{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:ITQ6WULMHRXLBJ5276TTC5WXWF","short_pith_number":"pith:ITQ6WULM","canonical_record":{"source":{"id":"2402.11115","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2024-02-16T22:40:15Z","cross_cats_sorted":[],"title_canon_sha256":"50115398cccc4bf97c091eb2babd4d5ffd6961692d3dba8b2ae8ce66e2f2342b","abstract_canon_sha256":"f9f56fc80f61e3699f221f36feab2c9d10ed11936370cc500265a83b04ff843e"},"schema_version":"1.0"},"canonical_sha256":"44e1eb516c3c6eb0a7baffa73176d7b15173e26a276504e006972b86de0bd72f","source":{"kind":"arxiv","id":"2402.11115","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.11115","created_at":"2026-07-05T07:46:34Z"},{"alias_kind":"arxiv_version","alias_value":"2402.11115v1","created_at":"2026-07-05T07:46:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.11115","created_at":"2026-07-05T07:46:34Z"},{"alias_kind":"pith_short_12","alias_value":"ITQ6WULMHRXL","created_at":"2026-07-05T07:46:34Z"},{"alias_kind":"pith_short_16","alias_value":"ITQ6WULMHRXLBJ52","created_at":"2026-07-05T07:46:34Z"},{"alias_kind":"pith_short_8","alias_value":"ITQ6WULM","created_at":"2026-07-05T07:46:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:ITQ6WULMHRXLBJ5276TTC5WXWF","target":"record","payload":{"canonical_record":{"source":{"id":"2402.11115","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2024-02-16T22:40:15Z","cross_cats_sorted":[],"title_canon_sha256":"50115398cccc4bf97c091eb2babd4d5ffd6961692d3dba8b2ae8ce66e2f2342b","abstract_canon_sha256":"f9f56fc80f61e3699f221f36feab2c9d10ed11936370cc500265a83b04ff843e"},"schema_version":"1.0"},"canonical_sha256":"44e1eb516c3c6eb0a7baffa73176d7b15173e26a276504e006972b86de0bd72f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:46:34.267511Z","signature_b64":"BEdYg8VWIOrGQ6DulH1WzVfP3yzraxiQfxLvrZhPHDP62YKLzcdlAjSbzHwctaQgXQOgWL02L6P3zGfkq6CoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44e1eb516c3c6eb0a7baffa73176d7b15173e26a276504e006972b86de0bd72f","last_reissued_at":"2026-07-05T07:46:34.267047Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:46:34.267047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.11115","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":"2026-07-05T07:46:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zw2oAhSFfkFlAvOpK8EGX6NXWprDikSu4AYw2dykKztztZ4B11gWFyZcN+nB6T3uH1ft125/GrTKDtlX7QTpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T00:23:57.374768Z"},"content_sha256":"839f0b4dd111a4313c66c07a36822024fe0d386be6d985920a231072d2fcffc8","schema_version":"1.0","event_id":"sha256:839f0b4dd111a4313c66c07a36822024fe0d386be6d985920a231072d2fcffc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:ITQ6WULMHRXLBJ5276TTC5WXWF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transverse linear stability of one-dimensional solitary gravity water waves","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changzhen Sun (LMB), Fr\\'ed\\'eric Rousset (LMO)","submitted_at":"2024-02-16T22:40:15Z","abstract_excerpt":"In this paper, we establish the transverse linear asymptotic stability of one-dimensional small-amplitude solitary waves of the gravity water-waves system. More precisely, we show that the semigroup of the linearized operator about the solitary wave decays exponentially within a spectral subspace supplementary to the space generated by the spectral projection on continuous resonant modes. The key element of the proof is to establish suitable uniform resolvent estimates. To achieve this, we use different arguments depending on the size of the transverse frequencies. For high transverse frequenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.11115","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.11115/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":"2026-07-05T07:46:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g2vw5ePfjt3jkrN/1aTgaWkkuaNjztp3lzCcGTubdZEeI9N4i1fnD9KL/RohsqCNoALg54O+ydRAXoR5V69ACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T00:23:57.375562Z"},"content_sha256":"e94ae8c81d3e2bc5c3dd00fedd41bb03bb436dee774e0d463f15e4a1f16e6c6b","schema_version":"1.0","event_id":"sha256:e94ae8c81d3e2bc5c3dd00fedd41bb03bb436dee774e0d463f15e4a1f16e6c6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ITQ6WULMHRXLBJ5276TTC5WXWF/bundle.json","state_url":"https://pith.