{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:RRWGAUBKZHUMI7FPKGC2ECSSTC","short_pith_number":"pith:RRWGAUBK","canonical_record":{"source":{"id":"1205.0729","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-03T15:12:22Z","cross_cats_sorted":[],"title_canon_sha256":"77433b1c272609f0313aaf0caf9ce230a2932b75c5381c815fc1cf1a0c4ed775","abstract_canon_sha256":"1c0d18a9cb14a4e51543192ab161089e57959ad0d26847fe29858179acd5478c"},"schema_version":"1.0"},"canonical_sha256":"8c6c60502ac9e8c47caf5185a20a5298a45f05f899915dd3ec5059e3565be8bd","source":{"kind":"arxiv","id":"1205.0729","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0729","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0729v2","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0729","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"RRWGAUBKZHUM","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RRWGAUBKZHUMI7FP","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RRWGAUBK","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:RRWGAUBKZHUMI7FPKGC2ECSSTC","target":"record","payload":{"canonical_record":{"source":{"id":"1205.0729","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-03T15:12:22Z","cross_cats_sorted":[],"title_canon_sha256":"77433b1c272609f0313aaf0caf9ce230a2932b75c5381c815fc1cf1a0c4ed775","abstract_canon_sha256":"1c0d18a9cb14a4e51543192ab161089e57959ad0d26847fe29858179acd5478c"},"schema_version":"1.0"},"canonical_sha256":"8c6c60502ac9e8c47caf5185a20a5298a45f05f899915dd3ec5059e3565be8bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:05.578456Z","signature_b64":"XFh9NtNU1ursJCEAeM17AYAYjiOaVhgbpRa8AogjUOJjb8pLl2w4ctm2KuEZKZt5zwkhefr6TPAhSBfgbEp/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c6c60502ac9e8c47caf5185a20a5298a45f05f899915dd3ec5059e3565be8bd","last_reissued_at":"2026-05-18T03:54:05.577897Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:05.577897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.0729","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":"2026-05-18T03:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XDlV1LTOZ0ZyfxrtM3tXmDZPMBA1pkFMESz9iSqNc0Bbp3rWE7t7o2eg9lNDZYa6Zn76SyRnQ+y5tXlhuA6uBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:23:33.966214Z"},"content_sha256":"c5ff1799f5367880fa0a7d966d49cf6a153446b9220b7709afc72b44494e2b09","schema_version":"1.0","event_id":"sha256:c5ff1799f5367880fa0a7d966d49cf6a153446b9220b7709afc72b44494e2b09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:RRWGAUBKZHUMI7FPKGC2ECSSTC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dispersive limit from the Kawahara to the KdV equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luc Molinet (LMPT), Yuzhao Wang","submitted_at":"2012-05-03T15:12:22Z","abstract_excerpt":"We investigate the limit behavior of the solutions to the Kawahara equation $$ u_t +u_{3x} + \\varepsilon u_{5x} + u u_x =0, $$ as $ 0<\\varepsilon \\to 0 $. In this equation, the terms $ u_{3x} $ and $ \\varepsilon u_{5x} $ do compete together and do cancel each other at frequencies of order $ 1/\\sqrt{\\varepsilon} $. This prohibits the use of a standard dispersive approach for this problem. Nervertheless, by combining different dispersive approaches according to the range of spaces frequencies, we succeed in proving that the solutions to this equation converges in $ C([0,T];H^1(\\R)) $ towards the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0729","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":"2026-05-18T03:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BEP2mW/C4wmonoq1IUReP0UXcn69SVo0/X/dlHun+IPnUYygJiAsGkF4Qj2tR3SsDxb8nNthZckthqB/pKGuCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:23:33.966895Z"},"content_sha256":"c1571ddb91ff059d16f99f8ac9b22ae235bf642c7f4717f6ab2de80c0ec30258","schema_version":"1.0","event_id":"sha256:c1571ddb91ff059d16f99f8ac9b22ae235bf642c7f4717f6ab2de80c0ec30258"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RRWGAUBKZHUMI7FPKGC2ECSSTC/bundle.json","state_url":"https://pith