{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OVMVKNNNGVHIFAZJLFTHBXG6I2","short_pith_number":"pith:OVMVKNNN","canonical_record":{"source":{"id":"1505.02032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-08T13:27:13Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"5f9f50c36801407930c8d1f4012a7f7d563072471042c66420bfa661fca93ea2","abstract_canon_sha256":"cf32d2e24f7cf07a142bce6766cc0322dcc6f70eb43b598c19ef3ca5f012b2cc"},"schema_version":"1.0"},"canonical_sha256":"75595535ad354e828329596670dcde46913d617863d9822874733d4a03750937","source":{"kind":"arxiv","id":"1505.02032","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02032","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02032v1","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02032","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"OVMVKNNNGVHI","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OVMVKNNNGVHIFAZJ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OVMVKNNN","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OVMVKNNNGVHIFAZJLFTHBXG6I2","target":"record","payload":{"canonical_record":{"source":{"id":"1505.02032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-08T13:27:13Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"5f9f50c36801407930c8d1f4012a7f7d563072471042c66420bfa661fca93ea2","abstract_canon_sha256":"cf32d2e24f7cf07a142bce6766cc0322dcc6f70eb43b598c19ef3ca5f012b2cc"},"schema_version":"1.0"},"canonical_sha256":"75595535ad354e828329596670dcde46913d617863d9822874733d4a03750937","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:08.556563Z","signature_b64":"trkr8lmck9qRa3uB3k1Jedj8x/FnuF9Hd0L3sF2QBKzNSgrhKkLzm0m0oAdS3bo21N9g3tx3FcI5ZaFlvfN0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75595535ad354e828329596670dcde46913d617863d9822874733d4a03750937","last_reissued_at":"2026-05-18T01:12:08.556092Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:08.556092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.02032","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":"2026-05-18T01:12:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h5tTEtSrqizwkY5A69dEBg+w2sR2vmuvZMlqsvpLLFAepwUcmeKm8KLl9ZiR0KJLOzskkyFDKaSEDzm+s/VRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:23:40.814629Z"},"content_sha256":"e8973dbf506e786adb2ce18b2bc437a266ce71868d1b7420e30683b6d98511a9","schema_version":"1.0","event_id":"sha256:e8973dbf506e786adb2ce18b2bc437a266ce71868d1b7420e30683b6d98511a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OVMVKNNNGVHIFAZJLFTHBXG6I2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the wind generation of water waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Chongchun Zeng, Jalal Shatah, Oliver Buhler, Samuel Walsh","submitted_at":"2015-05-08T13:27:13Z","abstract_excerpt":"In this work, we consider the mathematical theory of wind generated water waves. This entails determining the stability properties of the family of laminar flow solutions to the two-phase interface Euler equation. We present a rigorous derivation of the linearized evolution equations about an arbitrary steady solution, and, using this, we give a complete proof of the instability criterion of Miles. Our analysis is valid even in the presence of surface tension and a vortex sheet (discontinuity in the tangential velocity across the air--sea interface). We are thus able to give a unified equation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02032","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":"2026-05-18T01:12:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mjiW5MYmiICFNuYCsdAy9OvhqnKZwJuyf6QIJKF+soSthLNCDv7rDw9aZESQ+Ec+ebYPu0SXkn9LB+rD8tEvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:23:40.815428Z"},"content_sha256":"8adeb50b244c1a9927a7931c190ba1209ab30f6a652ef996541966bacafeae23","schema_version":"1.0","event_id":"sha256:8adeb50b244c1a9927a7931c190ba1209ab30f6a652ef996541966bacafeae23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OVMVKNNNGVHIFAZJLFTHBXG6I2/bundle.json","state_url":"https://pith.science/pith/OVMVKNNNGVHIFAZJLFTHBXG6I2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OVMVKNNNGVHIFAZJLFTHBXG6I2/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":"2026-05-31T23:23:40Z","links":{"resolver":"https://pith.science/pith/OVMVKNNNGVHIFAZJLFTHBXG6I2","bundle":"https://pith.science/pith/OVMVKNNNGVHIFAZJLFTHBXG6I2/bundle.json","state":"https://pith.science/pith/OVMVKNNNGVHIFAZJLFTHBXG6I2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OVMVKNNNGVHIFAZJLFTHBXG6I2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OVMVKNNNGVHIFAZJLFTHBXG6I2","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":"cf32d2e24f7cf07a142bce6766cc0322dcc6f70eb43b598c19ef3ca5f012b2cc","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-08T13:27:13Z","title_canon_sha256":"5f9f50c36801407930c8d1f4012a7f7d563072471042c66420bfa661fca93ea2"},"schema_version":"1.0","source":{"id":"1505.02032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02032","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02032v1","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02032","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"OVMVKNNNGVHI","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OVMVKNNNGVHIFAZJ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OVMVKNNN","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:8adeb50b244c1a9927a7931c190ba1209ab30f6a652ef996541966bacafeae23","target":"graph","created_at":"2026-05-18T01:12:08Z","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 work, we consider the mathematical theory of wind generated water waves. This entails determining the stability properties of the family of laminar flow solutions to the two-phase interface Euler equation. We present a rigorous derivation of the linearized evolution equations about an arbitrary steady solution, and, using this, we give a complete proof of the instability criterion of Miles. Our analysis is valid even in the presence of surface tension and a vortex sheet (discontinuity in the tangential velocity across the air--sea interface). We are thus able to give a unified equation","authors_text":"Chongchun Zeng, Jalal Shatah, Oliver Buhler, Samuel Walsh","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-08T13:27:13Z","title":"On the wind generation of water waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02032","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:e8973dbf506e786adb2ce18b2bc437a266ce71868d1b7420e30683b6d98511a9","target":"record","created_at":"2026-05-18T01:12:08Z","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":"cf32d2e24f7cf07a142bce6766cc0322dcc6f70eb43b598c19ef3ca5f012b2cc","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-08T13:27:13Z","title_canon_sha256":"5f9f50c36801407930c8d1f4012a7f7d563072471042c66420bfa661fca93ea2"},"schema_version":"1.0","source":{"id":"1505.02032","kind":"arxiv","version":1}},"canonical_sha256":"75595535ad354e828329596670dcde46913d617863d9822874733d4a03750937","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75595535ad354e828329596670dcde46913d617863d9822874733d4a03750937","first_computed_at":"2026-05-18T01:12:08.556092Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:08.556092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"trkr8lmck9qRa3uB3k1Jedj8x/FnuF9Hd0L3sF2QBKzNSgrhKkLzm0m0oAdS3bo21N9g3tx3FcI5ZaFlvfN0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:08.556563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8973dbf506e786adb2ce18b2bc437a266ce71868d1b7420e30683b6d98511a9","sha256:8adeb50b244c1a9927a7931c190ba1209ab30f6a652ef996541966bacafeae23"],"state_sha256":"750bba7908467062c1fc2136e4b1c25c672a53097720e1380c87b8af8aa53d84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hdZA2/pjGiOuiaRwQMyUnk3mb2zPnHQ5HU2KsSPBxAsIwpe0HmV58bIqs2MYPq+JEwuW3Q6aXTKSUo6kxcJACw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:23:40.819627Z","bundle_sha256":"33937133d90d2b2a5b024661c666fb2fe06a4a79bf4e0ff8b111c2fad5c95ec0"}}