{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6EIMMR2I6NWO4KOZW22ADBMYMT","short_pith_number":"pith:6EIMMR2I","canonical_record":{"source":{"id":"1009.0494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-02T18:04:49Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"8e6ab5d5607cf4e6d304765c4d615a67df2b0076026b6091fc8c4e1551f54d4f","abstract_canon_sha256":"2df690772d0982570ceb4521d9c3dffbc39ca9a66f63455626118ffd63ee2a3e"},"schema_version":"1.0"},"canonical_sha256":"f110c64748f36cee29d9b6b401859864fe5a4ff11192dc486681cf25c35b4bad","source":{"kind":"arxiv","id":"1009.0494","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0494","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0494v1","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0494","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"6EIMMR2I6NWO","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6EIMMR2I6NWO4KOZ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6EIMMR2I","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6EIMMR2I6NWO4KOZW22ADBMYMT","target":"record","payload":{"canonical_record":{"source":{"id":"1009.0494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-02T18:04:49Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"8e6ab5d5607cf4e6d304765c4d615a67df2b0076026b6091fc8c4e1551f54d4f","abstract_canon_sha256":"2df690772d0982570ceb4521d9c3dffbc39ca9a66f63455626118ffd63ee2a3e"},"schema_version":"1.0"},"canonical_sha256":"f110c64748f36cee29d9b6b401859864fe5a4ff11192dc486681cf25c35b4bad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:26.505612Z","signature_b64":"zl9pVRLX2v3MyPneALY6tKR8v8WlPe7HLi+a/xMA2IbPFjwovhLoOy8YS8N1ZNmx5pFQGHMO0tHHNrjCtQuHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f110c64748f36cee29d9b6b401859864fe5a4ff11192dc486681cf25c35b4bad","last_reissued_at":"2026-05-18T04:41:26.505145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:26.505145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.0494","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":"2026-05-18T04:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vuya3PQh9YmO/bv7OrJ9Cn/XXEHluKBtlqrWucn8R7MCFGgfg03qCWZpE5z6EfFaG6/dw/yd1fN6wGubOC3EDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:00:30.366788Z"},"content_sha256":"98fd3c62c19e808baae7c4942a27d28ae9f3eef5a80286f6117c652b43c7716b","schema_version":"1.0","event_id":"sha256:98fd3c62c19e808baae7c4942a27d28ae9f3eef5a80286f6117c652b43c7716b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6EIMMR2I6NWO4KOZW22ADBMYMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic linear stability of solitary water waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"math.AP","authors_text":"(2) Virginia Polytechnic Institute, Blacksburg), Pittsburgh, Robert L. Pego (1), Shu-Ming Sun (2) ((1) Carnegie Mellon University, State University","submitted_at":"2010-09-02T18:04:49Z","abstract_excerpt":"We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0494","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":"2026-05-18T04:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"riSPxggNxxtAd+V5vqTzaeI/7CqGLxQ3rMiTEnk2hkNXb4dOVnk9kji0w5i7fXeBzSeRCdlTN6bx6t+OWux/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:00:30.367140Z"},"content_sha256":"eb52bca29a402b33776bd7c3836a85ab45de91230a8577991df7a71c3595299c","schema_version":"1.0","event_id":"sha256:eb52bca29a402b33776bd7c3836a85ab45de91230a8577991df7a71c3595299c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6EIMMR2I6NWO4KOZW22ADBMYMT/bundle.json","state_url":"https://pith.science/pith/6EIMMR2I6NWO4KOZW22ADBMYMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6EIMMR2I6NWO4KOZW22ADBMYMT/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":"2026-06-03T10:00:30Z","links":{"resolver":"https://pith.science/pith/6EIMMR2I6NWO4KOZW22ADBMYMT","bundle":"https://pith.science/pith/6EIMMR2I6NWO4KOZW22ADBMYMT/bundle.json","state":"https://pith.science/pith/6EIMMR2I6NWO4KOZW22ADBMYMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6EIMMR2I6NWO4KOZW22ADBMYMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6EIMMR2I6NWO4KOZW22ADBMYMT","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":"2df690772d0982570ceb4521d9c3dffbc39ca9a66f63455626118ffd63ee2a3e","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-02T18:04:49Z","title_canon_sha256":"8e6ab5d5607cf4e6d304765c4d615a67df2b0076026b6091fc8c4e1551f54d4f"},"schema_version":"1.0","source":{"id":"1009.0494","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0494","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0494v1","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0494","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"6EIMMR2I6NWO","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6EIMMR2I6NWO4KOZ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6EIMMR2I","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:eb52bca29a402b33776bd7c3836a85ab45de91230a8577991df7a71c3595299c","target":"graph","created_at":"2026-05-18T04:41:26Z","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 prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This ","authors_text":"(2) Virginia Polytechnic Institute, Blacksburg), Pittsburgh, Robert L. Pego (1), Shu-Ming Sun (2) ((1) Carnegie Mellon University, State University","cross_cats":["nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-02T18:04:49Z","title":"Asymptotic linear stability of solitary water waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0494","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":"sha256:98fd3c62c19e808baae7c4942a27d28ae9f3eef5a80286f6117c652b43c7716b","target":"record","created_at":"2026-05-18T04:41:26Z","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":"2df690772d0982570ceb4521d9c3dffbc39ca9a66f63455626118ffd63ee2a3e","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-02T18:04:49Z","title_canon_sha256":"8e6ab5d5607cf4e6d304765c4d615a67df2b0076026b6091fc8c4e1551f54d4f"},"schema_version":"1.0","source":{"id":"1009.0494","kind":"arxiv","version":1}},"canonical_sha256":"f110c64748f36cee29d9b6b401859864fe5a4ff11192dc486681cf25c35b4bad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f110c64748f36cee29d9b6b401859864fe5a4ff11192dc486681cf25c35b4bad","first_computed_at":"2026-05-18T04:41:26.505145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:26.505145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zl9pVRLX2v3MyPneALY6tKR8v8WlPe7HLi+a/xMA2IbPFjwovhLoOy8YS8N1ZNmx5pFQGHMO0tHHNrjCtQuHBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:26.505612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0494","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98fd3c62c19e808baae7c4942a27d28ae9f3eef5a80286f6117c652b43c7716b","sha256:eb52bca29a402b33776bd7c3836a85ab45de91230a8577991df7a71c3595299c"],"state_sha256":"7c185b7f7ab95e3eae552971138d5d95fda478515e3b3c0c34c1fcb1af5f0c4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pDHfUWg4RL5dzZjiJS1vemltkonKtaWBSvnZEFqkdvXYlnA7m1LJRj68KQFBUL7bq2oe8olwkY6bJ6TluMzkDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:00:30.369207Z","bundle_sha256":"a8e0f47ee2ddabef223cf0e91ac13ec2afee849cbcdc50d407c2800842c6ef0b"}}