{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:WAP5XXZ5736SX7W36XW7KJA6NP","short_pith_number":"pith:WAP5XXZ5","schema_version":"1.0","canonical_sha256":"b01fdbdf3dfefd2bfedbf5edf5241e6bd076091d82dce7db642c43c25f9f6969","source":{"kind":"arxiv","id":"1509.04894","version":1},"attestation_state":"computed","paper":{"title":"Continuity of the spectra for families of magnetic operators on Z^d","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"D. Parra, S. Richard","submitted_at":"2015-09-16T11:57:24Z","abstract_excerpt":"For families of magnetic self-adjoint operators on ${\\mathbb Z}^d$ whose symbols and magnetic fields depend continuously on a parameter $\\epsilon$, it is shown that the main spectral properties of these operators also vary continuously with respect to $\\epsilon$. The proof is based on an algebraic setting involving twisted crossed product C*-algebras."},"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":"1509.04894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-16T11:57:24Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"db70542e6cbcfb5f7dd4d0eff030ea998606f1030fc2fddd22310075f3ae1a8a","abstract_canon_sha256":"36e069335799aedb7a4c3e02bee21ac9a39b80c2f7db06c544ab3683a085ce72"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:00.686292Z","signature_b64":"qVJrH4GlEBOq4lwZEKeFvQCH2w2BACLLQyCSkn89kPQv0EMGp5CDiiyh1x2NHOsnfyRRW2iNad7YHmDjGQ/EDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b01fdbdf3dfefd2bfedbf5edf5241e6bd076091d82dce7db642c43c25f9f6969","last_reissued_at":"2026-05-17T23:51:00.685651Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:00.685651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuity of the spectra for families of magnetic operators on Z^d","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"D. Parra, S. Richard","submitted_at":"2015-09-16T11:57:24Z","abstract_excerpt":"For families of magnetic self-adjoint operators on ${\\mathbb Z}^d$ whose symbols and magnetic fields depend continuously on a parameter $\\epsilon$, it is shown that the main spectral properties of these operators also vary continuously with respect to $\\epsilon$. The proof is based on an algebraic setting involving twisted crossed product C*-algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04894","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":"1509.04894","created_at":"2026-05-17T23:51:00.685753+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.04894v1","created_at":"2026-05-17T23:51:00.685753+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04894","created_at":"2026-05-17T23:51:00.685753+00:00"},{"alias_kind":"pith_short_12","alias_value":"WAP5XXZ5736S","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"WAP5XXZ5736SX7W3","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"WAP5XXZ5","created_at":"2026-05-18T12:29:47.479230+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/WAP5XXZ5736SX7W36XW7KJA6NP","json":"https://pith.science/pith/WAP5XXZ5736SX7W36XW7KJA6NP.json","graph_json":"https://pith.science/api/pith-number/WAP5XXZ5736SX7W36XW7KJA6NP/graph.json","events_json":"https://pith.science/api/pith-number/WAP5XXZ5736SX7W36XW7KJA6NP/events.json","paper":"https://pith.science/paper/WAP5XXZ5"},"agent_actions":{"view_html":"https://pith.science/pith/WAP5XXZ5736SX7W36XW7KJA6NP","download_json":"https://pith.science/pith/WAP5XXZ5736SX7W36XW7KJA6NP.json","view_paper":"https://pith.science/paper/WAP5XXZ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.04894&json=true","fetch_graph":"https://pith.science/api/pith-number/WAP5XXZ5736SX7W36XW7KJA6NP/graph.json","fetch_events":"https://pith.science/api/pith-number/WAP5XXZ5736SX7W36XW7KJA6NP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WAP5XXZ5736SX7W36XW7KJA6NP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WAP5XXZ5736SX7W36XW7KJA6NP/action/storage_attestation","attest_author":"https://pith.science/pith/WAP5XXZ5736SX7W36XW7KJA6NP/action/author_attestation","sign_citation":"https://pith.science/pith/WAP5XXZ5736SX7W36XW7KJA6NP/action/citation_signature","submit_replication":"https://pith.science/pith/WAP5XXZ5736SX7W36XW7KJA6NP/action/replication_record"}},"created_at":"2026-05-17T23:51:00.685753+00:00","updated_at":"2026-05-17T23:51:00.685753+00:00"}