{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:LBTFXYIEM6WJJ5ETRPPQSPSIDV","short_pith_number":"pith:LBTFXYIE","canonical_record":{"source":{"id":"cond-mat/0404600","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.soft","submitted_at":"2004-04-25T01:18:35Z","cross_cats_sorted":[],"title_canon_sha256":"c6a5e43c1a5f95f5579584995c1b8683c605f1e18be97a09c77f3932b1788603","abstract_canon_sha256":"1696a959ff755dfd41cded77826db73ade300ce6a75acdbfc32be95659bfa044"},"schema_version":"1.0"},"canonical_sha256":"58665be10467ac94f4938bdf093e481d6a3f125f2532ddbb38f78ddf80b9fd87","source":{"kind":"arxiv","id":"cond-mat/0404600","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0404600","created_at":"2026-05-18T01:39:58Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0404600v1","created_at":"2026-05-18T01:39:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0404600","created_at":"2026-05-18T01:39:58Z"},{"alias_kind":"pith_short_12","alias_value":"LBTFXYIEM6WJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"LBTFXYIEM6WJJ5ET","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"LBTFXYIE","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:LBTFXYIEM6WJJ5ETRPPQSPSIDV","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0404600","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.soft","submitted_at":"2004-04-25T01:18:35Z","cross_cats_sorted":[],"title_canon_sha256":"c6a5e43c1a5f95f5579584995c1b8683c605f1e18be97a09c77f3932b1788603","abstract_canon_sha256":"1696a959ff755dfd41cded77826db73ade300ce6a75acdbfc32be95659bfa044"},"schema_version":"1.0"},"canonical_sha256":"58665be10467ac94f4938bdf093e481d6a3f125f2532ddbb38f78ddf80b9fd87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:58.256773Z","signature_b64":"1nnzAtqPkdZ5+tuxkJxFljtTpeBRe+buAcKYbIJwqpCT3IBW4rTMIbDwErQ25pgYXhJ/rZc/lXvf0fzlL/zqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58665be10467ac94f4938bdf093e481d6a3f125f2532ddbb38f78ddf80b9fd87","last_reissued_at":"2026-05-18T01:39:58.256167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:58.256167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0404600","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:39:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZtUHLJs5ce3h7SkqNRi07T2gQeSMOrRYkkfYjQjhua0sYsRmVzT4FQf0VomQr5JlnyTFt7tqVWapS5mGBzSRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T16:13:26.450636Z"},"content_sha256":"03b68182b1f55309610d5a0508b9cf697f55b1b41e9dd6b9638c4f728c759354","schema_version":"1.0","event_id":"sha256:03b68182b1f55309610d5a0508b9cf697f55b1b41e9dd6b9638c4f728c759354"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:LBTFXYIEM6WJJ5ETRPPQSPSIDV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modulational and Parametric Instabilities of the Discrete Nonlinear Schr\\\"odinger Equation","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"A.R. Bishop, A. Smerzi, P.G. Kevrekidis, Z. Rapti","submitted_at":"2004-04-25T01:18:35Z","abstract_excerpt":"We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{\\\"o}dinger equation setting. The principal motivation for our study stems from the dynamics of Bose-Einstein condensates trapped in a deep optical lattice. We find that under periodic variations of the heights of the interwell barriers (or equivalently of the scattering length), additionally to the modulational instability, a window of parametric instability becomes available to the system. We explore this instability through multiple-scale analysis and identify it numerically. Its pri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0404600","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:39:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jh46NDdnVUaQLP4csuv/6CVOVpYeytTiqYhT9j/feofCqtQwLji8aEcZJ7gKdDcvjyYxM03kZZ2MEHmamqI7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T16:13:26.450996Z"},"content_sha256":"aa9397eae8960173b8f8b45b0f9e3513e9eaf87c4db14da7713b5c2df640535e","schema_version":"1.0","event_id":"sha256:aa9397eae8960173b8f8b45b0f9e3513e9eaf87c4db14da7713b5c2df640535e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBTFXYIEM6WJJ5ETRPPQSPSIDV/bundle.json","state_url":"https://pith.science/pith/LBTFXYIEM6WJJ5ETRPPQSPSIDV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBTFXYIEM6WJJ5ETRPPQSPSIDV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-19T16:13:26Z","links":{"resolver":"https://pith.science/pith/LBTFXYIEM6WJJ5ETRPPQSPSIDV","bundle":"https://pith.science/pith/LBTFXYIEM6WJJ5ETRPPQSPSIDV/bundle.json","state":"https://pith.science/pith/LBTFXYIEM6WJJ5ETRPPQSPSIDV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBTFXYIEM6WJJ5ETRPPQSPSIDV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:LBTFXYIEM6WJJ5ETRPPQSPSIDV","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":"1696a959ff755dfd41cded77826db73ade300ce6a75acdbfc32be95659bfa044","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.soft","submitted_at":"2004-04-25T01:18:35Z","title_canon_sha256":"c6a5e43c1a5f95f5579584995c1b8683c605f1e18be97a09c77f3932b1788603"},"schema_version":"1.0","source":{"id":"cond-mat/0404600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0404600","created_at":"2026-05-18T01:39:58Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0404600v1","created_at":"2026-05-18T01:39:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0404600","created_at":"2026-05-18T01:39:58Z"},{"alias_kind":"pith_short_12","alias_value":"LBTFXYIEM6WJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"LBTFXYIEM6WJJ5ET","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"LBTFXYIE","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:aa9397eae8960173b8f8b45b0f9e3513e9eaf87c4db14da7713b5c2df640535e","target":"graph","created_at":"2026-05-18T01:39:58Z","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 examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{\\\"o}dinger equation setting. The principal motivation for our study stems from the dynamics of Bose-Einstein condensates trapped in a deep optical lattice. We find that under periodic variations of the heights of the interwell barriers (or equivalently of the scattering length), additionally to the modulational instability, a window of parametric instability becomes available to the system. We explore this instability through multiple-scale analysis and identify it numerically. Its pri","authors_text":"A.R. Bishop, A. Smerzi, P.G. Kevrekidis, Z. Rapti","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.soft","submitted_at":"2004-04-25T01:18:35Z","title":"Modulational and Parametric Instabilities of the Discrete Nonlinear Schr\\\"odinger Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0404600","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":"sha256:03b68182b1f55309610d5a0508b9cf697f55b1b41e9dd6b9638c4f728c759354","target":"record","created_at":"2026-05-18T01:39:58Z","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":"1696a959ff755dfd41cded77826db73ade300ce6a75acdbfc32be95659bfa044","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.soft","submitted_at":"2004-04-25T01:18:35Z","title_canon_sha256":"c6a5e43c1a5f95f5579584995c1b8683c605f1e18be97a09c77f3932b1788603"},"schema_version":"1.0","source":{"id":"cond-mat/0404600","kind":"arxiv","version":1}},"canonical_sha256":"58665be10467ac94f4938bdf093e481d6a3f125f2532ddbb38f78ddf80b9fd87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58665be10467ac94f4938bdf093e481d6a3f125f2532ddbb38f78ddf80b9fd87","first_computed_at":"2026-05-18T01:39:58.256167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:58.256167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1nnzAtqPkdZ5+tuxkJxFljtTpeBRe+buAcKYbIJwqpCT3IBW4rTMIbDwErQ25pgYXhJ/rZc/lXvf0fzlL/zqCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:58.256773Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0404600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03b68182b1f55309610d5a0508b9cf697f55b1b41e9dd6b9638c4f728c759354","sha256:aa9397eae8960173b8f8b45b0f9e3513e9eaf87c4db14da7713b5c2df640535e"],"state_sha256":"ca56ba6d12434a1f7bbfc45bcf561140177d639431bb7b9dcb237117547572a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TFTaJGvbxJVK7CfpTUl+VouvRLZ6G5sLS7GLIAuJmwtklPgXjtDvo1LQoZkZpwx9yGBmiOQmO7p/ScQpYpL2AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T16:13:26.452951Z","bundle_sha256":"52f245ba5abb66bd966a368985e962487875c822473335a8210f655d0ac038c2"}}