{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:TEG3IG2ATZGH27LV3VJMI3V3MO","short_pith_number":"pith:TEG3IG2A","canonical_record":{"source":{"id":"2309.08445","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-15T14:47:20Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"75ce38d3ba4c64fa845c7f884aaa6f7870221da6a2b272e3fd73218cc6ae55fa","abstract_canon_sha256":"7a6124da45a4f427dffd0d1d2cb6a5414cbbe452d1f43285f0b3401498a26ae0"},"schema_version":"1.0"},"canonical_sha256":"990db41b409e4c7d7d75dd52c46ebb63a471fb653a129400e10e6a2c483027f2","source":{"kind":"arxiv","id":"2309.08445","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.08445","created_at":"2026-07-05T06:52:07Z"},{"alias_kind":"arxiv_version","alias_value":"2309.08445v2","created_at":"2026-07-05T06:52:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.08445","created_at":"2026-07-05T06:52:07Z"},{"alias_kind":"pith_short_12","alias_value":"TEG3IG2ATZGH","created_at":"2026-07-05T06:52:07Z"},{"alias_kind":"pith_short_16","alias_value":"TEG3IG2ATZGH27LV","created_at":"2026-07-05T06:52:07Z"},{"alias_kind":"pith_short_8","alias_value":"TEG3IG2A","created_at":"2026-07-05T06:52:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:TEG3IG2ATZGH27LV3VJMI3V3MO","target":"record","payload":{"canonical_record":{"source":{"id":"2309.08445","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-15T14:47:20Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"75ce38d3ba4c64fa845c7f884aaa6f7870221da6a2b272e3fd73218cc6ae55fa","abstract_canon_sha256":"7a6124da45a4f427dffd0d1d2cb6a5414cbbe452d1f43285f0b3401498a26ae0"},"schema_version":"1.0"},"canonical_sha256":"990db41b409e4c7d7d75dd52c46ebb63a471fb653a129400e10e6a2c483027f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:52:07.975403Z","signature_b64":"ZQjJf/mMqhg9s8/T3jk9/Wm2ozi73Aceurmxo8Dhs3Izjva3DJFCjBZIwW1mUHXKWmpCqZFtqiGaS33AtBbpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"990db41b409e4c7d7d75dd52c46ebb63a471fb653a129400e10e6a2c483027f2","last_reissued_at":"2026-07-05T06:52:07.974937Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:52:07.974937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.08445","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":"2026-07-05T06:52:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tJZpVwDz9Xld5yQ0hYXIBqSVxkBJgZ4j8jN++DdJNlbp7VjSlGjCRWeD+/glMc7zCLaaPCgvvYqCmJLj/BhjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T00:03:36.676382Z"},"content_sha256":"94b04af062a912cc44b77680e7eac2b517b2b2a9a67a64449c37fa8467155380","schema_version":"1.0","event_id":"sha256:94b04af062a912cc44b77680e7eac2b517b2b2a9a67a64449c37fa8467155380"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:TEG3IG2ATZGH27LV3VJMI3V3MO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limiting absorption principles and linear inviscid damping in the Euler-Boussinesq system in the periodic channel","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Marc Nualart, Michele Coti Zelati","submitted_at":"2023-09-15T14:47:20Z","abstract_excerpt":"We consider the long-time behavior of solutions to the two dimensional non-homogeneous Euler equations under the Boussinesq approximation posed on a periodic channel. We study the linearized system near a linearly stratified Couette flow and prove inviscid damping of the perturbed density and velocity field for any positive Richardson number, with optimal rates. Our methods are based on time-decay properties of oscillatory integrals obtained using a limiting absorption principle, and require a careful understanding of the asymptotic expansion of the generalized eigenfunction near the critical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.08445","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/2309.08445/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":"2026-07-05T06:52:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YfVxKbk81O1K7vbZXtocGkwxqofBibTiiCfo72U1QLaeili1onC+tJTwvQ/a9lESZMkqLFSZTvF/sneS5jl/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T00:03:36.676915Z"},"content_sha256":"73dda60aacd2b1de7200756641e210910abde2fd42712a5ff8c162ad4f5300a6","schema_version":"1.0","event_id":"sha256:73dda60aacd2b1de7200756641e210910abde2fd42712a5ff8c162ad4f5300a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TEG3IG2ATZGH27LV3VJMI3V3MO/bundle.json","state_url":"https://pith.science/pith/TEG3IG2ATZGH27LV3