{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7UWIDGXITZ6W4ZSAZY4CUFS4XH","short_pith_number":"pith:7UWIDGXI","schema_version":"1.0","canonical_sha256":"fd2c819ae89e7d6e6640ce382a165cb9e256b4cfc296b9ba4655ff81ea780583","source":{"kind":"arxiv","id":"1309.6080","version":1},"attestation_state":"computed","paper":{"title":"On the lowest energy of a 3D magnetic hamiltonian with axisymmetric potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Nicolas Popoff","submitted_at":"2013-09-24T08:34:44Z","abstract_excerpt":"We study the bottom of the spectrum of a magnetic hamiltonian with axisymmetrical potential in R3. The associated magnetic field is planar, unitary and non-constant. The problem reduces to a 1D-family of singular Sturm-Liouville operators on the half-line. We study to associated band functions and we compare it to the \"de Gennes\" operators arising in the study of a 2D-hamiltonian with monodimensional, odd and discontinuous magnetic field. We show in particular that the lowest energy is higher in dimension 3."},"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":"1309.6080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-09-24T08:34:44Z","cross_cats_sorted":[],"title_canon_sha256":"e7413139e7d5f5b1e4c07a6f85e9904a166adffa6ab88cc858334e2f150c3518","abstract_canon_sha256":"5834c8b429c2a32f75cb96bf402b8cd86ce521248a3e07dcc7089a3647625cc5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:24.043532Z","signature_b64":"bl3R3KDeiamTgsbl7HBfxzlgKmvYfSwZDlTDrxU36+VRcJYD46MoIW6ZB/O8EncplSUzOIMfDN/jGOwXXlmeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd2c819ae89e7d6e6640ce382a165cb9e256b4cfc296b9ba4655ff81ea780583","last_reissued_at":"2026-05-18T03:12:24.042743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:24.042743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the lowest energy of a 3D magnetic hamiltonian with axisymmetric potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Nicolas Popoff","submitted_at":"2013-09-24T08:34:44Z","abstract_excerpt":"We study the bottom of the spectrum of a magnetic hamiltonian with axisymmetrical potential in R3. The associated magnetic field is planar, unitary and non-constant. The problem reduces to a 1D-family of singular Sturm-Liouville operators on the half-line. We study to associated band functions and we compare it to the \"de Gennes\" operators arising in the study of a 2D-hamiltonian with monodimensional, odd and discontinuous magnetic field. We show in particular that the lowest energy is higher in dimension 3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6080","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":"1309.6080","created_at":"2026-05-18T03:12:24.042892+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.6080v1","created_at":"2026-05-18T03:12:24.042892+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6080","created_at":"2026-05-18T03:12:24.042892+00:00"},{"alias_kind":"pith_short_12","alias_value":"7UWIDGXITZ6W","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"7UWIDGXITZ6W4ZSA","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"7UWIDGXI","created_at":"2026-05-18T12:27:38.830355+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/7UWIDGXITZ6W4ZSAZY4CUFS4XH","json":"https://pith.science/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH.json","graph_json":"https://pith.science/api/pith-number/7UWIDGXITZ6W4ZSAZY4CUFS4XH/graph.json","events_json":"https://pith.science/api/pith-number/7UWIDGXITZ6W4ZSAZY4CUFS4XH/events.json","paper":"https://pith.science/paper/7UWIDGXI"},"agent_actions":{"view_html":"https://pith.science/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH","download_json":"https://pith.science/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH.json","view_paper":"https://pith.science/paper/7UWIDGXI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.6080&json=true","fetch_graph":"https://pith.science/api/pith-number/7UWIDGXITZ6W4ZSAZY4CUFS4XH/graph.json","fetch_events":"https://pith.science/api/pith-number/7UWIDGXITZ6W4ZSAZY4CUFS4XH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH/action/storage_attestation","attest_author":"https://pith.science/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH/action/author_attestation","sign_citation":"https://pith.science/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH/action/citation_signature","submit_replication":"https://pith.science/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH/action/replication_record"}},"created_at":"2026-05-18T03:12:24.042892+00:00","updated_at":"2026-05-18T03:12:24.042892+00:00"}