{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JWT6DF2G2OSEM5Q62WUNFMSSYN","short_pith_number":"pith:JWT6DF2G","canonical_record":{"source":{"id":"1104.2555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-13T17:12:21Z","cross_cats_sorted":[],"title_canon_sha256":"4d11c701cba946f1641387c15a0ccc3ef8a4812b781f9048ade71691b6c9a8c6","abstract_canon_sha256":"22fff0769044c06535856cefe849625e3f94043b4ffe9df76c6371b60485be07"},"schema_version":"1.0"},"canonical_sha256":"4da7e19746d3a446761ed5a8d2b252c34e7cb88e50bc7380f67a310b1c7c1f2c","source":{"kind":"arxiv","id":"1104.2555","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2555","created_at":"2026-05-18T02:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2555v1","created_at":"2026-05-18T02:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2555","created_at":"2026-05-18T02:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"JWT6DF2G2OSE","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JWT6DF2G2OSEM5Q6","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JWT6DF2G","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JWT6DF2G2OSEM5Q62WUNFMSSYN","target":"record","payload":{"canonical_record":{"source":{"id":"1104.2555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-13T17:12:21Z","cross_cats_sorted":[],"title_canon_sha256":"4d11c701cba946f1641387c15a0ccc3ef8a4812b781f9048ade71691b6c9a8c6","abstract_canon_sha256":"22fff0769044c06535856cefe849625e3f94043b4ffe9df76c6371b60485be07"},"schema_version":"1.0"},"canonical_sha256":"4da7e19746d3a446761ed5a8d2b252c34e7cb88e50bc7380f67a310b1c7c1f2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:29.777282Z","signature_b64":"7em07d2M9v6jBGtnrImjtdCCA581omlJH4OC+dSxFUfjENJXgnez9/WyhiNqP/aJWn+aT9tMkG1UCwpUcU0+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4da7e19746d3a446761ed5a8d2b252c34e7cb88e50bc7380f67a310b1c7c1f2c","last_reissued_at":"2026-05-18T02:02:29.776576Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:29.776576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.2555","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":"2026-05-18T02:02:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qDqlbh/vapnhXyldP2OtN02G/LWZqzvDEDqPdQNV4VjVbUBjt/4arKNM7OAilCQFq/TNpmRbg/7gwtFqv3XqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:22:33.610722Z"},"content_sha256":"16e33fba9659596ad01880217e9fdafadfb5eb74a10d8bf9b7249264389917f4","schema_version":"1.0","event_id":"sha256:16e33fba9659596ad01880217e9fdafadfb5eb74a10d8bf9b7249264389917f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JWT6DF2G2OSEM5Q62WUNFMSSYN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability and instability of the KdV solitary wave under the KP-I flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fr\\'ed\\'eric Rousset, Nikolay Tzvetkov","submitted_at":"2011-04-13T17:12:21Z","abstract_excerpt":"We consider the KP-I and gKP-I equations in $\\mathbb{R}\\times (\\mathbb{R}/2\\pi \\mathbb{Z})$. We prove that the KdV soliton with subcritical speed $0<c<c^*$ is orbitally stable under the global KP-I flow constructed by Ionescu and Kenig \\cite{IK}. For supercritical speeds $c>c^*$, in the spirit of the work by Duyckaerts and Merle \\cite{DM}, we sharpen our previous instability result and construct a global solution which is different from the solitary wave and its translates and which converges to the solitary wave as time goes to infinity. This last result also holds for the gKP-I equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2555","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":"2026-05-18T02:02:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1JT382MjmhBih2ahCujkaHBjYwX1wbLaU64o1pqRIt5105sv4RroQ9xH6L/vxZRPxr0c7JnnZG8o8Tdm9TJvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:22:33.611072Z"},"content_sha256":"4fbcd652b03ba3b66824fdf821de8db50ebb6f3d1e324073f86fba5be52bf50b","schema_version":"1.0","event_id":"sha256:4fbcd652b03ba3b66824fdf821de8db50ebb6f3d1e324073f86fba5be52bf50b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JWT6DF2G2OSEM5Q62WUNFMSSYN/bundle.json","state_url":"https://pith.science/pith