VJMI3V3MO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TEG3IG2ATZGH27LV3VJMI3V3MO/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":"2026-08-22T00:03:36Z","links":{"resolver":"https://pith.science/pith/TEG3IG2ATZGH27LV3VJMI3V3MO","bundle":"https://pith.science/pith/TEG3IG2ATZGH27LV3VJMI3V3MO/bundle.json","state":"https://pith.science/pith/TEG3IG2ATZGH27LV3VJMI3V3MO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TEG3IG2ATZGH27LV3VJMI3V3MO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:TEG3IG2ATZGH27LV3VJMI3V3MO","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":"7a6124da45a4f427dffd0d1d2cb6a5414cbbe452d1f43285f0b3401498a26ae0","cross_cats_sorted":["physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-15T14:47:20Z","title_canon_sha256":"75ce38d3ba4c64fa845c7f884aaa6f7870221da6a2b272e3fd73218cc6ae55fa"},"schema_version":"1.0","source":{"id":"2309.08445","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.08445","created_at":"2026-07-05T06:52:07Z"},{"alias_kind":"arxiv_version","alias_value":"2309.08445v2","created_at":"2026-07-05T06:52:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.08445","created_at":"2026-07-05T06:52:07Z"},{"alias_kind":"pith_short_12","alias_value":"TEG3IG2ATZGH","created_at":"2026-07-05T06:52:07Z"},{"alias_kind":"pith_short_16","alias_value":"TEG3IG2ATZGH27LV","created_at":"2026-07-05T06:52:07Z"},{"alias_kind":"pith_short_8","alias_value":"TEG3IG2A","created_at":"2026-07-05T06:52:07Z"}],"graph_snapshots":[{"event_id":"sha256:73dda60aacd2b1de7200756641e210910abde2fd42712a5ff8c162ad4f5300a6","target":"graph","created_at":"2026-07-05T06:52:07Z","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/2309.08445/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the long-time behavior of solutions to the two dimensional non-homogeneous Euler equations under the Boussinesq approximation posed on a periodic channel. We study the linearized system near a linearly stratified Couette flow and prove inviscid damping of the perturbed density and velocity field for any positive Richardson number, with optimal rates. Our methods are based on time-decay properties of oscillatory integrals obtained using a limiting absorption principle, and require a careful understanding of the asymptotic expansion of the generalized eigenfunction near the critical ","authors_text":"Marc Nualart, Michele Coti Zelati","cross_cats":["physics.flu-dyn"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-15T14:47:20Z","title":"Limiting absorption principles and linear inviscid damping in the Euler-Boussinesq system in the periodic channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.08445","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":"sha256:94b04af062a912cc44b77680e7eac2b517b2b2a9a67a64449c37fa8467155380","target":"record","created_at":"2026-07-05T06:52:07Z","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":"7a6124da45a4f427dffd0d1d2cb6a5414cbbe452d1f43285f0b3401498a26ae0","cross_cats_sorted":["physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-15T14:47:20Z","title_canon_sha256":"75ce38d3ba4c64fa845c7f884aaa6f7870221da6a2b272e3fd73218cc6ae55fa"},"schema_version":"1.0","source":{"id":"2309.08445","kind":"arxiv","version":2}},"canonical_sha256":"990db41b409e4c7d7d75dd52c46ebb63a471fb653a129400e10e6a2c483027f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"990db41b409e4c7d7d75dd52c46ebb63a471fb653a129400e10e6a2c483027f2","first_computed_at":"2026-07-05T06:52:07.974937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:52:07.974937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZQjJf/mMqhg9s8/T3jk9/Wm2ozi73Aceurmxo8Dhs3Izjva3DJFCjBZIwW1mUHXKWmpCqZFtqiGaS33AtBbpAw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:52:07.975403Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.08445","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94b04af062a912cc44b77680e7eac2b517b2b2a9a67a64449c37fa8467155380","sha256:73dda60aacd2b1de7200756641e210910abde2fd42712a5ff8c162ad4f5300a6"],"state_sha256":"90310f6ce915c76b85a53eb11b21623024d0f811359526b105454bdad1cb4dc7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WH4ci/TeWecJjiO12fJiCKTSqAqeGt7N78i1iE7aYp/XqHOB8PREjukD2zRS29JnX5iSzM7NsYCCByK8IQchAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T00:03:36.681837Z","bundle_sha256":"ab665a803dd73e698e4dfe2e5704e7e231f5fedb664ad841f93c7407f7a0702a"}}