{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:7XQ4OSN7LNSFFTT4AMTCTUKO5E","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":"b024a7650c9ecdc9b4542da5c017a361568221a1f258d8ed3ee217053c4df371","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-09-10T13:34:39Z","title_canon_sha256":"069f300919eedbd0a336d533cc38244acef82b2a43d485758dfb24e7703c60a6"},"schema_version":"1.0","source":{"id":"0909.1942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.1942","created_at":"2026-05-18T02:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"0909.1942v1","created_at":"2026-05-18T02:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1942","created_at":"2026-05-18T02:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"7XQ4OSN7LNSF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7XQ4OSN7LNSFFTT4","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7XQ4OSN7","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:0ec67df183361c19195552ce33a6ebc0b5b2c979785b8b5576ca12cde5221845","target":"graph","created_at":"2026-05-18T02:11:57Z","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"},"paper":{"abstract_excerpt":"In this paper we construct and approximate breathers in the DNLS model starting from the continuous limit: such periodic solutions are obtained as perturbations of the ground state of the NLS model in $H^1(\\RR^n)$, with $n=1,2$. In both the dimensions we recover the Sievers-Takeno (ST) and the Page (P) modes; furthermore, in $\\RR^2$ also the two hybrid (H) modes are constructed. The proof is based on the interpolation of the lattice using the Finite Element Method (FEM).","authors_text":"D. Bambusi, T. Penati","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-09-10T13:34:39Z","title":"Continuous approximation of breathers in one and two dimensional DNLS lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1942","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:d39c7edc3ca268fc3994b78c0b8f181ba65fb9af70887cfc9303ee045a5466ed","target":"record","created_at":"2026-05-18T02:11:57Z","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":"b024a7650c9ecdc9b4542da5c017a361568221a1f258d8ed3ee217053c4df371","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-09-10T13:34:39Z","title_canon_sha256":"069f300919eedbd0a336d533cc38244acef82b2a43d485758dfb24e7703c60a6"},"schema_version":"1.0","source":{"id":"0909.1942","kind":"arxiv","version":1}},"canonical_sha256":"fde1c749bf5b6452ce7c032629d14ee91f1893301e01ba4f289a0752e1e32967","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fde1c749bf5b6452ce7c032629d14ee91f1893301e01ba4f289a0752e1e32967","first_computed_at":"2026-05-18T02:11:57.466656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:11:57.466656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wcoXKr6K405NNYYWiN4uTdEBOLfS8wQEDhCo0+Ko+LqKgUVLIoMoyrHREM5z5cJ+Av+fTW/iM0G6vrxixWxKAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:11:57.467425Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.1942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d39c7edc3ca268fc3994b78c0b8f181ba65fb9af70887cfc9303ee045a5466ed","sha256:0ec67df183361c19195552ce33a6ebc0b5b2c979785b8b5576ca12cde5221845"],"state_sha256":"f0226130d76f54a8101f310d68bbe1c51be6f7661a5ef9e4f12ce732db54ff59"}