{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UVN6LS6QZS4LDO4VDBE3ZTDK32","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":"8da8bf3d162ea2cd1063101ecdcc9be1247ba7ddee2ae74670a6a7c875ef1d2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-13T23:53:53Z","title_canon_sha256":"03d905b67f0b19a343c48c9f4d730086f32da5a86ecc1a83c69377ac5e6c6088"},"schema_version":"1.0","source":{"id":"1908.04890","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04890","created_at":"2026-07-04T23:55:57Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04890v1","created_at":"2026-07-04T23:55:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04890","created_at":"2026-07-04T23:55:57Z"},{"alias_kind":"pith_short_12","alias_value":"UVN6LS6QZS4L","created_at":"2026-07-04T23:55:57Z"},{"alias_kind":"pith_short_16","alias_value":"UVN6LS6QZS4LDO4V","created_at":"2026-07-04T23:55:57Z"},{"alias_kind":"pith_short_8","alias_value":"UVN6LS6Q","created_at":"2026-07-04T23:55:57Z"}],"graph_snapshots":[{"event_id":"sha256:e3efda81406f9a858ebdd0114b3548f337e9d24984f90addc9631696b972c094","target":"graph","created_at":"2026-07-04T23:55:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.04890/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the existence and asymptotic expansion of a large class of solutions to nonlinear Helmholtz equations of the form \\begin{equation*} (\\Delta - \\lambda^2) u = N[u], \\end{equation*} where $\\Delta = -\\sum_j \\partial^2_j$ is the Laplacian on $\\mathbb{R}^n$ with sign convention that it is positive as an operator, $\\lambda$ is a positive real number, and $N[u]$ is a nonlinear operator that is a sum of monomials of degree $\\geq p$ in $u$, $\\overline{u}$ and their derivatives of order up to two, for some $p \\geq 2$. Nonlinear Helmholtz eigenfunctions with $N[u]= \\pm |u|^{p-1} u$ were first con","authors_text":"Andrew Hassell, Jacob Shapiro, Jesse Gell-Redman, Junyong Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-13T23:53:53Z","title":"Existence and asymptotics of nonlinear Helmholtz eigenfunctions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04890","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":"sha256:23252318002b31504d2fd4f9a62c953cb0a71c4db3e4a0176f5a3e07393cf542","target":"record","created_at":"2026-07-04T23:55:57Z","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":"8da8bf3d162ea2cd1063101ecdcc9be1247ba7ddee2ae74670a6a7c875ef1d2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-13T23:53:53Z","title_canon_sha256":"03d905b67f0b19a343c48c9f4d730086f32da5a86ecc1a83c69377ac5e6c6088"},"schema_version":"1.0","source":{"id":"1908.04890","kind":"arxiv","version":1}},"canonical_sha256":"a55be5cbd0ccb8b1bb951849bccc6ade8e7f4d784e0a44ce9ce0e6c11e54be6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a55be5cbd0ccb8b1bb951849bccc6ade8e7f4d784e0a44ce9ce0e6c11e54be6c","first_computed_at":"2026-07-04T23:55:57.830839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:55:57.830839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Q7cJA1B3fYByOQq0te3VMiD3ENvVLo51eaMqhLLejfiD6x3yle9Ptd27D3O7YgA1k36xun2KhV/Eax+JFnRDw==","signature_status":"signed_v1","signed_at":"2026-07-04T23:55:57.831226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04890","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23252318002b31504d2fd4f9a62c953cb0a71c4db3e4a0176f5a3e07393cf542","sha256:e3efda81406f9a858ebdd0114b3548f337e9d24984f90addc9631696b972c094"],"state_sha256":"2f18c7f0605ef7b8db6fe6bebbe62cf762548eaf302cc54ef58c75ab5b139a73"}