{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VER7L4ZAALGYFBVRLN46APZ6GW","short_pith_number":"pith:VER7L4ZA","schema_version":"1.0","canonical_sha256":"a923f5f32002cd8286b15b79e03f3e358bdf764316ee982995ecd68179b01248","source":{"kind":"arxiv","id":"1701.06727","version":1},"attestation_state":"computed","paper":{"title":"Regular approximations of spectra of singular discrete linear Hamiltonian systems with one singular endpoint?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Yan Liu, Yuming Shi","submitted_at":"2017-01-24T04:29:42Z","abstract_excerpt":"This paper is concerned with regular approximations of spectra of singular discrete linear Hamiltonian systems with one singular endpoint. For any given self-adjoint subspace extension (SSE) of the corresponding minimal subspace, its spectrum can be approximated by eigenvalues of a sequence of induced regular SSEs, generated by the same difference expression on smaller finite intervals. It is shown that every SSE of the minimal subspace has a pure discrete spectrum, and the k-th eigenvalue of any given SSE is exactly the limit of the k-th eigenvalues of the induced regular SSEs; that is, spect"},"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":"1701.06727","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-01-24T04:29:42Z","cross_cats_sorted":[],"title_canon_sha256":"3fecfdbfd55b81fe5ac7dc443d83a8d7c0ea3dd7e10f440dd1adace408495e65","abstract_canon_sha256":"424534e744819f9c6087ca356f0fbc057a6e8e22ae9533c9fad2ed5754dcf522"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:12.299379Z","signature_b64":"heTEFASrqO4LDklyBA96SYXoBpkvw3grIYbczwbGFhaD3elCYh7o5FqPH8xZy0HR+05JpIoVkML/wgDAYGLuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a923f5f32002cd8286b15b79e03f3e358bdf764316ee982995ecd68179b01248","last_reissued_at":"2026-05-18T00:52:12.298990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:12.298990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regular approximations of spectra of singular discrete linear Hamiltonian systems with one singular endpoint?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Yan Liu, Yuming Shi","submitted_at":"2017-01-24T04:29:42Z","abstract_excerpt":"This paper is concerned with regular approximations of spectra of singular discrete linear Hamiltonian systems with one singular endpoint. For any given self-adjoint subspace extension (SSE) of the corresponding minimal subspace, its spectrum can be approximated by eigenvalues of a sequence of induced regular SSEs, generated by the same difference expression on smaller finite intervals. It is shown that every SSE of the minimal subspace has a pure discrete spectrum, and the k-th eigenvalue of any given SSE is exactly the limit of the k-th eigenvalues of the induced regular SSEs; that is, spect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06727","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":"1701.06727","created_at":"2026-05-18T00:52:12.299052+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.06727v1","created_at":"2026-05-18T00:52:12.299052+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06727","created_at":"2026-05-18T00:52:12.299052+00:00"},{"alias_kind":"pith_short_12","alias_value":"VER7L4ZAALGY","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VER7L4ZAALGYFBVR","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VER7L4ZA","created_at":"2026-05-18T12:31:49.984773+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/VER7L4ZAALGYFBVRLN46APZ6GW","json":"https://pith.science/pith/VER7L4ZAALGYFBVRLN46APZ6GW.json","graph_json":"https://pith.science/api/pith-number/VER7L4ZAALGYFBVRLN46APZ6GW/graph.json","events_json":"https://pith.science/api/pith-number/VER7L4ZAALGYFBVRLN46APZ6GW/events.json","paper":"https://pith.science/paper/VER7L4ZA"},"agent_actions":{"view_html":"https://pith.science/pith/VER7L4ZAALGYFBVRLN46APZ6GW","download_json":"https://pith.science/pith/VER7L4ZAALGYFBVRLN46APZ6GW.json","view_paper":"https://pith.science/paper/VER7L4ZA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.06727&json=true","fetch_graph":"https://pith.science/api/pith-number/VER7L4ZAALGYFBVRLN46APZ6GW/graph.json","fetch_events":"https://pith.science/api/pith-number/VER7L4ZAALGYFBVRLN46APZ6GW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VER7L4ZAALGYFBVRLN46APZ6GW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VER7L4ZAALGYFBVRLN46APZ6GW/action/storage_attestation","attest_author":"https://pith.science/pith/VER7L4ZAALGYFBVRLN46APZ6GW/action/author_attestation","sign_citation":"https://pith.science/pith/VER7L4ZAALGYFBVRLN46APZ6GW/action/citation_signature","submit_replication":"https://pith.science/pith/VER7L4ZAALGYFBVRLN46APZ6GW/action/replication_record"}},"created_at":"2026-05-18T00:52:12.299052+00:00","updated_at":"2026-05-18T00:52:12.299052+00:00"}