{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:TEEGGRSBP3NVLB7XRRL2NMUOVH","short_pith_number":"pith:TEEGGRSB","schema_version":"1.0","canonical_sha256":"99086346417edb5587f78c57a6b28ea9f4ed6ce8183e65bd508a468f90c07e19","source":{"kind":"arxiv","id":"0704.2562","version":3},"attestation_state":"computed","paper":{"title":"Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Ian Wood, Malcolm Brown, Marco Marletta, Serguei Naboko","submitted_at":"2007-04-19T15:33:09Z","abstract_excerpt":"Starting with an adjoint pair of operators, under suitable abstract versions of standard PDE hypotheses, we consider the Weyl M-function of extensions of the operators. The extensions are determined by abstract boundary conditions and we establish results on the relationship between the M-function as an analytic function of a spectral parameter and the spectrum of the extension. We also give an example where the M-function does not contain the whole spectral information of the resolvent, and show that the results can be applied to elliptic PDEs where the M-function corresponds to the Dirichlet"},"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":"0704.2562","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.SP","submitted_at":"2007-04-19T15:33:09Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"8ca8f1171c3c94c7c7e9c775bb648b8d9e95671e12f479267c891b6d5cbbbad7","abstract_canon_sha256":"5922b90ce283eec274e67518708faa56c5509e629808a7fc4308db8f905c9394"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:12.768940Z","signature_b64":"c++cQ5wfIFjW/ZRhDpmwEnqqUAxd2UMuTPCPK5QP6nsEtl8VHYvtUMPY1JUws7Rk5W+dwppIDZdcnqh0/M2/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99086346417edb5587f78c57a6b28ea9f4ed6ce8183e65bd508a468f90c07e19","last_reissued_at":"2026-05-18T02:58:12.768121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:12.768121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Ian Wood, Malcolm Brown, Marco Marletta, Serguei Naboko","submitted_at":"2007-04-19T15:33:09Z","abstract_excerpt":"Starting with an adjoint pair of operators, under suitable abstract versions of standard PDE hypotheses, we consider the Weyl M-function of extensions of the operators. The extensions are determined by abstract boundary conditions and we establish results on the relationship between the M-function as an analytic function of a spectral parameter and the spectrum of the extension. We also give an example where the M-function does not contain the whole spectral information of the resolvent, and show that the results can be applied to elliptic PDEs where the M-function corresponds to the Dirichlet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.2562","kind":"arxiv","version":3},"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":"0704.2562","created_at":"2026-05-18T02:58:12.768267+00:00"},{"alias_kind":"arxiv_version","alias_value":"0704.2562v3","created_at":"2026-05-18T02:58:12.768267+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.2562","created_at":"2026-05-18T02:58:12.768267+00:00"},{"alias_kind":"pith_short_12","alias_value":"TEEGGRSBP3NV","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"TEEGGRSBP3NVLB7X","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"TEEGGRSB","created_at":"2026-05-18T12:25:56.245647+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/TEEGGRSBP3NVLB7XRRL2NMUOVH","json":"https://pith.science/pith/TEEGGRSBP3NVLB7XRRL2NMUOVH.json","graph_json":"https://pith.science/api/pith-number/TEEGGRSBP3NVLB7XRRL2NMUOVH/graph.json","events_json":"https://pith.science/api/pith-number/TEEGGRSBP3NVLB7XRRL2NMUOVH/events.json","paper":"https://pith.science/paper/TEEGGRSB"},"agent_actions":{"view_html":"https://pith.science/pith/TEEGGRSBP3NVLB7XRRL2NMUOVH","download_json":"https://pith.science/pith/TEEGGRSBP3NVLB7XRRL2NMUOVH.json","view_paper":"https://pith.science/paper/TEEGGRSB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0704.2562&json=true","fetch_graph":"https://pith.science/api/pith-number/TEEGGRSBP3NVLB7XRRL2NMUOVH/graph.json","fetch_events":"https://pith.science/api/pith-number/TEEGGRSBP3NVLB7XRRL2NMUOVH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TEEGGRSBP3NVLB7XRRL2NMUOVH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TEEGGRSBP3NVLB7XRRL2NMUOVH/action/storage_attestation","attest_author":"https://pith.science/pith/TEEGGRSBP3NVLB7XRRL2NMUOVH/action/author_attestation","sign_citation":"https://pith.science/pith/TEEGGRSBP3NVLB7XRRL2NMUOVH/action/citation_signature","submit_replication":"https://pith.science/pith/TEEGGRSBP3NVLB7XRRL2NMUOVH/action/replication_record"}},"created_at":"2026-05-18T02:58:12.768267+00:00","updated_at":"2026-05-18T02:58:12.768267+00:00"}