{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:EG64KDUR2P2HNNRLD274BSFZV6","short_pith_number":"pith:EG64KDUR","schema_version":"1.0","canonical_sha256":"21bdc50e91d3f476b62b1ebfc0c8b9afbf0c14459b3998cc0268ef0ff5b1df9f","source":{"kind":"arxiv","id":"1212.6798","version":2},"attestation_state":"computed","paper":{"title":"An example of unitary equivalence between self-adjoint extensions and their parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.FA","authors_text":"Konstantin Pankrashkin","submitted_at":"2012-12-31T00:42:28Z","abstract_excerpt":"The spectral problem for self-adjoint extensions is studied using the machinery of boundary triplets. For a class of symmetric operators having Weyl functions of a special type we calculate explicitly the spectral projections in the form of operator-valued integrals. This allows one to give a constructive proof of the fact that, in certain intervals, the resulting self-adjoint extensions are unitarily equivalent to a certain parameterizing operator acting in a smaller space, and one is able to provide an explicit form the associated unitary transform. Applications to differential operators on "},"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":"1212.6798","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-31T00:42:28Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"5d311a56e6fcd1a06faed81c56475d7280c6c193aa209d59e22918e31b1fc5a7","abstract_canon_sha256":"6b18dea7ff7d20c10bf83f9ff096b9097c8eba8a74e52bb850025467aa6a04b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:21.694933Z","signature_b64":"rVxEO4CEBBEx7aN1aQK7xpJ+Qp7DT/SgSEEQIDRZTjIxvyvCt3yMJ3lNNqnd6BcK8EGtBpcvvl8PN/q7G46EBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21bdc50e91d3f476b62b1ebfc0c8b9afbf0c14459b3998cc0268ef0ff5b1df9f","last_reissued_at":"2026-05-18T03:13:21.693962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:21.693962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An example of unitary equivalence between self-adjoint extensions and their parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.FA","authors_text":"Konstantin Pankrashkin","submitted_at":"2012-12-31T00:42:28Z","abstract_excerpt":"The spectral problem for self-adjoint extensions is studied using the machinery of boundary triplets. For a class of symmetric operators having Weyl functions of a special type we calculate explicitly the spectral projections in the form of operator-valued integrals. This allows one to give a constructive proof of the fact that, in certain intervals, the resulting self-adjoint extensions are unitarily equivalent to a certain parameterizing operator acting in a smaller space, and one is able to provide an explicit form the associated unitary transform. Applications to differential operators on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6798","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":"1212.6798","created_at":"2026-05-18T03:13:21.694084+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.6798v2","created_at":"2026-05-18T03:13:21.694084+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6798","created_at":"2026-05-18T03:13:21.694084+00:00"},{"alias_kind":"pith_short_12","alias_value":"EG64KDUR2P2H","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"EG64KDUR2P2HNNRL","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"EG64KDUR","created_at":"2026-05-18T12:27:04.183437+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/EG64KDUR2P2HNNRLD274BSFZV6","json":"https://pith.science/pith/EG64KDUR2P2HNNRLD274BSFZV6.json","graph_json":"https://pith.science/api/pith-number/EG64KDUR2P2HNNRLD274BSFZV6/graph.json","events_json":"https://pith.science/api/pith-number/EG64KDUR2P2HNNRLD274BSFZV6/events.json","paper":"https://pith.science/paper/EG64KDUR"},"agent_actions":{"view_html":"https://pith.science/pith/EG64KDUR2P2HNNRLD274BSFZV6","download_json":"https://pith.science/pith/EG64KDUR2P2HNNRLD274BSFZV6.json","view_paper":"https://pith.science/paper/EG64KDUR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.6798&json=true","fetch_graph":"https://pith.science/api/pith-number/EG64KDUR2P2HNNRLD274BSFZV6/graph.json","fetch_events":"https://pith.science/api/pith-number/EG64KDUR2P2HNNRLD274BSFZV6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EG64KDUR2P2HNNRLD274BSFZV6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EG64KDUR2P2HNNRLD274BSFZV6/action/storage_attestation","attest_author":"https://pith.science/pith/EG64KDUR2P2HNNRLD274BSFZV6/action/author_attestation","sign_citation":"https://pith.science/pith/EG64KDUR2P2HNNRLD274BSFZV6/action/citation_signature","submit_replication":"https://pith.science/pith/EG64KDUR2P2HNNRLD274BSFZV6/action/replication_record"}},"created_at":"2026-05-18T03:13:21.694084+00:00","updated_at":"2026-05-18T03:13:21.694084+00:00"}