/JWT6DF2G2OSEM5Q62WUNFMSSYN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JWT6DF2G2OSEM5Q62WUNFMSSYN/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":"2026-06-25T08:22:33Z","links":{"resolver":"https://pith.science/pith/JWT6DF2G2OSEM5Q62WUNFMSSYN","bundle":"https://pith.science/pith/JWT6DF2G2OSEM5Q62WUNFMSSYN/bundle.json","state":"https://pith.science/pith/JWT6DF2G2OSEM5Q62WUNFMSSYN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JWT6DF2G2OSEM5Q62WUNFMSSYN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JWT6DF2G2OSEM5Q62WUNFMSSYN","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":"22fff0769044c06535856cefe849625e3f94043b4ffe9df76c6371b60485be07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-13T17:12:21Z","title_canon_sha256":"4d11c701cba946f1641387c15a0ccc3ef8a4812b781f9048ade71691b6c9a8c6"},"schema_version":"1.0","source":{"id":"1104.2555","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2555","created_at":"2026-05-18T02:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2555v1","created_at":"2026-05-18T02:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2555","created_at":"2026-05-18T02:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"JWT6DF2G2OSE","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JWT6DF2G2OSEM5Q6","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JWT6DF2G","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:4fbcd652b03ba3b66824fdf821de8db50ebb6f3d1e324073f86fba5be52bf50b","target":"graph","created_at":"2026-05-18T02:02:29Z","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 consider the KP-I and gKP-I equations in $\\mathbb{R}\\times (\\mathbb{R}/2\\pi \\mathbb{Z})$. We prove that the KdV soliton with subcritical speed $0<c<c^*$ is orbitally stable under the global KP-I flow constructed by Ionescu and Kenig \\cite{IK}. For supercritical speeds $c>c^*$, in the spirit of the work by Duyckaerts and Merle \\cite{DM}, we sharpen our previous instability result and construct a global solution which is different from the solitary wave and its translates and which converges to the solitary wave as time goes to infinity. This last result also holds for the gKP-I equation.","authors_text":"Fr\\'ed\\'eric Rousset, Nikolay Tzvetkov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-13T17:12:21Z","title":"Stability and instability of the KdV solitary wave under the KP-I flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2555","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":"sha256:16e33fba9659596ad01880217e9fdafadfb5eb74a10d8bf9b7249264389917f4","target":"record","created_at":"2026-05-18T02:02:29Z","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":"22fff0769044c06535856cefe849625e3f94043b4ffe9df76c6371b60485be07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-13T17:12:21Z","title_canon_sha256":"4d11c701cba946f1641387c15a0ccc3ef8a4812b781f9048ade71691b6c9a8c6"},"schema_version":"1.0","source":{"id":"1104.2555","kind":"arxiv","version":1}},"canonical_sha256":"4da7e19746d3a446761ed5a8d2b252c34e7cb88e50bc7380f67a310b1c7c1f2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4da7e19746d3a446761ed5a8d2b252c34e7cb88e50bc7380f67a310b1c7c1f2c","first_computed_at":"2026-05-18T02:02:29.776576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:29.776576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7em07d2M9v6jBGtnrImjtdCCA581omlJH4OC+dSxFUfjENJXgnez9/WyhiNqP/aJWn+aT9tMkG1UCwpUcU0+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:29.777282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.2555","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16e33fba9659596ad01880217e9fdafadfb5eb74a10d8bf9b7249264389917f4","sha256:4fbcd652b03ba3b66824fdf821de8db50ebb6f3d1e324073f86fba5be52bf50b"],"state_sha256":"7c868779b4f5238c507bdbc56242a397c2c976ad078333bc940835ca605f5c63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fng0YbjxEGbTc9lbfXffW20mUYAge76rDzKExWZqP9YtigYqhuCTOlEi5hrm8+yfdDV5AFkn2KJ69G752crJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:22:33.613072Z","bundle_sha256":"a80ecda0b74dc4c5b01d5d322751d3ced17218439232ac54d923ce41a38c659b"}}