{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SLBF3RXHJ3KVQQQO6VXO4LJMNC","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":"b49d8ccde872c68e60e769790a94f607ac2853e67a591177c0dcde38b2b5fe15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-07T09:41:59Z","title_canon_sha256":"805c71dab2c39c8e834d33995ff314dabca1d915998ab7fc19fcf2d5c6517fb7"},"schema_version":"1.0","source":{"id":"1501.01415","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01415","created_at":"2026-05-18T01:33:16Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01415v2","created_at":"2026-05-18T01:33:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01415","created_at":"2026-05-18T01:33:16Z"},{"alias_kind":"pith_short_12","alias_value":"SLBF3RXHJ3KV","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SLBF3RXHJ3KVQQQO","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SLBF3RXH","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:edfd23ac5eafdc3567c0065ea04eac6835b0dfbd240dde3daefe3caaf17cae0c","target":"graph","created_at":"2026-05-18T01:33:16Z","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 consider the one-dimensional cubic fractional nonlinear Schr\\\"odinger equation $$i\\partial_tu-(-\\Delta)^\\sigma u+|u|^{2}u=0,$$ where $\\sigma \\in (\\frac12,1)$ and the operator $(-\\Delta)^\\sigma$ is the fractional Laplacian of symbol $|\\xi|^{2\\sigma}$. Despite of lack of any Galilean-type invariance, we construct a new class of traveling soliton solutions of the form $$u(t,x)=e^{-it(|k|^{2\\sigma}-\\omega^{2\\sigma})}Q_{\\omega,k}(x-2t\\sigma|k|^{2\\sigma-2}k),\\quad k\\in\\mathbb{R},\\ \\omega>0$$ by a rather involved variational argument.","authors_text":"Yannick Sire, Younghun Hong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-07T09:41:59Z","title":"A new class of Traveling Solitons for cubic Fractional Nonlinear Schrodinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01415","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":"sha256:5d216b9515f22c4f973b8eb014347f4f5df9a79a3b2a1d81462b93a587d17320","target":"record","created_at":"2026-05-18T01:33:16Z","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":"b49d8ccde872c68e60e769790a94f607ac2853e67a591177c0dcde38b2b5fe15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-07T09:41:59Z","title_canon_sha256":"805c71dab2c39c8e834d33995ff314dabca1d915998ab7fc19fcf2d5c6517fb7"},"schema_version":"1.0","source":{"id":"1501.01415","kind":"arxiv","version":2}},"canonical_sha256":"92c25dc6e74ed558420ef56eee2d2c6888fd63ac36bb462e41840d4871c6f485","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92c25dc6e74ed558420ef56eee2d2c6888fd63ac36bb462e41840d4871c6f485","first_computed_at":"2026-05-18T01:33:16.215280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:16.215280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IH8M/2RncBcIcsMnhrxZ0AVcsyFVo+scB1n7YyqCMolRg0unrlywEM4v2km8VIWeQOGpojmXoiIrpiAeZvo5Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:16.216021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01415","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d216b9515f22c4f973b8eb014347f4f5df9a79a3b2a1d81462b93a587d17320","sha256:edfd23ac5eafdc3567c0065ea04eac6835b0dfbd240dde3daefe3caaf17cae0c"],"state_sha256":"9e3a377f9bed8748b3b539f9bcab0640607619b1b55dc4718511e3d4ed5d74ee"}