{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KF6XYHAKMUKF6QF3YQ4C6XSK76","short_pith_number":"pith:KF6XYHAK","canonical_record":{"source":{"id":"1011.3453","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-15T17:09:52Z","cross_cats_sorted":[],"title_canon_sha256":"3dccdc8c8834319d6dec93802cf6da8f6623d75af0b45da69a0d86f103fafa61","abstract_canon_sha256":"12edb39cf35bf1cbb62b744b2f194ed1d72954c69d4e42ef3ae220742dcd44ee"},"schema_version":"1.0"},"canonical_sha256":"517d7c1c0a65145f40bbc4382f5e4affb2e6f0fd9af88c0a16bc542a6e40932c","source":{"kind":"arxiv","id":"1011.3453","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3453","created_at":"2026-05-18T04:35:46Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3453v2","created_at":"2026-05-18T04:35:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3453","created_at":"2026-05-18T04:35:46Z"},{"alias_kind":"pith_short_12","alias_value":"KF6XYHAKMUKF","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KF6XYHAKMUKF6QF3","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KF6XYHAK","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KF6XYHAKMUKF6QF3YQ4C6XSK76","target":"record","payload":{"canonical_record":{"source":{"id":"1011.3453","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-15T17:09:52Z","cross_cats_sorted":[],"title_canon_sha256":"3dccdc8c8834319d6dec93802cf6da8f6623d75af0b45da69a0d86f103fafa61","abstract_canon_sha256":"12edb39cf35bf1cbb62b744b2f194ed1d72954c69d4e42ef3ae220742dcd44ee"},"schema_version":"1.0"},"canonical_sha256":"517d7c1c0a65145f40bbc4382f5e4affb2e6f0fd9af88c0a16bc542a6e40932c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:46.740656Z","signature_b64":"enCXEswI8eYrBq+GcUiQVA+psW7f4BvdhYHxWfFa6a0lkyJoNji8ANX9ONUk7dWgcFYtyfEY/kqWy76a5sXzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"517d7c1c0a65145f40bbc4382f5e4affb2e6f0fd9af88c0a16bc542a6e40932c","last_reissued_at":"2026-05-18T04:35:46.739992Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:46.739992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.3453","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":"2026-05-18T04:35:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SsByq/yEmOSKMkg9YCmROfAvbctiSrS3WGdM5rk/XG1lJ0Kno53/Ptvgib7ohAPmMs110+4pbNry5jy/RmfTCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:22:25.191636Z"},"content_sha256":"abf7fd537a2d1ba3ff82838fe3102aef9eab2dbd34992770d33075af803d6150","schema_version":"1.0","event_id":"sha256:abf7fd537a2d1ba3ff82838fe3102aef9eab2dbd34992770d33075af803d6150"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KF6XYHAKMUKF6QF3YQ4C6XSK76","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear Stability for the Periodic and Non-Periodic Zakharov System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlos Banquet, Jaime Angulo","submitted_at":"2010-11-15T17:09:52Z","abstract_excerpt":"We prove the existence of a smooth curve of periodic traveling wave solutions for the Zakharov system. We also show that this type of solutions are nonlinear stable by the periodic flow generated for the system mentioned before. An improvement of the work of Ya Ping is made, we prove the stability of the solitary wave solutions associated to the Zakharov system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3453","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":""},"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":"2026-05-18T04:35:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VHvWdVDlF4INaJ7JtGQMSveyEFkFrjBQzC+zyp3iWGON+V5d38JgA4J+WkxJGb03Lj9mLVXs7kiNpAj7uaEFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:22:25.191979Z"},"content_sha256":"411ad5a48cd0a37a769a8b474574f92d4b6c3d24d34a0a7a2b4e45d10169908e","schema_version":"1.0","event_id":"sha256:411ad5a48cd0a37a769a8b474574f92d4b6c3d24d34a0a7a2b4e45d10169908e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KF6XYHAKMUKF6QF3YQ4C6XSK76/bundle.json