{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:KWTVJ4E22DCZKRQOXAJ27RGQ5P","short_pith_number":"pith:KWTVJ4E2","schema_version":"1.0","canonical_sha256":"55a754f09ad0c595460eb813afc4d0ebd156dcc8e095ce74c719255ae497b04f","source":{"kind":"arxiv","id":"math-ph/0612070","version":1},"attestation_state":"computed","paper":{"title":"Spectral estimates for two-dimensional Schroedinger operators with application to quantum layers","license":"","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Hynek Kovarik, Semjon Vugalter, Timo Weidl","submitted_at":"2006-12-21T13:42:50Z","abstract_excerpt":"A logarithmic type Lieb-Thirring inequality for two-dimensional Schroedinger operators is established. The result is applied to prove spectral estimates on trapped modes in quantum layers."},"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":"math-ph/0612070","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-12-21T13:42:50Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"544027e18165f4506a1dbbe4b6d16733492057b0654008bf127de249e9b68f78","abstract_canon_sha256":"6fb2df11e572f376b61cbeba3092d50b9afd397794de54b79b3fb00ab30c3793"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:21.847154Z","signature_b64":"qkGlzc7wrBoqJKiaZoU4wqE78mRvrDwGiFxqkDm3TL6tpgyfqHqRZ6tJEmEbKdro3Ufz/8S9yXlMNY5Qpn6nCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55a754f09ad0c595460eb813afc4d0ebd156dcc8e095ce74c719255ae497b04f","last_reissued_at":"2026-05-18T04:40:21.846372Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:21.846372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral estimates for two-dimensional Schroedinger operators with application to quantum layers","license":"","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Hynek Kovarik, Semjon Vugalter, Timo Weidl","submitted_at":"2006-12-21T13:42:50Z","abstract_excerpt":"A logarithmic type Lieb-Thirring inequality for two-dimensional Schroedinger operators is established. The result is applied to prove spectral estimates on trapped modes in quantum layers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0612070","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":"math-ph/0612070","created_at":"2026-05-18T04:40:21.846476+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0612070v1","created_at":"2026-05-18T04:40:21.846476+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0612070","created_at":"2026-05-18T04:40:21.846476+00:00"},{"alias_kind":"pith_short_12","alias_value":"KWTVJ4E22DCZ","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"KWTVJ4E22DCZKRQO","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"KWTVJ4E2","created_at":"2026-05-18T12:25:54.717736+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/KWTVJ4E22DCZKRQOXAJ27RGQ5P","json":"https://pith.science/pith/KWTVJ4E22DCZKRQOXAJ27RGQ5P.json","graph_json":"https://pith.science/api/pith-number/KWTVJ4E22DCZKRQOXAJ27RGQ5P/graph.json","events_json":"https://pith.science/api/pith-number/KWTVJ4E22DCZKRQOXAJ27RGQ5P/events.json","paper":"https://pith.science/paper/KWTVJ4E2"},"agent_actions":{"view_html":"https://pith.science/pith/KWTVJ4E22DCZKRQOXAJ27RGQ5P","download_json":"https://pith.science/pith/KWTVJ4E22DCZKRQOXAJ27RGQ5P.json","view_paper":"https://pith.science/paper/KWTVJ4E2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0612070&json=true","fetch_graph":"https://pith.science/api/pith-number/KWTVJ4E22DCZKRQOXAJ27RGQ5P/graph.json","fetch_events":"https://pith.science/api/pith-number/KWTVJ4E22DCZKRQOXAJ27RGQ5P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KWTVJ4E22DCZKRQOXAJ27RGQ5P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KWTVJ4E22DCZKRQOXAJ27RGQ5P/action/storage_attestation","attest_author":"https://pith.science/pith/KWTVJ4E22DCZKRQOXAJ27RGQ5P/action/author_attestation","sign_citation":"https://pith.science/pith/KWTVJ4E22DCZKRQOXAJ27RGQ5P/action/citation_signature","submit_replication":"https://pith.science/pith/KWTVJ4E22DCZKRQOXAJ27RGQ5P/action/replication_record"}},"created_at":"2026-05-18T04:40:21.846476+00:00","updated_at":"2026-05-18T04:40:21.846476+00:00"}