{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:27WKZUAFNUWZ5ICKVQSPYF5R2H","short_pith_number":"pith:27WKZUAF","schema_version":"1.0","canonical_sha256":"d7ecacd0056d2d9ea04aac24fc17b1d1ff9715fc2fbb55d0128df7f644da9d96","source":{"kind":"arxiv","id":"1906.07908","version":1},"attestation_state":"computed","paper":{"title":"A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Rupert L. Frank, Zhou Gang","submitted_at":"2019-06-19T04:31:24Z","abstract_excerpt":"We discuss a one-dimensional version of the Landau-Pekar equations, which are a system of coupled differential equations with two different time scales. We derive an approximation on the slow time scale in the spirit of a non-linear adiabatic theorem. Dispersive estimates for solutions of the Schr\\\"odinger equation with time-dependent potential are a key technical ingredient in our proof."},"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":"1906.07908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-19T04:31:24Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"cdfa5c515bf887c87dd7b119c9267d2ab5e102976bb976f41fb711f68132b2a0","abstract_canon_sha256":"bf0d0aeb993621b3c92651bea86a130a6c512ad328785368936329f13bacdbe0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:57.331498Z","signature_b64":"hCpgF2gAdfkCGGeMAp7X+/i9FtvVU7UMNsU8tMvjxe1HCWBbYEUNaACgDiZAy3Q38+dqoJCpIZGuVTiAU4buAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7ecacd0056d2d9ea04aac24fc17b1d1ff9715fc2fbb55d0128df7f644da9d96","last_reissued_at":"2026-05-17T23:42:57.330890Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:57.330890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Rupert L. Frank, Zhou Gang","submitted_at":"2019-06-19T04:31:24Z","abstract_excerpt":"We discuss a one-dimensional version of the Landau-Pekar equations, which are a system of coupled differential equations with two different time scales. We derive an approximation on the slow time scale in the spirit of a non-linear adiabatic theorem. Dispersive estimates for solutions of the Schr\\\"odinger equation with time-dependent potential are a key technical ingredient in our proof."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07908","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":"1906.07908","created_at":"2026-05-17T23:42:57.330965+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.07908v1","created_at":"2026-05-17T23:42:57.330965+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.07908","created_at":"2026-05-17T23:42:57.330965+00:00"},{"alias_kind":"pith_short_12","alias_value":"27WKZUAFNUWZ","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"27WKZUAFNUWZ5ICK","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"27WKZUAF","created_at":"2026-05-18T12:33:07.085635+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/27WKZUAFNUWZ5ICKVQSPYF5R2H","json":"https://pith.science/pith/27WKZUAFNUWZ5ICKVQSPYF5R2H.json","graph_json":"https://pith.science/api/pith-number/27WKZUAFNUWZ5ICKVQSPYF5R2H/graph.json","events_json":"https://pith.science/api/pith-number/27WKZUAFNUWZ5ICKVQSPYF5R2H/events.json","paper":"https://pith.science/paper/27WKZUAF"},"agent_actions":{"view_html":"https://pith.science/pith/27WKZUAFNUWZ5ICKVQSPYF5R2H","download_json":"https://pith.science/pith/27WKZUAFNUWZ5ICKVQSPYF5R2H.json","view_paper":"https://pith.science/paper/27WKZUAF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.07908&json=true","fetch_graph":"https://pith.science/api/pith-number/27WKZUAFNUWZ5ICKVQSPYF5R2H/graph.json","fetch_events":"https://pith.science/api/pith-number/27WKZUAFNUWZ5ICKVQSPYF5R2H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/27WKZUAFNUWZ5ICKVQSPYF5R2H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/27WKZUAFNUWZ5ICKVQSPYF5R2H/action/storage_attestation","attest_author":"https://pith.science/pith/27WKZUAFNUWZ5ICKVQSPYF5R2H/action/author_attestation","sign_citation":"https://pith.science/pith/27WKZUAFNUWZ5ICKVQSPYF5R2H/action/citation_signature","submit_replication":"https://pith.science/pith/27WKZUAFNUWZ5ICKVQSPYF5R2H/action/replication_record"}},"created_at":"2026-05-17T23:42:57.330965+00:00","updated_at":"2026-05-17T23:42:57.330965+00:00"}