{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:GOLLL2TPMZZJI3WGSVUQWIRR3J","short_pith_number":"pith:GOLLL2TP","schema_version":"1.0","canonical_sha256":"3396b5ea6f6672946ec695690b2231da660b1301adaf5a1086d14e8978aea380","source":{"kind":"arxiv","id":"1408.1103","version":2},"attestation_state":"computed","paper":{"title":"The Morse and Maslov indices for multidimensional Schr\\\"odinger operators with matrix-valued potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.SG"],"primary_cat":"math.SP","authors_text":"Alim Sukhtayev, Christopher K.R.T. Jones, Graham Cox, Yuri Latushkin","submitted_at":"2014-08-05T20:08:02Z","abstract_excerpt":"We study the Schr\\\"odinger operator $L=-\\Delta+V$ on a star-shaped domain $\\Omega$ in $\\mathbb{R}^d$ with Lipschitz boundary $\\partial\\Omega$. The operator is equipped with quite general Dirichlet- or Robin-type boundary conditions induced by operators between $H^{1/2}(\\partial\\Omega)$ and $H^{-1/2}(\\partial\\Omega)$, and the potential takes values in the set of symmetric $N\\times N$ matrices. By shrinking the domain and rescaling the operator we obtain a path in the Fredholm-Lagrangian-Grassmannian of the subspace of $H^{1/2}(\\partial\\Omega)\\times H^{-1/2}(\\partial\\Omega)$ corresponding to the"},"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":"1408.1103","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-08-05T20:08:02Z","cross_cats_sorted":["math.AP","math.FA","math.SG"],"title_canon_sha256":"06381fa1c7f356edf957ec7c8a6f9be8329c2333faec63ea55184ed7564b5dcb","abstract_canon_sha256":"527c0cd031e92042e52d28dfd7015a2e46234271191b70ad8cb99bd075475e78"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:41.785053Z","signature_b64":"SXz3UBglhGxLPEKvEG0ZIK8dhsYbF02hctenz01yRs86KraLOhh8tPUqTaapDGIhKryGdkJKnEfC+c2A917jBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3396b5ea6f6672946ec695690b2231da660b1301adaf5a1086d14e8978aea380","last_reissued_at":"2026-05-18T01:57:41.784460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:41.784460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Morse and Maslov indices for multidimensional Schr\\\"odinger operators with matrix-valued potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.SG"],"primary_cat":"math.SP","authors_text":"Alim Sukhtayev, Christopher K.R.T. Jones, Graham Cox, Yuri Latushkin","submitted_at":"2014-08-05T20:08:02Z","abstract_excerpt":"We study the Schr\\\"odinger operator $L=-\\Delta+V$ on a star-shaped domain $\\Omega$ in $\\mathbb{R}^d$ with Lipschitz boundary $\\partial\\Omega$. The operator is equipped with quite general Dirichlet- or Robin-type boundary conditions induced by operators between $H^{1/2}(\\partial\\Omega)$ and $H^{-1/2}(\\partial\\Omega)$, and the potential takes values in the set of symmetric $N\\times N$ matrices. By shrinking the domain and rescaling the operator we obtain a path in the Fredholm-Lagrangian-Grassmannian of the subspace of $H^{1/2}(\\partial\\Omega)\\times H^{-1/2}(\\partial\\Omega)$ corresponding to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1103","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":"1408.1103","created_at":"2026-05-18T01:57:41.784559+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.1103v2","created_at":"2026-05-18T01:57:41.784559+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1103","created_at":"2026-05-18T01:57:41.784559+00:00"},{"alias_kind":"pith_short_12","alias_value":"GOLLL2TPMZZJ","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"GOLLL2TPMZZJI3WG","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"GOLLL2TP","created_at":"2026-05-18T12:28:30.664211+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/GOLLL2TPMZZJI3WGSVUQWIRR3J","json":"https://pith.science/pith/GOLLL2TPMZZJI3WGSVUQWIRR3J.json","graph_json":"https://pith.science/api/pith-number/GOLLL2TPMZZJI3WGSVUQWIRR3J/graph.json","events_json":"https://pith.science/api/pith-number/GOLLL2TPMZZJI3WGSVUQWIRR3J/events.json","paper":"https://pith.science/paper/GOLLL2TP"},"agent_actions":{"view_html":"https://pith.science/pith/GOLLL2TPMZZJI3WGSVUQWIRR3J","download_json":"https://pith.science/pith/GOLLL2TPMZZJI3WGSVUQWIRR3J.json","view_paper":"https://pith.science/paper/GOLLL2TP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.1103&json=true","fetch_graph":"https://pith.science/api/pith-number/GOLLL2TPMZZJI3WGSVUQWIRR3J/graph.json","fetch_events":"https://pith.science/api/pith-number/GOLLL2TPMZZJI3WGSVUQWIRR3J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GOLLL2TPMZZJI3WGSVUQWIRR3J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GOLLL2TPMZZJI3WGSVUQWIRR3J/action/storage_attestation","attest_author":"https://pith.science/pith/GOLLL2TPMZZJI3WGSVUQWIRR3J/action/author_attestation","sign_citation":"https://pith.science/pith/GOLLL2TPMZZJI3WGSVUQWIRR3J/action/citation_signature","submit_replication":"https://pith.science/pith/GOLLL2TPMZZJI3WGSVUQWIRR3J/action/replication_record"}},"created_at":"2026-05-18T01:57:41.784559+00:00","updated_at":"2026-05-18T01:57:41.784559+00:00"}