","state_url":"https://pith.science/pith/KF6XYHAKMUKF6QF3YQ4C6XSK76/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KF6XYHAKMUKF6QF3YQ4C6XSK76/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":"2026-06-21T09:22:25Z","links":{"resolver":"https://pith.science/pith/KF6XYHAKMUKF6QF3YQ4C6XSK76","bundle":"https://pith.science/pith/KF6XYHAKMUKF6QF3YQ4C6XSK76/bundle.json","state":"https://pith.science/pith/KF6XYHAKMUKF6QF3YQ4C6XSK76/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KF6XYHAKMUKF6QF3YQ4C6XSK76/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KF6XYHAKMUKF6QF3YQ4C6XSK76","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":"12edb39cf35bf1cbb62b744b2f194ed1d72954c69d4e42ef3ae220742dcd44ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-15T17:09:52Z","title_canon_sha256":"3dccdc8c8834319d6dec93802cf6da8f6623d75af0b45da69a0d86f103fafa61"},"schema_version":"1.0","source":{"id":"1011.3453","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3453","created_at":"2026-05-18T04:35:46Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3453v2","created_at":"2026-05-18T04:35:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3453","created_at":"2026-05-18T04:35:46Z"},{"alias_kind":"pith_short_12","alias_value":"KF6XYHAKMUKF","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KF6XYHAKMUKF6QF3","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KF6XYHAK","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:411ad5a48cd0a37a769a8b474574f92d4b6c3d24d34a0a7a2b4e45d10169908e","target":"graph","created_at":"2026-05-18T04:35:46Z","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 the existence of a smooth curve of periodic traveling wave solutions for the Zakharov system. We also show that this type of solutions are nonlinear stable by the periodic flow generated for the system mentioned before. An improvement of the work of Ya Ping is made, we prove the stability of the solitary wave solutions associated to the Zakharov system.","authors_text":"Carlos Banquet, Jaime Angulo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-15T17:09:52Z","title":"Nonlinear Stability for the Periodic and Non-Periodic Zakharov System"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3453","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:abf7fd537a2d1ba3ff82838fe3102aef9eab2dbd34992770d33075af803d6150","target":"record","created_at":"2026-05-18T04:35:46Z","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":"12edb39cf35bf1cbb62b744b2f194ed1d72954c69d4e42ef3ae220742dcd44ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-15T17:09:52Z","title_canon_sha256":"3dccdc8c8834319d6dec93802cf6da8f6623d75af0b45da69a0d86f103fafa61"},"schema_version":"1.0","source":{"id":"1011.3453","kind":"arxiv","version":2}},"canonical_sha256":"517d7c1c0a65145f40bbc4382f5e4affb2e6f0fd9af88c0a16bc542a6e40932c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"517d7c1c0a65145f40bbc4382f5e4affb2e6f0fd9af88c0a16bc542a6e40932c","first_computed_at":"2026-05-18T04:35:46.739992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:46.739992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"enCXEswI8eYrBq+GcUiQVA+psW7f4BvdhYHxWfFa6a0lkyJoNji8ANX9ONUk7dWgcFYtyfEY/kqWy76a5sXzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:46.740656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3453","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abf7fd537a2d1ba3ff82838fe3102aef9eab2dbd34992770d33075af803d6150","sha256:411ad5a48cd0a37a769a8b474574f92d4b6c3d24d34a0a7a2b4e45d10169908e"],"state_sha256":"73bd6ae89be67c56db1f64030ab2c04a7f4a6f685d9b98a76dabb982df0bc1b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MpVhLr2UY+s23BpU0svV7NeA/eYISyh10sXy1Q61rL4x60QDU8/aFnGVHcgUzGC4+sLmDCGz1PoOgfwhAUPmCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T09:22:25.193918Z","bundle_sha256":"465fdc7be5f7e8d539b01789477c9b13b0ceb3acd50a12aae97698116c0124c1"}}