.science/pith/RRWGAUBKZHUMI7FPKGC2ECSSTC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RRWGAUBKZHUMI7FPKGC2ECSSTC/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":"2026-05-25T14:23:33Z","links":{"resolver":"https://pith.science/pith/RRWGAUBKZHUMI7FPKGC2ECSSTC","bundle":"https://pith.science/pith/RRWGAUBKZHUMI7FPKGC2ECSSTC/bundle.json","state":"https://pith.science/pith/RRWGAUBKZHUMI7FPKGC2ECSSTC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RRWGAUBKZHUMI7FPKGC2ECSSTC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RRWGAUBKZHUMI7FPKGC2ECSSTC","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":"1c0d18a9cb14a4e51543192ab161089e57959ad0d26847fe29858179acd5478c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-03T15:12:22Z","title_canon_sha256":"77433b1c272609f0313aaf0caf9ce230a2932b75c5381c815fc1cf1a0c4ed775"},"schema_version":"1.0","source":{"id":"1205.0729","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0729","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0729v2","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0729","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"RRWGAUBKZHUM","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RRWGAUBKZHUMI7FP","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RRWGAUBK","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:c1571ddb91ff059d16f99f8ac9b22ae235bf642c7f4717f6ab2de80c0ec30258","target":"graph","created_at":"2026-05-18T03:54:05Z","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 investigate the limit behavior of the solutions to the Kawahara equation $$ u_t +u_{3x} + \\varepsilon u_{5x} + u u_x =0, $$ as $ 0<\\varepsilon \\to 0 $. In this equation, the terms $ u_{3x} $ and $ \\varepsilon u_{5x} $ do compete together and do cancel each other at frequencies of order $ 1/\\sqrt{\\varepsilon} $. This prohibits the use of a standard dispersive approach for this problem. Nervertheless, by combining different dispersive approaches according to the range of spaces frequencies, we succeed in proving that the solutions to this equation converges in $ C([0,T];H^1(\\R)) $ towards the","authors_text":"Luc Molinet (LMPT), Yuzhao Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-03T15:12:22Z","title":"Dispersive limit from the Kawahara to the KdV equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0729","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:c5ff1799f5367880fa0a7d966d49cf6a153446b9220b7709afc72b44494e2b09","target":"record","created_at":"2026-05-18T03:54:05Z","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":"1c0d18a9cb14a4e51543192ab161089e57959ad0d26847fe29858179acd5478c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-03T15:12:22Z","title_canon_sha256":"77433b1c272609f0313aaf0caf9ce230a2932b75c5381c815fc1cf1a0c4ed775"},"schema_version":"1.0","source":{"id":"1205.0729","kind":"arxiv","version":2}},"canonical_sha256":"8c6c60502ac9e8c47caf5185a20a5298a45f05f899915dd3ec5059e3565be8bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c6c60502ac9e8c47caf5185a20a5298a45f05f899915dd3ec5059e3565be8bd","first_computed_at":"2026-05-18T03:54:05.577897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:05.577897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XFh9NtNU1ursJCEAeM17AYAYjiOaVhgbpRa8AogjUOJjb8pLl2w4ctm2KuEZKZt5zwkhefr6TPAhSBfgbEp/CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:05.578456Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0729","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5ff1799f5367880fa0a7d966d49cf6a153446b9220b7709afc72b44494e2b09","sha256:c1571ddb91ff059d16f99f8ac9b22ae235bf642c7f4717f6ab2de80c0ec30258"],"state_sha256":"7ec0d0da829339cce409981d62947123e89828878a7fb3cea1e2730a9be314e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dOD6AS0oYmQoayjh0XkkoZr3G2Cj4IE6LrpyfkM/Bw6cBuyIEwVdNF30ExM9JlhEWtClB5dGl0Gc0rpcE8FWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T14:23:33.970863Z","bundle_sha256":"119ebafee48531edeba9ba4b7f2054516b0e5e31b2569239a6bc4d5360ef5c65"}}