{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KA2BUT55W4ZRJTIMYJONWRSKJT","short_pith_number":"pith:KA2BUT55","canonical_record":{"source":{"id":"1211.2001","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-11-08T21:55:54Z","cross_cats_sorted":["gr-qc","hep-th"],"title_canon_sha256":"d7b67e9946c767f24a0268ecea43c24c2a6fae81783df56f4d33f92e0716182b","abstract_canon_sha256":"df22c5e79bdc718ec92d12c8ad6833cc4271862052b7a21a326cd2c08496b177"},"schema_version":"1.0"},"canonical_sha256":"50341a4fbdb73314cd0cc25cdb464a4cdaa0585a91117f36a5f4b0b383ab5917","source":{"kind":"arxiv","id":"1211.2001","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2001","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2001v3","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2001","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"KA2BUT55W4ZR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KA2BUT55W4ZRJTIM","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KA2BUT55","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KA2BUT55W4ZRJTIMYJONWRSKJT","target":"record","payload":{"canonical_record":{"source":{"id":"1211.2001","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-11-08T21:55:54Z","cross_cats_sorted":["gr-qc","hep-th"],"title_canon_sha256":"d7b67e9946c767f24a0268ecea43c24c2a6fae81783df56f4d33f92e0716182b","abstract_canon_sha256":"df22c5e79bdc718ec92d12c8ad6833cc4271862052b7a21a326cd2c08496b177"},"schema_version":"1.0"},"canonical_sha256":"50341a4fbdb73314cd0cc25cdb464a4cdaa0585a91117f36a5f4b0b383ab5917","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:56.288137Z","signature_b64":"OTjx7spooaesy9fI9dTiP88WErGBQ8HwA5nVsnU9iM1Q/t76+qhwNv9Q4+JbCXDlqh6vKdMNyAThj9D+MjuxDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50341a4fbdb73314cd0cc25cdb464a4cdaa0585a91117f36a5f4b0b383ab5917","last_reissued_at":"2026-05-18T02:52:56.287429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:56.287429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.2001","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:52:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GCvw8YE2DNGv7xq2s+cyAnFX0CIhszaLwlFjkiQOv7HAdr1kCeVfMIm/ansDO9Ma3Mj3x+0k2iBhsVgmjenIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:06:50.548974Z"},"content_sha256":"6bf5c432a28b4f8df1ba7583593bea9f83c94cbcef7b93c9f8375d478b6f8096","schema_version":"1.0","event_id":"sha256:6bf5c432a28b4f8df1ba7583593bea9f83c94cbcef7b93c9f8375d478b6f8096"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KA2BUT55W4ZRJTIMYJONWRSKJT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Undulations from amplified low frequency surface waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th"],"primary_cat":"physics.flu-dyn","authors_text":"Antonin Coutant, Renaud Parentani","submitted_at":"2012-11-08T21:55:54Z","abstract_excerpt":"We study the scattering of gravity waves in longitudinal inhomogeneous stationary flows. When the flow becomes supercritical, counterflow propagating shallow waves are blocked and converted into deep waves. We show that the reflected waves are amplified in such a way that, in the zero-frequency limit, the free surface develops an undulation, i.e., a zero-frequency wave of large amplitude with nodes located at specific places. This amplification involves negative energy waves, and implies that the unperturbed flat surface is unstable against incoming perturbations of arbitrary small amplitude. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2001","kind":"arxiv","version":3},"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":"2026-05-18T02:52:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oih4BhNBBAKPmLDMi7KJfXocwAEPB6Q85Kp+uNAVN/k6wtb5tUBIGJRbtjPTTaVyHu37dfUd2ZQ+tkEffRsUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:06:50.549337Z"},"content_sha256":"e093889ec27d6b3623aad3a5846d302df426fca0bf7d9dcfc33f85c82641d7d1","schema_version":"1.0","event_id":"sha256:e093889ec27d6b3623aad3a5846d302df426fca0bf7d9dcfc33f85c82641d7d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KA2BUT55W4ZRJTIMYJONWRSKJT/bundle.json","state_url":"https://pith.science/pith/KA2BUT55