{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MQNIHLMBHZWVOF7T2BGTOI66G4","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":"7b45337c7efc6a485c6395a90c6e2daa61c0579c0301ef6f041d9aa8b841ee6c","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-01-03T11:58:19Z","title_canon_sha256":"1ae63c705b332f657fd8547e012d10e15e3ab0f0dbee3722ac5f3d9f4d562272"},"schema_version":"1.0","source":{"id":"1101.0501","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.0501","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1101.0501v1","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0501","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"MQNIHLMBHZWV","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MQNIHLMBHZWVOF7T","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MQNIHLMB","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:a3394e38f42407fc2cfea1f60c9bb66ee8d43839d3c5e2093977f284df57630a","target":"graph","created_at":"2026-05-18T04:20:23Z","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 study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schr\\\"{o}dinger (DNLS) equation, including a local linear or nonlinear defect. Discrete solitons pinned to the defects are investigated by means of the numerical continuation from the anti-continuum limit and also using the variational approximation (VA), which features a good agreement for strongly localized modes. The models with the time-modulated strengths of the linear or nonlinear defect are considered too. In that case, one can temporarily shift the critical norm, b","authors_text":"Boris A. Malomed, Valeriy A. Brazhnyi","cross_cats":["physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-01-03T11:58:19Z","title":"Localization and delocalization of two-dimensional discrete solitons pinned to linear and nonlinear defects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0501","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":"sha256:3aa62f86e4466f0c4ad1f2f893c51a68aa80db505d1fb17b3e5aceb6e30a8c53","target":"record","created_at":"2026-05-18T04:20:23Z","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":"7b45337c7efc6a485c6395a90c6e2daa61c0579c0301ef6f041d9aa8b841ee6c","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-01-03T11:58:19Z","title_canon_sha256":"1ae63c705b332f657fd8547e012d10e15e3ab0f0dbee3722ac5f3d9f4d562272"},"schema_version":"1.0","source":{"id":"1101.0501","kind":"arxiv","version":1}},"canonical_sha256":"641a83ad813e6d5717f3d04d3723de370b27707f71247bab6bb731dc2dcc5c5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"641a83ad813e6d5717f3d04d3723de370b27707f71247bab6bb731dc2dcc5c5c","first_computed_at":"2026-05-18T04:20:23.195965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:23.195965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"202qhoW5xHby1UX7SbSccLtkerj2MeCrdye+HyTqwEdYbYD2LHaPK0Fqtts5kBSc/U9AETly9ADuBowFasLBDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:23.196611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.0501","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3aa62f86e4466f0c4ad1f2f893c51a68aa80db505d1fb17b3e5aceb6e30a8c53","sha256:a3394e38f42407fc2cfea1f60c9bb66ee8d43839d3c5e2093977f284df57630a"],"state_sha256":"51080afa4caf4e06e9bb3b164a9f6cf3c4569b736a1813ef842ec5ab8a2f6ada"}