{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BEDNO6QYPPHFR72WGTKSJC2IYZ","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":"5087664eebc96936d32b9ed6ebec14882b26d18a725e12788b62780ecfd44bce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-26T15:56:25Z","title_canon_sha256":"a7cc2403613c61c2efa2dc4ba9ac326c597fcbc5b56ebab576acaa3083fa679a"},"schema_version":"1.0","source":{"id":"1710.09775","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09775","created_at":"2026-05-18T00:05:19Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09775v2","created_at":"2026-05-18T00:05:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09775","created_at":"2026-05-18T00:05:19Z"},{"alias_kind":"pith_short_12","alias_value":"BEDNO6QYPPHF","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BEDNO6QYPPHFR72W","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BEDNO6QY","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:63538fa3d242f1a3aa09b10d49898708bb3e45e90913f4974dd32a41b205227c","target":"graph","created_at":"2026-05-18T00:05:19Z","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 study the mixed dispersion fourth order nonlinear Schr\\\"odinger equation \\begin{equation*} %\\tag{\\protect{4NLS}}\\label{4nls} i \\partial_t \\psi -\\gamma \\Delta^2 \\psi +\\beta \\Delta \\psi +|\\psi|^{2\\sigma} \\psi =0\\ \\text{in}\\ \\R \\times\\R^N, \\end{equation*} where $\\gamma,\\sigma>0$ and $\\beta \\in \\R$. We focus on standing wave solutions, namely solutions of the form $\\psi (x,t)=e^{i\\alpha t}u(x)$, for some $\\alpha \\in \\R$. This ansatz yields the fourth-order elliptic equation \\begin{equation*} %\\tag{\\protect{*}}\\label{4nlsstar} \\gamma \\Delta^2 u -\\beta \\Delta u +\\alpha u =|u|^{2\\sigma} u. \\end{eq","authors_text":"Denis Bonheure, Ederson Moreira dos Santos, Jean-Baptiste Cast\\'eras, Robson Nascimento","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-26T15:56:25Z","title":"Orbitally stable standing waves of a mixed dispersion nonlinear Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09775","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":"sha256:9a4e26da7fc5e59f68868ae40afa0c03e71893bbc850b447ae2dab827be0edfc","target":"record","created_at":"2026-05-18T00:05:19Z","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":"5087664eebc96936d32b9ed6ebec14882b26d18a725e12788b62780ecfd44bce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-26T15:56:25Z","title_canon_sha256":"a7cc2403613c61c2efa2dc4ba9ac326c597fcbc5b56ebab576acaa3083fa679a"},"schema_version":"1.0","source":{"id":"1710.09775","kind":"arxiv","version":2}},"canonical_sha256":"0906d77a187bce58ff5634d5248b48c64944ee747b6441ab62cee2d173e21492","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0906d77a187bce58ff5634d5248b48c64944ee747b6441ab62cee2d173e21492","first_computed_at":"2026-05-18T00:05:19.634230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:19.634230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NADSHNZPeGRKkWWBa1e/NW8bW/M6F66yz7MoCNB0+5c8K+pZZzamZeCydHDd8dlQ+uQxEWo3yjJvWsns95OSDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:19.634742Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.09775","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a4e26da7fc5e59f68868ae40afa0c03e71893bbc850b447ae2dab827be0edfc","sha256:63538fa3d242f1a3aa09b10d49898708bb3e45e90913f4974dd32a41b205227c"],"state_sha256":"fc919a7acb909711b7c97a2b0229de32e4f0a31fa423cde0b02b4184294dde0c"}