W4ZRJTIMYJONWRSKJT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KA2BUT55W4ZRJTIMYJONWRSKJT/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":"2026-05-30T11:06:50Z","links":{"resolver":"https://pith.science/pith/KA2BUT55W4ZRJTIMYJONWRSKJT","bundle":"https://pith.science/pith/KA2BUT55W4ZRJTIMYJONWRSKJT/bundle.json","state":"https://pith.science/pith/KA2BUT55W4ZRJTIMYJONWRSKJT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KA2BUT55W4ZRJTIMYJONWRSKJT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KA2BUT55W4ZRJTIMYJONWRSKJT","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":"df22c5e79bdc718ec92d12c8ad6833cc4271862052b7a21a326cd2c08496b177","cross_cats_sorted":["gr-qc","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-11-08T21:55:54Z","title_canon_sha256":"d7b67e9946c767f24a0268ecea43c24c2a6fae81783df56f4d33f92e0716182b"},"schema_version":"1.0","source":{"id":"1211.2001","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2001","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2001v3","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2001","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"KA2BUT55W4ZR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KA2BUT55W4ZRJTIM","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KA2BUT55","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:e093889ec27d6b3623aad3a5846d302df426fca0bf7d9dcfc33f85c82641d7d1","target":"graph","created_at":"2026-05-18T02:52:56Z","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":"We study the scattering of gravity waves in longitudinal inhomogeneous stationary flows. When the flow becomes supercritical, counterflow propagating shallow waves are blocked and converted into deep waves. We show that the reflected waves are amplified in such a way that, in the zero-frequency limit, the free surface develops an undulation, i.e., a zero-frequency wave of large amplitude with nodes located at specific places. This amplification involves negative energy waves, and implies that the unperturbed flat surface is unstable against incoming perturbations of arbitrary small amplitude. ","authors_text":"Antonin Coutant, Renaud Parentani","cross_cats":["gr-qc","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-11-08T21:55:54Z","title":"Undulations from amplified low frequency surface waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2001","kind":"arxiv","version":3},"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":"sha256:6bf5c432a28b4f8df1ba7583593bea9f83c94cbcef7b93c9f8375d478b6f8096","target":"record","created_at":"2026-05-18T02:52:56Z","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":"df22c5e79bdc718ec92d12c8ad6833cc4271862052b7a21a326cd2c08496b177","cross_cats_sorted":["gr-qc","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-11-08T21:55:54Z","title_canon_sha256":"d7b67e9946c767f24a0268ecea43c24c2a6fae81783df56f4d33f92e0716182b"},"schema_version":"1.0","source":{"id":"1211.2001","kind":"arxiv","version":3}},"canonical_sha256":"50341a4fbdb73314cd0cc25cdb464a4cdaa0585a91117f36a5f4b0b383ab5917","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50341a4fbdb73314cd0cc25cdb464a4cdaa0585a91117f36a5f4b0b383ab5917","first_computed_at":"2026-05-18T02:52:56.287429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:56.287429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OTjx7spooaesy9fI9dTiP88WErGBQ8HwA5nVsnU9iM1Q/t76+qhwNv9Q4+JbCXDlqh6vKdMNyAThj9D+MjuxDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:56.288137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.2001","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bf5c432a28b4f8df1ba7583593bea9f83c94cbcef7b93c9f8375d478b6f8096","sha256:e093889ec27d6b3623aad3a5846d302df426fca0bf7d9dcfc33f85c82641d7d1"],"state_sha256":"3d9d391ed1fa01dde1226da00f737032bb0a2a385d061607c47ef728d21fbd00"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PTCGG42YMpdgZm5g5HhWz8p4FJJxdYdc1rnqmRXTLvlvCkG51yZFgNyYVkok7MaiDLQP1016zjPc71Z+DSZSAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T11:06:50.551536Z","bundle_sha256":"a4a72794b2e5a344d502fc9b439afb923afdff1224cf0140236f4069f47ea3d3"}}