{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2FAUPFJALFTVWC3NGICOPKERLX","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":"86ae6ac75e723cef5a67d7c75aeb27e08ddaca5fab7733c591680f9ef22d4717","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-24T07:34:03Z","title_canon_sha256":"cd6eb0b2341c1cd6d998156fa0c1e3adbae1e47339048d0f33f195dec662af81"},"schema_version":"1.0","source":{"id":"1603.07455","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07455","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07455v1","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07455","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"2FAUPFJALFTV","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2FAUPFJALFTVWC3N","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2FAUPFJA","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:96b5a9229e4eb6394f158fcd3615900723abc3616439910cc932eed48953448a","target":"graph","created_at":"2026-05-18T01:18:20Z","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 that a linear d-dimensional Schr{\\\"o}dinger equation on $\\mathbb{R}^d$  with harmonic potential $|x|^2$ and small t-quasiperiodic potential $i\\partial\\_t u -- \\Delta u + |x|^2 u + \\epsilon V (t\\omega, x)u = 0, x \\in \\mathbb{R}^d$  reduces to an autonomous system for most values of the frequency vector $\\omega \\in \\mathbb{R}^n$. As a consequence any solution of such a linear PDE is almost periodic in time and remains bounded in all Sobolev norms.","authors_text":"Beno\\^it Gr\\'ebert (LMJL), Eric Paturel (LMJL)","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-24T07:34:03Z","title":"On reducibility of Quantum Harmonic Oscillator on $\\mathbb{R}^d$ with quasiperiodic in time potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07455","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:c838547c51155aaba9cf66447b3852668df90e0d06b42fff6cb35779bcbc512c","target":"record","created_at":"2026-05-18T01:18:20Z","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":"86ae6ac75e723cef5a67d7c75aeb27e08ddaca5fab7733c591680f9ef22d4717","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-24T07:34:03Z","title_canon_sha256":"cd6eb0b2341c1cd6d998156fa0c1e3adbae1e47339048d0f33f195dec662af81"},"schema_version":"1.0","source":{"id":"1603.07455","kind":"arxiv","version":1}},"canonical_sha256":"d14147952059675b0b6d3204e7a8915ddf2a5abcf589a610bc4b06d846a84fca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d14147952059675b0b6d3204e7a8915ddf2a5abcf589a610bc4b06d846a84fca","first_computed_at":"2026-05-18T01:18:20.877001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:20.877001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ItdAPXyNtiuBXoEeQyZXzRoqvAAeQ9ykIWjj9apWzD2PHrZFrIc6yaG8az/7vwSuhphPJ3oX7O8SSdhmi3SrBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:20.877588Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07455","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c838547c51155aaba9cf66447b3852668df90e0d06b42fff6cb35779bcbc512c","sha256:96b5a9229e4eb6394f158fcd3615900723abc3616439910cc932eed48953448a"],"state_sha256":"0538cbc6867cf2924169092ecdca9c71c02d0731314d29ab945e70199c21d954"}