{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OJNQTN25VD6NA67G2P4GYHYU7H","short_pith_number":"pith:OJNQTN25","schema_version":"1.0","canonical_sha256":"725b09b75da8fcd07be6d3f86c1f14f9e84408acc8a0f1fdde3128a191567edb","source":{"kind":"arxiv","id":"1409.1262","version":2},"attestation_state":"computed","paper":{"title":"On weak and strong solution operators for evolution equations coming from quadratic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.AP","authors_text":"Alexandru Aleman, Joe Viola","submitted_at":"2014-09-03T21:11:34Z","abstract_excerpt":"We identify, through a change of variables, solution operators for evolution equations with generators given by certain simple first-order differential operators acting on Fock spaces. This analysis applies, through unitary equivalence, to a broad class of supersymmetric quadratic multiplication-differentiation operators acting on $L^2(\\Bbb{R}^n)$ which includes the elliptic and weakly elliptic quadratic operators. We demonstrate a variety of sharp results on boundedness, decay, and return to equilibrium for these solution operators, connecting the short-time behavior with the range of the sym"},"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":"1409.1262","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-03T21:11:34Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"9318d7018509055997fe7420cf138ee8d4f522e5aaa2fa60aa56f566c1e61c29","abstract_canon_sha256":"ec4468278a907b31cac6e2504c0fbb8197a8e0fb88881f7795b4da5a24c9ae15"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:13.717227Z","signature_b64":"HbWqiXE02bC6QNbdR/AzISaPCC3TduEECDhtx0y0jLXuiLGKgS8o175tMWRy0vPKmeBQgnlLRh+HcxI7ekT2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"725b09b75da8fcd07be6d3f86c1f14f9e84408acc8a0f1fdde3128a191567edb","last_reissued_at":"2026-05-18T01:11:13.716745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:13.716745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On weak and strong solution operators for evolution equations coming from quadratic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.AP","authors_text":"Alexandru Aleman, Joe Viola","submitted_at":"2014-09-03T21:11:34Z","abstract_excerpt":"We identify, through a change of variables, solution operators for evolution equations with generators given by certain simple first-order differential operators acting on Fock spaces. This analysis applies, through unitary equivalence, to a broad class of supersymmetric quadratic multiplication-differentiation operators acting on $L^2(\\Bbb{R}^n)$ which includes the elliptic and weakly elliptic quadratic operators. We demonstrate a variety of sharp results on boundedness, decay, and return to equilibrium for these solution operators, connecting the short-time behavior with the range of the sym"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1262","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1409.1262","created_at":"2026-05-18T01:11:13.716814+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.1262v2","created_at":"2026-05-18T01:11:13.716814+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1262","created_at":"2026-05-18T01:11:13.716814+00:00"},{"alias_kind":"pith_short_12","alias_value":"OJNQTN25VD6N","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"OJNQTN25VD6NA67G","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"OJNQTN25","created_at":"2026-05-18T12:28:41.024544+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/OJNQTN25VD6NA67G2P4GYHYU7H","json":"https://pith.science/pith/OJNQTN25VD6NA67G2P4GYHYU7H.json","graph_json":"https://pith.science/api/pith-number/OJNQTN25VD6NA67G2P4GYHYU7H/graph.json","events_json":"https://pith.science/api/pith-number/OJNQTN25VD6NA67G2P4GYHYU7H/events.json","paper":"https://pith.science/paper/OJNQTN25"},"agent_actions":{"view_html":"https://pith.science/pith/OJNQTN25VD6NA67G2P4GYHYU7H","download_json":"https://pith.science/pith/OJNQTN25VD6NA67G2P4GYHYU7H.json","view_paper":"https://pith.science/paper/OJNQTN25","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.1262&json=true","fetch_graph":"https://pith.science/api/pith-number/OJNQTN25VD6NA67G2P4GYHYU7H/graph.json","fetch_events":"https://pith.science/api/pith-number/OJNQTN25VD6NA67G2P4GYHYU7H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OJNQTN25VD6NA67G2P4GYHYU7H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OJNQTN25VD6NA67G2P4GYHYU7H/action/storage_attestation","attest_author":"https://pith.science/pith/OJNQTN25VD6NA67G2P4GYHYU7H/action/author_attestation","sign_citation":"https://pith.science/pith/OJNQTN25VD6NA67G2P4GYHYU7H/action/citation_signature","submit_replication":"https://pith.science/pith/OJNQTN25VD6NA67G2P4GYHYU7H/action/replication_record"}},"created_at":"2026-05-18T01:11:13.716814+00:00","updated_at":"2026-05-18T01:11:13.716814+00:00"}