{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:BK5LD3XFR2TNGLBIKMXRSSUZ2H","short_pith_number":"pith:BK5LD3XF","schema_version":"1.0","canonical_sha256":"0abab1eee58ea6d32c28532f194a99d1fd4dafd04ef2aa921196090582d4035f","source":{"kind":"arxiv","id":"1301.0682","version":2},"attestation_state":"computed","paper":{"title":"On Spectral Theory for Schr\\\"odinger Operators with Operator-Valued Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Fritz Gesztesy, Maxim Zinchenko, Rudi Weikard","submitted_at":"2013-01-04T07:26:26Z","abstract_excerpt":"Given a complex, separable Hilbert space $\\cH$, we consider differential expressions of the type $\\tau = - (d^2/dx^2) + V(x)$, with $x \\in (a,\\infty)$ or $x \\in \\bbR$. Here $V$ denotes a bounded operator-valued potential $V(\\cdot) \\in \\cB(\\cH)$ such that $V(\\cdot)$ is weakly measurable and the operator norm $\\|V(\\cdot)\\|_{\\cB(\\cH)}$ is locally integrable.\n  We consider self-adjoint half-line $L^2$-realizations $H_{\\alpha}$ in $L^2((a,\\infty); dx; \\cH)$ associated with $\\tau$, assuming $a$ to be a regular endpoint necessitating a boundary condition of the type $\\sin(\\alpha)u'(a) + \\cos(\\alpha)u"},"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":"1301.0682","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-01-04T07:26:26Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"79c74c8b780c84c0ca53cc3fca75e7561d63e490a598d9c89aa35aa226cf6d67","abstract_canon_sha256":"56d08305c46ff6420af85b736f0f43e0b40a0b93be7c4b3a11cdfa208b5121f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:41.158520Z","signature_b64":"+ys35TogzILcTg/Ix77v4IIsqtne7mSi3BtAow89CEzUy/MvCMBD2PJd35ZiDdmnpZruudKFREUIqEkJGokjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0abab1eee58ea6d32c28532f194a99d1fd4dafd04ef2aa921196090582d4035f","last_reissued_at":"2026-05-18T03:30:41.157680Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:41.157680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Spectral Theory for Schr\\\"odinger Operators with Operator-Valued Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Fritz Gesztesy, Maxim Zinchenko, Rudi Weikard","submitted_at":"2013-01-04T07:26:26Z","abstract_excerpt":"Given a complex, separable Hilbert space $\\cH$, we consider differential expressions of the type $\\tau = - (d^2/dx^2) + V(x)$, with $x \\in (a,\\infty)$ or $x \\in \\bbR$. Here $V$ denotes a bounded operator-valued potential $V(\\cdot) \\in \\cB(\\cH)$ such that $V(\\cdot)$ is weakly measurable and the operator norm $\\|V(\\cdot)\\|_{\\cB(\\cH)}$ is locally integrable.\n  We consider self-adjoint half-line $L^2$-realizations $H_{\\alpha}$ in $L^2((a,\\infty); dx; \\cH)$ associated with $\\tau$, assuming $a$ to be a regular endpoint necessitating a boundary condition of the type $\\sin(\\alpha)u'(a) + \\cos(\\alpha)u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0682","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":""},"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":"1301.0682","created_at":"2026-05-18T03:30:41.157823+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.0682v2","created_at":"2026-05-18T03:30:41.157823+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0682","created_at":"2026-05-18T03:30:41.157823+00:00"},{"alias_kind":"pith_short_12","alias_value":"BK5LD3XFR2TN","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"BK5LD3XFR2TNGLBI","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"BK5LD3XF","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/BK5LD3XFR2TNGLBIKMXRSSUZ2H","json":"https://pith.science/pith/BK5LD3XFR2TNGLBIKMXRSSUZ2H.json","graph_json":"https://pith.science/api/pith-number/BK5LD3XFR2TNGLBIKMXRSSUZ2H/graph.json","events_json":"https://pith.science/api/pith-number/BK5LD3XFR2TNGLBIKMXRSSUZ2H/events.json","paper":"https://pith.science/paper/BK5LD3XF"},"agent_actions":{"view_html":"https://pith.science/pith/BK5LD3XFR2TNGLBIKMXRSSUZ2H","download_json":"https://pith.science/pith/BK5LD3XFR2TNGLBIKMXRSSUZ2H.json","view_paper":"https://pith.science/paper/BK5LD3XF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.0682&json=true","fetch_graph":"https://pith.science/api/pith-number/BK5LD3XFR2TNGLBIKMXRSSUZ2H/graph.json","fetch_events":"https://pith.science/api/pith-number/BK5LD3XFR2TNGLBIKMXRSSUZ2H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BK5LD3XFR2TNGLBIKMXRSSUZ2H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BK5LD3XFR2TNGLBIKMXRSSUZ2H/action/storage_attestation","attest_author":"https://pith.science/pith/BK5LD3XFR2TNGLBIKMXRSSUZ2H/action/author_attestation","sign_citation":"https://pith.science/pith/BK5LD3XFR2TNGLBIKMXRSSUZ2H/action/citation_signature","submit_replication":"https://pith.science/pith/BK5LD3XFR2TNGLBIKMXRSSUZ2H/action/replication_record"}},"created_at":"2026-05-18T03:30:41.157823+00:00","updated_at":"2026-05-18T03:30:41.157823+00:00"}