{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OET32B4XUCYN7UUT3MH4PNEHLO","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":"0c331955bcd0ed035644a678577fc8d2e5ab492cbeefd714a7026cdbe229ba26","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-31T07:08:22Z","title_canon_sha256":"364508118cb84b122425e6edb2fd0fc36b4f733bb098619357436d1f00e7ac26"},"schema_version":"1.0","source":{"id":"1108.6136","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.6136","created_at":"2026-05-18T02:00:44Z"},{"alias_kind":"arxiv_version","alias_value":"1108.6136v2","created_at":"2026-05-18T02:00:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.6136","created_at":"2026-05-18T02:00:44Z"},{"alias_kind":"pith_short_12","alias_value":"OET32B4XUCYN","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OET32B4XUCYN7UUT","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OET32B4X","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:3dac418713380e71453e29a56f6ccd50871a6e4522ee6020f82fed0ef667b009","target":"graph","created_at":"2026-05-18T02:00:44Z","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 a general class of discrete nonlinear Schroedinger equations (DNLS) on the lattice $h \\mathbb{Z}$ with mesh size $h>0$. In the continuum limit when $h \\to 0$, we prove that the limiting dynamics are given by a nonlinear Schroedinger equation (NLS) on $\\mathbb{R}$ with the fractional Laplacian $(-\\Delta)^\\alpha$ as dispersive symbol. In particular, we obtain that fractional powers $1/2 < \\alpha < 1$ arise from long-range lattice interactions when passing to the continuum limit, whereas NLS with the non-fractional Laplacian $-\\Delta$ describes the dispersion in the continuum limit fo","authors_text":"Enno Lenzmann, Gigliola Staffilani, Kay Kirkpatrick","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-31T07:08:22Z","title":"On the continuum limit for discrete NLS with long-range lattice interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6136","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":"sha256:6fe6ec8a1fdafb35c4863b11f8aaa3485e2d97e7baa40f0bbd2b3fe97ed2fbfa","target":"record","created_at":"2026-05-18T02:00:44Z","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":"0c331955bcd0ed035644a678577fc8d2e5ab492cbeefd714a7026cdbe229ba26","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-31T07:08:22Z","title_canon_sha256":"364508118cb84b122425e6edb2fd0fc36b4f733bb098619357436d1f00e7ac26"},"schema_version":"1.0","source":{"id":"1108.6136","kind":"arxiv","version":2}},"canonical_sha256":"7127bd0797a0b0dfd293db0fc7b4875bbcc8d707a0c7d7efe7fba46b56ec4ba9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7127bd0797a0b0dfd293db0fc7b4875bbcc8d707a0c7d7efe7fba46b56ec4ba9","first_computed_at":"2026-05-18T02:00:44.230112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:44.230112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+AySz3znshgqRIDVJsXiZVpfd56CPtE+lIHDEi6MZi9DNqC6DOSyz6pLznNRneSrVocfeBwJHCpp5feXIiv1Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:44.230611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.6136","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fe6ec8a1fdafb35c4863b11f8aaa3485e2d97e7baa40f0bbd2b3fe97ed2fbfa","sha256:3dac418713380e71453e29a56f6ccd50871a6e4522ee6020f82fed0ef667b009"],"state_sha256":"3b5456b0f11021c6a97316f40363b028f7cfbb2aa45ca644a287e14c851e9cca"}