{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UTPILFYM6YHAYWYXQEANJ6PL3J","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":"2b9afd40176f66e3d2870f49ac54ab11ebe9cb9cbb0f74bda0241df4ef1327d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-02T10:13:48Z","title_canon_sha256":"4f950f03cfaaf29986d4422a634396e015821d43a4899bf09bfd2083572f879d"},"schema_version":"1.0","source":{"id":"1606.00606","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00606","created_at":"2026-05-18T01:03:18Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00606v2","created_at":"2026-05-18T01:03:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00606","created_at":"2026-05-18T01:03:18Z"},{"alias_kind":"pith_short_12","alias_value":"UTPILFYM6YHA","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UTPILFYM6YHAYWYX","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UTPILFYM","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:d208f796c37a2f2ca582472953d80f8eacee2a5168b2e006bd8e3aeaecf9da83","target":"graph","created_at":"2026-05-18T01:03:18Z","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 nonlinear stationary Schr\\\"odinger equation \\begin{equation*}\n  -\\Delta u -\\lambda u= Q(x)|u|^{p-2}u, \\qquad \\text{in }\\mathbb{R}^N \\end{equation*} in the case where $N \\geq 3$, $p$ is a superlinear, subcritical exponent, $Q$ is a bounded, nonnegative and nontrivial weight function with compact support in $\\mathbb{R}^N$ and $\\lambda \\in \\mathbb{R}$ is a parameter. Under further restrictions either on the exponent $p$ or on the shape of $Q$, we establish the existence of a continuous branch $\\mathcal{C}$ of nontrivial solutions to this equation which intersects $\\{\\lambda \\} \\ti","authors_text":"Gilles Ev\\'equoz, Tobias Weth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-02T10:13:48Z","title":"Branch continuation inside the essential spectrum for the nonlinear Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00606","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:cef648c7ea1ffa167fab008d6ebe2b19c903f54a171dff121c5297e64b2972f8","target":"record","created_at":"2026-05-18T01:03:18Z","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":"2b9afd40176f66e3d2870f49ac54ab11ebe9cb9cbb0f74bda0241df4ef1327d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-02T10:13:48Z","title_canon_sha256":"4f950f03cfaaf29986d4422a634396e015821d43a4899bf09bfd2083572f879d"},"schema_version":"1.0","source":{"id":"1606.00606","kind":"arxiv","version":2}},"canonical_sha256":"a4de85970cf60e0c5b178100d4f9ebda5b558e375d168b47f36c969f3c93df8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4de85970cf60e0c5b178100d4f9ebda5b558e375d168b47f36c969f3c93df8a","first_computed_at":"2026-05-18T01:03:18.748464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:18.748464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tlDO7CjDn4pZMBK1oBSN5azvlLPZJvOIw+wp0LsYpGkzTGqQtw86CNaSdvmNhywFR3qjGnQBdlHu5lQnF2KdCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:18.749033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00606","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cef648c7ea1ffa167fab008d6ebe2b19c903f54a171dff121c5297e64b2972f8","sha256:d208f796c37a2f2ca582472953d80f8eacee2a5168b2e006bd8e3aeaecf9da83"],"state_sha256":"988312c6a813f8eda899ab5b5b26815e6964165b8a40df8730e0c98bcd5670cd"}