{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QZQ7HZU42TJCOOT7WUGK7D5QQQ","short_pith_number":"pith:QZQ7HZU4","canonical_record":{"source":{"id":"1412.3213","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-10T07:13:40Z","cross_cats_sorted":[],"title_canon_sha256":"afb3567a3b824c5ea01fdca42837806eb9ba22d2d75cb80fdf2c538f34f631f2","abstract_canon_sha256":"aad51eefda18395a37d9429888ad81ceab80e99e90baa809258d14b6d6e4d7f9"},"schema_version":"1.0"},"canonical_sha256":"8661f3e69cd4d2273a7fb50caf8fb0843c6e513813825b2d0b4763dd9d334993","source":{"kind":"arxiv","id":"1412.3213","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3213","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3213v2","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3213","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"pith_short_12","alias_value":"QZQ7HZU42TJC","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QZQ7HZU42TJCOOT7","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QZQ7HZU4","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QZQ7HZU42TJCOOT7WUGK7D5QQQ","target":"record","payload":{"canonical_record":{"source":{"id":"1412.3213","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-10T07:13:40Z","cross_cats_sorted":[],"title_canon_sha256":"afb3567a3b824c5ea01fdca42837806eb9ba22d2d75cb80fdf2c538f34f631f2","abstract_canon_sha256":"aad51eefda18395a37d9429888ad81ceab80e99e90baa809258d14b6d6e4d7f9"},"schema_version":"1.0"},"canonical_sha256":"8661f3e69cd4d2273a7fb50caf8fb0843c6e513813825b2d0b4763dd9d334993","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:30.914575Z","signature_b64":"gJqTGmaAZFhsd1VXc2lwJ9srSyef3WSXeYO12eWPLkQlO/4V+s/vvGtQGCPtztXMtf/3PNZsZFihGpp4Ur6gAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8661f3e69cd4d2273a7fb50caf8fb0843c6e513813825b2d0b4763dd9d334993","last_reissued_at":"2026-05-18T01:17:30.913876Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:30.913876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.3213","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O/T918tAeJVxIU1d4mNjyjBjuBbMG8YiAkIpQBpDCorE8ZAZkx9qly6tSJMVybLixb9unzIoLkB+WqWwlZkjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:27:56.571008Z"},"content_sha256":"d47044ba85d330ca44218e86d14e89c4bfabff95f425482c799436d105b18885","schema_version":"1.0","event_id":"sha256:d47044ba85d330ca44218e86d14e89c4bfabff95f425482c799436d105b18885"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QZQ7HZU42TJCOOT7WUGK7D5QQQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence and asymptotic stability of quasi-periodic solution of discrete NLS with potential in $\\mathbb{Z}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaya Maeda","submitted_at":"2014-12-10T07:13:40Z","abstract_excerpt":"We prove the existence of a 2-parameter family of small quasi-periodic in time solutions of discrete nonlinear Schr\\\"odinger equation (DNLS). We further show that all small solutions of DNLS decouples to this quasi-periodic solution and dispersive wave."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3213","kind":"arxiv","version":2},"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":"2026-05-18T01:17:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dzpLCgg8tnsj+SlooVKCUXZNEMw8sinSnow5zOKh2HBk19drcSdUxLqweHbbLemUdZfESYWabw6MCg54NCF0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:27:56.571651Z"},"content_sha256":"f30014a2ba0eb8e0f8e7f6ce3ba3b5f95762992684826fc82717ee5487c3b4b7","schema_version":"1.0","event_id":"sha256:f30014a2ba0eb8e0f8e7f6ce3ba3b5f95762992684826fc82717ee5487c3b4b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZQ7HZU42TJCOOT7WUGK7D5QQQ/bundle.json","state_url":"https://pith.science/pith/QZQ7HZU42TJCOOT7WUGK7D5QQQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZQ7HZU42TJCOOT7WUGK7D5QQQ/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":"2026-06-07T17:27:56Z","links":{"resolver":"https://pith.science/pith/QZQ7HZU42TJCOOT7WUGK7D5QQQ","bundle":"https://pith.science/pith/QZQ7HZU42TJCOOT7WUGK7D5QQQ/bundle.json","state":"https://pith.science/pith/QZQ7HZU42TJCOOT7WUGK7D5QQQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZQ7HZU42TJCOOT7WUGK7D5QQQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QZQ7HZU42TJCOOT7WUGK7D5QQQ","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":"aad51eefda18395a37d9429888ad81ceab80e99e90baa809258d14b6d6e4d7f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-10T07:13:40Z","title_canon_sha256":"afb3567a3b824c5ea01fdca42837806eb9ba22d2d75cb80fdf2c538f34f631f2"},"schema_version":"1.0","source":{"id":"1412.3213","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3213","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3213v2","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3213","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"pith_short_12","alias_value":"QZQ7HZU42TJC","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QZQ7HZU42TJCOOT7","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QZQ7HZU4","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:f30014a2ba0eb8e0f8e7f6ce3ba3b5f95762992684826fc82717ee5487c3b4b7","target":"graph","created_at":"2026-05-18T01:17:30Z","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 prove the existence of a 2-parameter family of small quasi-periodic in time solutions of discrete nonlinear Schr\\\"odinger equation (DNLS). We further show that all small solutions of DNLS decouples to this quasi-periodic solution and dispersive wave.","authors_text":"Masaya Maeda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-10T07:13:40Z","title":"Existence and asymptotic stability of quasi-periodic solution of discrete NLS with potential in $\\mathbb{Z}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3213","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:d47044ba85d330ca44218e86d14e89c4bfabff95f425482c799436d105b18885","target":"record","created_at":"2026-05-18T01:17:30Z","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":"aad51eefda18395a37d9429888ad81ceab80e99e90baa809258d14b6d6e4d7f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-10T07:13:40Z","title_canon_sha256":"afb3567a3b824c5ea01fdca42837806eb9ba22d2d75cb80fdf2c538f34f631f2"},"schema_version":"1.0","source":{"id":"1412.3213","kind":"arxiv","version":2}},"canonical_sha256":"8661f3e69cd4d2273a7fb50caf8fb0843c6e513813825b2d0b4763dd9d334993","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8661f3e69cd4d2273a7fb50caf8fb0843c6e513813825b2d0b4763dd9d334993","first_computed_at":"2026-05-18T01:17:30.913876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:30.913876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gJqTGmaAZFhsd1VXc2lwJ9srSyef3WSXeYO12eWPLkQlO/4V+s/vvGtQGCPtztXMtf/3PNZsZFihGpp4Ur6gAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:30.914575Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3213","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d47044ba85d330ca44218e86d14e89c4bfabff95f425482c799436d105b18885","sha256:f30014a2ba0eb8e0f8e7f6ce3ba3b5f95762992684826fc82717ee5487c3b4b7"],"state_sha256":"9261ed7cf484bf5ded903323103f51f1bcd6d50fbab79e2952087e68c0eb61c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9p12NJKf1uAVrJaXUcuOVup+rN0TwdpZQEn1ubPxbcwFeRCrrlNWZAoJhkFYNDNvDZilwrHc+3kw0sl++tU2DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:27:56.574937Z","bundle_sha256":"76a6f460b6cd60b5f5ce33276baf5a2c52c5ff2b64f954363d14e1c31b1951b9"}}