{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NO7KDN4R7HLO22MD643RGBL7Q2","short_pith_number":"pith:NO7KDN4R","canonical_record":{"source":{"id":"1806.08445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-06-21T22:46:39Z","cross_cats_sorted":[],"title_canon_sha256":"7b9b43ea15b0e375168c6663ee05cc5688aaf3d637114454fc52fae124b49a2b","abstract_canon_sha256":"41bba0def421795aee6df32b7508477da230279810654b407315b79441543370"},"schema_version":"1.0"},"canonical_sha256":"6bbea1b791f9d6ed6983f73713057f86b9553a89c79115adf101536cbdc30830","source":{"kind":"arxiv","id":"1806.08445","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.08445","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1806.08445v1","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.08445","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"NO7KDN4R7HLO","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NO7KDN4R7HLO22MD","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NO7KDN4R","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NO7KDN4R7HLO22MD643RGBL7Q2","target":"record","payload":{"canonical_record":{"source":{"id":"1806.08445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-06-21T22:46:39Z","cross_cats_sorted":[],"title_canon_sha256":"7b9b43ea15b0e375168c6663ee05cc5688aaf3d637114454fc52fae124b49a2b","abstract_canon_sha256":"41bba0def421795aee6df32b7508477da230279810654b407315b79441543370"},"schema_version":"1.0"},"canonical_sha256":"6bbea1b791f9d6ed6983f73713057f86b9553a89c79115adf101536cbdc30830","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:37.279235Z","signature_b64":"O5ssqra6/+w5UDw9NASS+IHgvWagRUs2UWotCk2gDFQgEaxnK4Cg5HCJ4NbsSgcsB7/onD19oXjkZQrfiPY/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bbea1b791f9d6ed6983f73713057f86b9553a89c79115adf101536cbdc30830","last_reissued_at":"2026-05-18T00:12:37.278434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:37.278434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.08445","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":"2026-05-18T00:12:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FrtTN1xne6MsHi5Wf8xvLeaM2jMegWuEht6wPeYemNNAg/ILAzmKTCxOhaBN/vU2AmxH7US14rbXI0rrULutCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:08:22.879494Z"},"content_sha256":"fc13d35e3165de2c8bd13074876cb205a1e98331b08ab8af4235c846119ed853","schema_version":"1.0","event_id":"sha256:fc13d35e3165de2c8bd13074876cb205a1e98331b08ab8af4235c846119ed853"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NO7KDN4R7HLO22MD643RGBL7Q2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of Periodic Travelling Wave Solutions to the Kawahara Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"B. Deconinck, O. Trichtchenko, R. Kollar","submitted_at":"2018-06-21T22:46:39Z","abstract_excerpt":"We analyse the stability of periodic, travelling-wave solutions to the Kawahara equation and some of its generalizations. We determine the parameter regime for which these solutions can exhibit resonance. By examining perturbations of small-amplitude solutions, we show that generalised resonance is a mechanism for high-frequency instabilities. We derive a quadratic equation which fully determines the stability region for these solutions. Focussing on perturbations of the small-amplitude solutions, we obtain asymptotic results for how their instabilities develop and grow. Numerical computation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08445","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":"2026-05-18T00:12:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HH20n2d/klLXzMgIs6R+PoVOACu+nzLXHsDchGoE1y4eBrn2ES6LbRYGbDRFTnEShpznh9vDerqG9Z4eq1JWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:08:22.880044Z"},"content_sha256":"8a51dac8a1de71c637ea358a9317779b9bcc519949c722cda265b95f237e70ab","schema_version":"1.0","event_id":"sha256:8a51dac8a1de71c637ea358a9317779b9bcc519949c722cda265b95f237e70ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NO7KDN4R7HLO22MD643RGBL7Q2/bundle.json","state_url":"https://pith.science/pith/NO7KDN4R7HLO22MD643RGBL7Q2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NO7KDN4R7HLO22MD643RGBL7Q2/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":"2026-06-06T20:08:22Z","links":{"resolver":"https://pith.science/pith/NO7KDN4R7HLO22MD643RGBL7Q2","bundle":"https://pith.science/pith/NO7KDN4R7HLO22MD643RGBL7Q2/bundle.json","state":"https://pith.science/pith/NO7KDN4R7HLO22MD643RGBL7Q2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NO7KDN4R7HLO22MD643RGBL7Q2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NO7KDN4R7HLO22MD643RGBL7Q2","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":"41bba0def421795aee6df32b7508477da230279810654b407315b79441543370","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-06-21T22:46:39Z","title_canon_sha256":"7b9b43ea15b0e375168c6663ee05cc5688aaf3d637114454fc52fae124b49a2b"},"schema_version":"1.0","source":{"id":"1806.08445","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.08445","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1806.08445v1","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.08445","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"NO7KDN4R7HLO","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NO7KDN4R7HLO22MD","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NO7KDN4R","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:8a51dac8a1de71c637ea358a9317779b9bcc519949c722cda265b95f237e70ab","target":"graph","created_at":"2026-05-18T00:12:37Z","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 analyse the stability of periodic, travelling-wave solutions to the Kawahara equation and some of its generalizations. We determine the parameter regime for which these solutions can exhibit resonance. By examining perturbations of small-amplitude solutions, we show that generalised resonance is a mechanism for high-frequency instabilities. We derive a quadratic equation which fully determines the stability region for these solutions. Focussing on perturbations of the small-amplitude solutions, we obtain asymptotic results for how their instabilities develop and grow. Numerical computation ","authors_text":"B. Deconinck, O. Trichtchenko, R. Kollar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-06-21T22:46:39Z","title":"Stability of Periodic Travelling Wave Solutions to the Kawahara Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08445","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:fc13d35e3165de2c8bd13074876cb205a1e98331b08ab8af4235c846119ed853","target":"record","created_at":"2026-05-18T00:12:37Z","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":"41bba0def421795aee6df32b7508477da230279810654b407315b79441543370","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-06-21T22:46:39Z","title_canon_sha256":"7b9b43ea15b0e375168c6663ee05cc5688aaf3d637114454fc52fae124b49a2b"},"schema_version":"1.0","source":{"id":"1806.08445","kind":"arxiv","version":1}},"canonical_sha256":"6bbea1b791f9d6ed6983f73713057f86b9553a89c79115adf101536cbdc30830","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bbea1b791f9d6ed6983f73713057f86b9553a89c79115adf101536cbdc30830","first_computed_at":"2026-05-18T00:12:37.278434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:37.278434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O5ssqra6/+w5UDw9NASS+IHgvWagRUs2UWotCk2gDFQgEaxnK4Cg5HCJ4NbsSgcsB7/onD19oXjkZQrfiPY/CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:37.279235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.08445","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc13d35e3165de2c8bd13074876cb205a1e98331b08ab8af4235c846119ed853","sha256:8a51dac8a1de71c637ea358a9317779b9bcc519949c722cda265b95f237e70ab"],"state_sha256":"935f4a7cae702e4ad0e17c25cafbce47c8e5934f95c45ee081ce5f956b4d8e57"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OusEVmkmRMsnsyzgCN2NBxc1KHb6nrvqvDxjS17WOwTwHG5tVYpNbG8sngH+1G1hSf2hStdktYSlOYouaSAYCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:08:22.883098Z","bundle_sha256":"a714c6eec5b209d281316c29469de007624532a78e8dbaa6c43733f44c55dd80"}}