{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:6NVQGZ2MDIXCIWZQ5FBXKEFZXR","short_pith_number":"pith:6NVQGZ2M","schema_version":"1.0","canonical_sha256":"f36b03674c1a2e245b30e9437510b9bc70e47d7d71d2a10c64a7c840510a179d","source":{"kind":"arxiv","id":"1904.03703","version":1},"attestation_state":"computed","paper":{"title":"Long time growth of Sobolev norms in time dependent semiclassical anharmonic oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Alberto Maspero, Emanuele Haus","submitted_at":"2019-04-07T18:19:26Z","abstract_excerpt":"We consider the semiclassical Schr\\\"odinger equation on $\\mathbb R^d$ given by $$\\mathrm{i} \\hbar \\partial_t \\psi = \\left(-\\frac{\\hbar^2}{2} \\Delta + W_l(x) \\right)\\psi + V(t,x)\\psi ,$$ where $W_l$ is an anharmonic trapping of the form $W_l(x)= \\frac{1}{2l}\\sum_{j=1}^d x_j^{2l}$, $l\\geq 2$ is an integer and $\\hbar$ is a semiclassical small parameter. We construct a smooth potential $V(t,x)$, bounded in time with its derivatives, and an initial datum such that the Sobolev norms of the solution grow at a logarithmic speed for all times of order $\\log^{\\frac12}(\\hbar^{-1})$. The proof relies on t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1904.03703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-07T18:19:26Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f195365cfe2bc1af14b8fb93c2de2d26c2b0580951fcd6ec2a985ffd81dc876a","abstract_canon_sha256":"366a70c36aa6b97b9e448dd6b6c0abfc25fe196040087d30f1d1400f4fbaf5f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:12.449346Z","signature_b64":"zMZXVzUxtOK78sDIuxWV4eC2AAjPrAhfbWjCaTwkXACJX8OCmixHPdrznnCK21odBm8Ha6fKwsb9MjRIWOBQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f36b03674c1a2e245b30e9437510b9bc70e47d7d71d2a10c64a7c840510a179d","last_reissued_at":"2026-05-17T23:49:12.448587Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:12.448587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long time growth of Sobolev norms in time dependent semiclassical anharmonic oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Alberto Maspero, Emanuele Haus","submitted_at":"2019-04-07T18:19:26Z","abstract_excerpt":"We consider the semiclassical Schr\\\"odinger equation on $\\mathbb R^d$ given by $$\\mathrm{i} \\hbar \\partial_t \\psi = \\left(-\\frac{\\hbar^2}{2} \\Delta + W_l(x) \\right)\\psi + V(t,x)\\psi ,$$ where $W_l$ is an anharmonic trapping of the form $W_l(x)= \\frac{1}{2l}\\sum_{j=1}^d x_j^{2l}$, $l\\geq 2$ is an integer and $\\hbar$ is a semiclassical small parameter. We construct a smooth potential $V(t,x)$, bounded in time with its derivatives, and an initial datum such that the Sobolev norms of the solution grow at a logarithmic speed for all times of order $\\log^{\\frac12}(\\hbar^{-1})$. The proof relies on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03703","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1904.03703","created_at":"2026-05-17T23:49:12.448731+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.03703v1","created_at":"2026-05-17T23:49:12.448731+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03703","created_at":"2026-05-17T23:49:12.448731+00:00"},{"alias_kind":"pith_short_12","alias_value":"6NVQGZ2MDIXC","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"6NVQGZ2MDIXCIWZQ","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"6NVQGZ2M","created_at":"2026-05-18T12:33:10.108867+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6NVQGZ2MDIXCIWZQ5FBXKEFZXR","json":"https://pith.science/pith/6NVQGZ2MDIXCIWZQ5FBXKEFZXR.json","graph_json":"https://pith.science/api/pith-number/6NVQGZ2MDIXCIWZQ5FBXKEFZXR/graph.json","events_json":"https://pith.science/api/pith-number/6NVQGZ2MDIXCIWZQ5FBXKEFZXR/events.json","paper":"https://pith.science/paper/6NVQGZ2M"},"agent_actions":{"view_html":"https://pith.science/pith/6NVQGZ2MDIXCIWZQ5FBXKEFZXR","download_json":"https://pith.science/pith/6NVQGZ2MDIXCIWZQ5FBXKEFZXR.json","view_paper":"https://pith.science/paper/6NVQGZ2M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.03703&json=true","fetch_graph":"https://pith.science/api/pith-number/6NVQGZ2MDIXCIWZQ5FBXKEFZXR/graph.json","fetch_events":"https://pith.science/api/pith-number/6NVQGZ2MDIXCIWZQ5FBXKEFZXR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6NVQGZ2MDIXCIWZQ5FBXKEFZXR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6NVQGZ2MDIXCIWZQ5FBXKEFZXR/action/storage_attestation","attest_author":"https://pith.science/pith/6NVQGZ2MDIXCIWZQ5FBXKEFZXR/action/author_attestation","sign_citation":"https://pith.science/pith/6NVQGZ2MDIXCIWZQ5FBXKEFZXR/action/citation_signature","submit_replication":"https://pith.science/pith/6NVQGZ2MDIXCIWZQ5FBXKEFZXR/action/replication_record"}},"created_at":"2026-05-17T23:49:12.448731+00:00","updated_at":"2026-05-17T23:49:12.448731+00:00"}