{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:VDEMHL6VYIKBDFEUNZJ6BH6BZP","short_pith_number":"pith:VDEMHL6V","schema_version":"1.0","canonical_sha256":"a8c8c3afd5c2141194946e53e09fc1cbfa594f79bc1661ca5bd23fad454abfcd","source":{"kind":"arxiv","id":"2412.21100","version":2},"attestation_state":"computed","paper":{"title":"Quantum tunneling and its absence in deep wells and strong magnetic fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mes-hall","math.AP","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Charles L. Fefferman, Jacob Shapiro, Michael I. Weinstein","submitted_at":"2024-12-30T17:24:48Z","abstract_excerpt":"We present new results on quantum tunneling between deep potential wells, in the presence of a strong constant magnetic field. We construct a family of double well potentials containing examples for which the low-energy eigenvalue splitting vanishes, and hence quantum tunneling is eliminated. Further, by deforming within this family, the magnetic ground state can be made to transition from symmetric to anti-symmetric. However, for typical double wells in a certain regime, tunneling is not suppressed, and we provide a lower bound for the eigenvalue splitting."},"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":"2412.21100","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-12-30T17:24:48Z","cross_cats_sorted":["cond-mat.mes-hall","math.AP","math.MP","quant-ph"],"title_canon_sha256":"150c1cc908fa3bae6023eec01cc15b4be04cb80496541bc39cf860e068c78fb5","abstract_canon_sha256":"3d09e34a6cd10d0cbf86dc9663845a12c4dc6544f768578f50d06ddadea74a76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:55:37.308992Z","signature_b64":"brzMa2XHvuUqj1uDTW+jRjHFmR178TEJEMo2nczjsQi4n88skEo6YaQ7pyYGI7isHRUjnupuz6PgC8jEtm7bCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8c8c3afd5c2141194946e53e09fc1cbfa594f79bc1661ca5bd23fad454abfcd","last_reissued_at":"2026-07-05T09:55:37.308435Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:55:37.308435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum tunneling and its absence in deep wells and strong magnetic fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mes-hall","math.AP","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Charles L. Fefferman, Jacob Shapiro, Michael I. Weinstein","submitted_at":"2024-12-30T17:24:48Z","abstract_excerpt":"We present new results on quantum tunneling between deep potential wells, in the presence of a strong constant magnetic field. We construct a family of double well potentials containing examples for which the low-energy eigenvalue splitting vanishes, and hence quantum tunneling is eliminated. Further, by deforming within this family, the magnetic ground state can be made to transition from symmetric to anti-symmetric. However, for typical double wells in a certain regime, tunneling is not suppressed, and we provide a lower bound for the eigenvalue splitting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.21100","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.21100/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2412.21100","created_at":"2026-07-05T09:55:37.308501+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.21100v2","created_at":"2026-07-05T09:55:37.308501+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.21100","created_at":"2026-07-05T09:55:37.308501+00:00"},{"alias_kind":"pith_short_12","alias_value":"VDEMHL6VYIKB","created_at":"2026-07-05T09:55:37.308501+00:00"},{"alias_kind":"pith_short_16","alias_value":"VDEMHL6VYIKBDFEU","created_at":"2026-07-05T09:55:37.308501+00:00"},{"alias_kind":"pith_short_8","alias_value":"VDEMHL6V","created_at":"2026-07-05T09:55:37.308501+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/VDEMHL6VYIKBDFEUNZJ6BH6BZP","json":"https://pith.science/pith/VDEMHL6VYIKBDFEUNZJ6BH6BZP.json","graph_json":"https://pith.science/api/pith-number/VDEMHL6VYIKBDFEUNZJ6BH6BZP/graph.json","events_json":"https://pith.science/api/pith-number/VDEMHL6VYIKBDFEUNZJ6BH6BZP/events.json","paper":"https://pith.science/paper/VDEMHL6V"},"agent_actions":{"view_html":"https://pith.science/pith/VDEMHL6VYIKBDFEUNZJ6BH6BZP","download_json":"https://pith.science/pith/VDEMHL6VYIKBDFEUNZJ6BH6BZP.json","view_paper":"https://pith.science/paper/VDEMHL6V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.21100&json=true","fetch_graph":"https://pith.science/api/pith-number/VDEMHL6VYIKBDFEUNZJ6BH6BZP/graph.json","fetch_events":"https://pith.science/api/pith-number/VDEMHL6VYIKBDFEUNZJ6BH6BZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VDEMHL6VYIKBDFEUNZJ6BH6BZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VDEMHL6VYIKBDFEUNZJ6BH6BZP/action/storage_attestation","attest_author":"https://pith.science/pith/VDEMHL6VYIKBDFEUNZJ6BH6BZP/action/author_attestation","sign_citation":"https://pith.science/pith/VDEMHL6VYIKBDFEUNZJ6BH6BZP/action/citation_signature","submit_replication":"https://pith.science/pith/VDEMHL6VYIKBDFEUNZJ6BH6BZP/action/replication_record"}},"created_at":"2026-07-05T09:55:37.308501+00:00","updated_at":"2026-07-05T09:55:37.308501+00:00"}