{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:X5BYLLI4RZRMBI4JKCFD3JWEQN","short_pith_number":"pith:X5BYLLI4","schema_version":"1.0","canonical_sha256":"bf4385ad1c8e62c0a389508a3da6c48360ce5ebf737d5295f5d040cc2a3166a6","source":{"kind":"arxiv","id":"1511.02376","version":2},"attestation_state":"computed","paper":{"title":"Scattering matrices and Dirichlet-to-Neumann maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Hagen Neidhardt, Jussi Behrndt, Mark M. Malamud","submitted_at":"2015-11-07T16:54:36Z","abstract_excerpt":"A general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator valued Titchmarsh-Weyl $m$-function is proved. This result is applied to scattering problems for different self-adjoint realizations of Schr\\\"{o}dinger operators on unbounded domains, Schr\\\"{o}dinger operators with singular potentials supported on hypersurfaces, and orthogonal couplings of Schr\\\"{o}dinger operators. In these applications the scattering matrix is expressed in an explicit form with the help of Dirichlet-to-Neumann maps."},"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":"1511.02376","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-07T16:54:36Z","cross_cats_sorted":["math.AP","math.MP","math.SP"],"title_canon_sha256":"f466e69a98e0801d5b1a9a41103e169939c0ca5a9fc5d48e51dd3f26fc076c0c","abstract_canon_sha256":"67f95920616e8c10139557e91d0b060e688cc858b4b6ed2bc4e3b352856e1f18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:57.784511Z","signature_b64":"szdn5G/q/82VEwsyIgc6PO3i7fEUYopa75n7i5vNLZr6bHTbIXhaAxir+w+I3OXbi5jnZLFfSKJ8lpFLXUKrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf4385ad1c8e62c0a389508a3da6c48360ce5ebf737d5295f5d040cc2a3166a6","last_reissued_at":"2026-05-18T01:11:57.784020Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:57.784020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scattering matrices and Dirichlet-to-Neumann maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Hagen Neidhardt, Jussi Behrndt, Mark M. Malamud","submitted_at":"2015-11-07T16:54:36Z","abstract_excerpt":"A general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator valued Titchmarsh-Weyl $m$-function is proved. This result is applied to scattering problems for different self-adjoint realizations of Schr\\\"{o}dinger operators on unbounded domains, Schr\\\"{o}dinger operators with singular potentials supported on hypersurfaces, and orthogonal couplings of Schr\\\"{o}dinger operators. In these applications the scattering matrix is expressed in an explicit form with the help of Dirichlet-to-Neumann maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02376","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":"1511.02376","created_at":"2026-05-18T01:11:57.784094+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.02376v2","created_at":"2026-05-18T01:11:57.784094+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02376","created_at":"2026-05-18T01:11:57.784094+00:00"},{"alias_kind":"pith_short_12","alias_value":"X5BYLLI4RZRM","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"X5BYLLI4RZRMBI4J","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"X5BYLLI4","created_at":"2026-05-18T12:29:47.479230+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/X5BYLLI4RZRMBI4JKCFD3JWEQN","json":"https://pith.science/pith/X5BYLLI4RZRMBI4JKCFD3JWEQN.json","graph_json":"https://pith.science/api/pith-number/X5BYLLI4RZRMBI4JKCFD3JWEQN/graph.json","events_json":"https://pith.science/api/pith-number/X5BYLLI4RZRMBI4JKCFD3JWEQN/events.json","paper":"https://pith.science/paper/X5BYLLI4"},"agent_actions":{"view_html":"https://pith.science/pith/X5BYLLI4RZRMBI4JKCFD3JWEQN","download_json":"https://pith.science/pith/X5BYLLI4RZRMBI4JKCFD3JWEQN.json","view_paper":"https://pith.science/paper/X5BYLLI4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.02376&json=true","fetch_graph":"https://pith.science/api/pith-number/X5BYLLI4RZRMBI4JKCFD3JWEQN/graph.json","fetch_events":"https://pith.science/api/pith-number/X5BYLLI4RZRMBI4JKCFD3JWEQN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X5BYLLI4RZRMBI4JKCFD3JWEQN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X5BYLLI4RZRMBI4JKCFD3JWEQN/action/storage_attestation","attest_author":"https://pith.science/pith/X5BYLLI4RZRMBI4JKCFD3JWEQN/action/author_attestation","sign_citation":"https://pith.science/pith/X5BYLLI4RZRMBI4JKCFD3JWEQN/action/citation_signature","submit_replication":"https://pith.science/pith/X5BYLLI4RZRMBI4JKCFD3JWEQN/action/replication_record"}},"created_at":"2026-05-18T01:11:57.784094+00:00","updated_at":"2026-05-18T01:11:57.784094+00:00"}