{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:4JGJ6AS2DPPTEY2N75YGR55W3B","short_pith_number":"pith:4JGJ6AS2","schema_version":"1.0","canonical_sha256":"e24c9f025a1bdf32634dff7068f7b6d850ed157fbe87b1ef95ef6992f60a8a70","source":{"kind":"arxiv","id":"2607.12600","version":1},"attestation_state":"computed","paper":{"title":"Bound states for the magnetic Neumann Laplacian in planar sectors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Ayman Kachmar, Mikael Sundqvist","submitted_at":"2026-07-14T10:19:18Z","abstract_excerpt":"We study the magnetic Neumann Laplacian in an infinite planar sector of opening $\\alpha\\in(0,\\pi)$ under a constant magnetic field. Building on earlier work by Bonnaillie-No\\\"el and collaborators and by Exner, Lotoreichik, and P\\'erez-Obiol, we prove that the bottom of the spectrum lies strictly below the half-plane threshold for every convex sector. Consequently, $H_\\alpha$ has a discrete ground-state eigenvalue for every $0<\\alpha<\\pi$. This resolves the bound-state problem for convex sectors, a model problem arising in the analysis of magnetic localization near corners and of the third crit"},"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":"2607.12600","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2026-07-14T10:19:18Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9d30752dc6813d59bcf302f0d1d2548cb9a79a94d785e45e00e1c0fba7712cd7","abstract_canon_sha256":"e38f32da86bbfc432a72f6d01a87dc0a2b1bf42592590702d30e0a9bf5a44d0c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-15T01:22:06.042581Z","signature_b64":"nbDMlkUpD2FMRWdN4QilJBT0T3uTO7Fq2J09QrF+oNzw7IiEP2v3feoMye2ErRMpYWyEWOi3ZQYUCpwNa6d0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e24c9f025a1bdf32634dff7068f7b6d850ed157fbe87b1ef95ef6992f60a8a70","last_reissued_at":"2026-07-15T01:22:06.041739Z","signature_status":"signed_v1","first_computed_at":"2026-07-15T01:22:06.041739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bound states for the magnetic Neumann Laplacian in planar sectors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Ayman Kachmar, Mikael Sundqvist","submitted_at":"2026-07-14T10:19:18Z","abstract_excerpt":"We study the magnetic Neumann Laplacian in an infinite planar sector of opening $\\alpha\\in(0,\\pi)$ under a constant magnetic field. Building on earlier work by Bonnaillie-No\\\"el and collaborators and by Exner, Lotoreichik, and P\\'erez-Obiol, we prove that the bottom of the spectrum lies strictly below the half-plane threshold for every convex sector. Consequently, $H_\\alpha$ has a discrete ground-state eigenvalue for every $0<\\alpha<\\pi$. This resolves the bound-state problem for convex sectors, a model problem arising in the analysis of magnetic localization near corners and of the third crit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12600","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.12600/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":"2607.12600","created_at":"2026-07-15T01:22:06.042167+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.12600v1","created_at":"2026-07-15T01:22:06.042167+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.12600","created_at":"2026-07-15T01:22:06.042167+00:00"},{"alias_kind":"pith_short_12","alias_value":"4JGJ6AS2DPPT","created_at":"2026-07-15T01:22:06.042167+00:00"},{"alias_kind":"pith_short_16","alias_value":"4JGJ6AS2DPPTEY2N","created_at":"2026-07-15T01:22:06.042167+00:00"},{"alias_kind":"pith_short_8","alias_value":"4JGJ6AS2","created_at":"2026-07-15T01:22:06.042167+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/4JGJ6AS2DPPTEY2N75YGR55W3B","json":"https://pith.science/pith/4JGJ6AS2DPPTEY2N75YGR55W3B.json","graph_json":"https://pith.science/api/pith-number/4JGJ6AS2DPPTEY2N75YGR55W3B/graph.json","events_json":"https://pith.science/api/pith-number/4JGJ6AS2DPPTEY2N75YGR55W3B/events.json","paper":"https://pith.science/paper/4JGJ6AS2"},"agent_actions":{"view_html":"https://pith.science/pith/4JGJ6AS2DPPTEY2N75YGR55W3B","download_json":"https://pith.science/pith/4JGJ6AS2DPPTEY2N75YGR55W3B.json","view_paper":"https://pith.science/paper/4JGJ6AS2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.12600&json=true","fetch_graph":"https://pith.science/api/pith-number/4JGJ6AS2DPPTEY2N75YGR55W3B/graph.json","fetch_events":"https://pith.science/api/pith-number/4JGJ6AS2DPPTEY2N75YGR55W3B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4JGJ6AS2DPPTEY2N75YGR55W3B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4JGJ6AS2DPPTEY2N75YGR55W3B/action/storage_attestation","attest_author":"https://pith.science/pith/4JGJ6AS2DPPTEY2N75YGR55W3B/action/author_attestation","sign_citation":"https://pith.science/pith/4JGJ6AS2DPPTEY2N75YGR55W3B/action/citation_signature","submit_replication":"https://pith.science/pith/4JGJ6AS2DPPTEY2N75YGR55W3B/action/replication_record"}},"created_at":"2026-07-15T01:22:06.042167+00:00","updated_at":"2026-07-15T01:22:06.042167+00:00"}