science/pith/ITQ6WULMHRXLBJ5276TTC5WXWF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ITQ6WULMHRXLBJ5276TTC5WXWF/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":"2026-08-18T00:23:57Z","links":{"resolver":"https://pith.science/pith/ITQ6WULMHRXLBJ5276TTC5WXWF","bundle":"https://pith.science/pith/ITQ6WULMHRXLBJ5276TTC5WXWF/bundle.json","state":"https://pith.science/pith/ITQ6WULMHRXLBJ5276TTC5WXWF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ITQ6WULMHRXLBJ5276TTC5WXWF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ITQ6WULMHRXLBJ5276TTC5WXWF","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":"f9f56fc80f61e3699f221f36feab2c9d10ed11936370cc500265a83b04ff843e","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2024-02-16T22:40:15Z","title_canon_sha256":"50115398cccc4bf97c091eb2babd4d5ffd6961692d3dba8b2ae8ce66e2f2342b"},"schema_version":"1.0","source":{"id":"2402.11115","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.11115","created_at":"2026-07-05T07:46:34Z"},{"alias_kind":"arxiv_version","alias_value":"2402.11115v1","created_at":"2026-07-05T07:46:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.11115","created_at":"2026-07-05T07:46:34Z"},{"alias_kind":"pith_short_12","alias_value":"ITQ6WULMHRXL","created_at":"2026-07-05T07:46:34Z"},{"alias_kind":"pith_short_16","alias_value":"ITQ6WULMHRXLBJ52","created_at":"2026-07-05T07:46:34Z"},{"alias_kind":"pith_short_8","alias_value":"ITQ6WULM","created_at":"2026-07-05T07:46:34Z"}],"graph_snapshots":[{"event_id":"sha256:e94ae8c81d3e2bc5c3dd00fedd41bb03bb436dee774e0d463f15e4a1f16e6c6b","target":"graph","created_at":"2026-07-05T07:46:34Z","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/2402.11115/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we establish the transverse linear asymptotic stability of one-dimensional small-amplitude solitary waves of the gravity water-waves system. More precisely, we show that the semigroup of the linearized operator about the solitary wave decays exponentially within a spectral subspace supplementary to the space generated by the spectral projection on continuous resonant modes. The key element of the proof is to establish suitable uniform resolvent estimates. To achieve this, we use different arguments depending on the size of the transverse frequencies. For high transverse frequenc","authors_text":"Changzhen Sun (LMB), Fr\\'ed\\'eric Rousset (LMO)","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2024-02-16T22:40:15Z","title":"Transverse linear stability of one-dimensional solitary gravity water waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.11115","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":"sha256:839f0b4dd111a4313c66c07a36822024fe0d386be6d985920a231072d2fcffc8","target":"record","created_at":"2026-07-05T07:46:34Z","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":"f9f56fc80f61e3699f221f36feab2c9d10ed11936370cc500265a83b04ff843e","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2024-02-16T22:40:15Z","title_canon_sha256":"50115398cccc4bf97c091eb2babd4d5ffd6961692d3dba8b2ae8ce66e2f2342b"},"schema_version":"1.0","source":{"id":"2402.11115","kind":"arxiv","version":1}},"canonical_sha256":"44e1eb516c3c6eb0a7baffa73176d7b15173e26a276504e006972b86de0bd72f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44e1eb516c3c6eb0a7baffa73176d7b15173e26a276504e006972b86de0bd72f","first_computed_at":"2026-07-05T07:46:34.267047Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:46:34.267047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BEdYg8VWIOrGQ6DulH1WzVfP3yzraxiQfxLvrZhPHDP62YKLzcdlAjSbzHwctaQgXQOgWL02L6P3zGfkq6CoAA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:46:34.267511Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.11115","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:839f0b4dd111a4313c66c07a36822024fe0d386be6d985920a231072d2fcffc8","sha256:e94ae8c81d3e2bc5c3dd00fedd41bb03bb436dee774e0d463f15e4a1f16e6c6b"],"state_sha256":"2d08bc16b9e086600ed9c96976d601f7dbf53a4c44c160e006ed1d5834c9e8cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UtmY0kQ8W42j+IEwwPuzMX7zTvZ2HRivWZ6eyEhZsWsWoHQSS7Lvs0IW5efPxBYdAjVHBWHjOvLbR64wOmn9Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T00:23:57.389117Z","bundle_sha256":"b758ec47ce6b5d312885b0179dc8cfe1444c3701fee5eb45b0145dbebeff5f22"}}