO9Obicb7SceNPLQDDcj+PombS9ELHrruR3bHhveJaXzEExFDWZaB1DUlZ4bjFo/w8FkAP/D5n1CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:45:26.402547Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.12827","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:084c6152038aacc348921b0fbe84045f8cf4ab577ec940041b1ed43be0e30c99","sha256:b4592ed7af2548e98bb25e064e6b961970d06d8d20b86066b3f268312cc6d98c"],"state_sha256":"6ea5bfb0f9765563bb257f373e42b121469a3f1f8fa4c88d5c663bfa1ee17824"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2kF2znLWvbagQX5nEibgdWX+19TBnNDqKjtyAE7UNpJV8IPOiizf8m5G2qs+euQhnrYJzTUWNQ3BHyL+kpt/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T07:47:27.262074Z","bundle_sha256":"c4ca5cd3b73cba9e52cee0ebb5ae2c7aa9b5f418dc8c51f775e2277b67f764bb"}}