{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:457B7RERQITKYMVVRGYWKQMXMH","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":"be62091bed68227e9bb518cf52e87cb90118bcc4d4883765b596144b26904539","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-20T04:07:54Z","title_canon_sha256":"65888dd09e6c07b6cab5e287150df7b7fbbcc7a62d59b62a48f68bc9d79d82e3"},"schema_version":"1.0","source":{"id":"1806.07542","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07542","created_at":"2026-05-18T00:12:47Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07542v1","created_at":"2026-05-18T00:12:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07542","created_at":"2026-05-18T00:12:47Z"},{"alias_kind":"pith_short_12","alias_value":"457B7RERQITK","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"457B7RERQITKYMVV","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"457B7RER","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:454760d48f54f0433f14932df7ca862c8709f32f7b93d800e8bd5b3963df0c15","target":"graph","created_at":"2026-05-18T00:12:47Z","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 discrete nonlinear Schr\\\"odinger equations (DNLS) on the lattice $h\\mathbb{Z}^d$ whose linear part is determined by the discrete Laplacian which accounts only for nearest neighbor interactions, or by its fractional power. We show that in the continuum limit $h\\to 0$, solutions to DNLS converge strongly in $L^2$ to those to the corresponding continuum equations, but a precise rate of convergence is also calculated. In particular cases, this result improves weak convergence in Kirkpatrick, Lenzmann and Staffilani \\cite{KLS}. Our proof is based on a suitable adjustment of dispersive P","authors_text":"Changhun Yang, Younghun Hong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-20T04:07:54Z","title":"Strong Convergence for Discrete Nonlinear Schr\\\"odinger equations in the Continuum Limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07542","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":"sha256:75205def962f3e8176155dab02a33664f21b4c5e7e64f4dbda9d7eafabbceadc","target":"record","created_at":"2026-05-18T00:12:47Z","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":"be62091bed68227e9bb518cf52e87cb90118bcc4d4883765b596144b26904539","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-20T04:07:54Z","title_canon_sha256":"65888dd09e6c07b6cab5e287150df7b7fbbcc7a62d59b62a48f68bc9d79d82e3"},"schema_version":"1.0","source":{"id":"1806.07542","kind":"arxiv","version":1}},"canonical_sha256":"e77e1fc4918226ac32b589b165419761e59da40f1320781f2385eec5ae54d7eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e77e1fc4918226ac32b589b165419761e59da40f1320781f2385eec5ae54d7eb","first_computed_at":"2026-05-18T00:12:47.446584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:47.446584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GMumcjPW1yQeChO9S0hjhVckDK+sIq0bdrXV52+wUORWPkDfj4lZKt1PT8J7k9FranOAQLXn4gahAs59BAozAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:47.447118Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07542","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75205def962f3e8176155dab02a33664f21b4c5e7e64f4dbda9d7eafabbceadc","sha256:454760d48f54f0433f14932df7ca862c8709f32f7b93d800e8bd5b3963df0c15"],"state_sha256":"c74ae3ef84ed469e28b5528f779b04e2017cef3dc9dc3693e235df835e72f218"}