{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:N7ZHPWM5UL43QDQU32V3VIFBGW","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":"86edc14387e7c0ec6676c3f8b0cb2f2c60163dc872f891252d8c310aa9099596","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-15T10:19:04Z","title_canon_sha256":"f7a83edd3d1aeb42d6c5736c55ca50c3ad2c8f61843f088faf33b4902da127d7"},"schema_version":"1.0","source":{"id":"1611.04771","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04771","created_at":"2026-05-18T00:58:49Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04771v1","created_at":"2026-05-18T00:58:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04771","created_at":"2026-05-18T00:58:49Z"},{"alias_kind":"pith_short_12","alias_value":"N7ZHPWM5UL43","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"N7ZHPWM5UL43QDQU","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"N7ZHPWM5","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:bd621facc3d5859b9e6ef7fe77a9c85f260dcf8585f296f6349dfd97cceabb1b","target":"graph","created_at":"2026-05-18T00:58:49Z","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":"The present paper deals with sufficient conditions for orbital stability of periodic waves of a general class of evolution equations supporting nonlinear dispersive waves. Our method can be seen as an extension to spatially periodic waves of the theory of solitary waves recently developed in \\cite{st}. Firstly, our main result do not depend on the parametrization of the periodic wave itself. Secondly, motived by the well known orbital stability criterion for solitary waves, we show that the same criterion holds for periodic waves. In addition, we show that the positiveness of the principal ent","authors_text":"Ademir Pastor, F\\'abio Natali, Giovana Alves","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-15T10:19:04Z","title":"Sufficient Conditions for Orbital Stability of Periodic Traveling Waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04771","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":"sha256:959101137653a4c2ed2d5685e49ff8875806a4e175389317243fcb128cec1e28","target":"record","created_at":"2026-05-18T00:58:49Z","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":"86edc14387e7c0ec6676c3f8b0cb2f2c60163dc872f891252d8c310aa9099596","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-15T10:19:04Z","title_canon_sha256":"f7a83edd3d1aeb42d6c5736c55ca50c3ad2c8f61843f088faf33b4902da127d7"},"schema_version":"1.0","source":{"id":"1611.04771","kind":"arxiv","version":1}},"canonical_sha256":"6ff277d99da2f9b80e14deabbaa0a135b11e1cba239ff4bfec36af4e0e8d767c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ff277d99da2f9b80e14deabbaa0a135b11e1cba239ff4bfec36af4e0e8d767c","first_computed_at":"2026-05-18T00:58:49.961171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:49.961171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BmgRYqpPuju+WNJKzBdyKaUto/zWOaOXi6pXhi9aCxP9ZNBBQY8slDbxXJIUC/KV8FiR8gcss+QvE2xJhSWMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:49.961763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04771","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:959101137653a4c2ed2d5685e49ff8875806a4e175389317243fcb128cec1e28","sha256:bd621facc3d5859b9e6ef7fe77a9c85f260dcf8585f296f6349dfd97cceabb1b"],"state_sha256":"029a9fcdf5f8e7bfe2443e0da47a192194723575a4aee5eaaf8e6f8a45ecd1e2"}