{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:PID6FL7Q2UTDE6J6TK5XXNXDVQ","short_pith_number":"pith:PID6FL7Q","schema_version":"1.0","canonical_sha256":"7a07e2aff0d52632793e9abb7bb6e3ac0fa2784e55bd0bb08c6080d74264a2c1","source":{"kind":"arxiv","id":"1009.3581","version":2},"attestation_state":"computed","paper":{"title":"A variational approach to dislocation problems for periodic Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Martin Kohlmann, Rainer Hempel","submitted_at":"2010-09-18T21:00:45Z","abstract_excerpt":"As a simple model for lattice defects like grain boundaries in solid state physics we consider potentials which are obtained from a periodic potential $V = V(x,y)$ on $\\R^2$ with period lattice $\\Z^2$ by setting $W_t(x,y) = V(x+t,y)$ for $x < 0$ and $W_t(x,y) = V(x,y)$ for $x \\ge 0$, for $t \\in [0,1]$. For Lipschitz-continuous $V$ it is shown that the Schr\\\"odinger operators $H_t = -\\Delta + W_t$ have spectrum (surface states) in the spectral gaps of $H_0$, for suitable $t \\in (0,1)$. We also discuss the density of these surface states as compared to the density of the bulk. Our approach is va"},"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":"1009.3581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-18T21:00:45Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"876a7709ae8dfe709b7799f10f4b4ba15f862c5b321b5b15188d92b19ad38c3b","abstract_canon_sha256":"16c8d3b5b1ebfc94971dc27acbbdecec7594104ade1c7544539088ce3728987e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:11.531792Z","signature_b64":"HKvR8WQ3svwC7K/i7V1fSs9NrdAXcfna/GsR3knTeOYqsB2I7lnCKHZElLWlosdEhPMhdG4zjWAHBunKABEZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a07e2aff0d52632793e9abb7bb6e3ac0fa2784e55bd0bb08c6080d74264a2c1","last_reissued_at":"2026-05-18T04:23:11.531366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:11.531366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A variational approach to dislocation problems for periodic Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Martin Kohlmann, Rainer Hempel","submitted_at":"2010-09-18T21:00:45Z","abstract_excerpt":"As a simple model for lattice defects like grain boundaries in solid state physics we consider potentials which are obtained from a periodic potential $V = V(x,y)$ on $\\R^2$ with period lattice $\\Z^2$ by setting $W_t(x,y) = V(x+t,y)$ for $x < 0$ and $W_t(x,y) = V(x,y)$ for $x \\ge 0$, for $t \\in [0,1]$. For Lipschitz-continuous $V$ it is shown that the Schr\\\"odinger operators $H_t = -\\Delta + W_t$ have spectrum (surface states) in the spectral gaps of $H_0$, for suitable $t \\in (0,1)$. We also discuss the density of these surface states as compared to the density of the bulk. Our approach is va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3581","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":"1009.3581","created_at":"2026-05-18T04:23:11.531433+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3581v2","created_at":"2026-05-18T04:23:11.531433+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3581","created_at":"2026-05-18T04:23:11.531433+00:00"},{"alias_kind":"pith_short_12","alias_value":"PID6FL7Q2UTD","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"PID6FL7Q2UTDE6J6","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"PID6FL7Q","created_at":"2026-05-18T12:26:12.377268+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/PID6FL7Q2UTDE6J6TK5XXNXDVQ","json":"https://pith.science/pith/PID6FL7Q2UTDE6J6TK5XXNXDVQ.json","graph_json":"https://pith.science/api/pith-number/PID6FL7Q2UTDE6J6TK5XXNXDVQ/graph.json","events_json":"https://pith.science/api/pith-number/PID6FL7Q2UTDE6J6TK5XXNXDVQ/events.json","paper":"https://pith.science/paper/PID6FL7Q"},"agent_actions":{"view_html":"https://pith.science/pith/PID6FL7Q2UTDE6J6TK5XXNXDVQ","download_json":"https://pith.science/pith/PID6FL7Q2UTDE6J6TK5XXNXDVQ.json","view_paper":"https://pith.science/paper/PID6FL7Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3581&json=true","fetch_graph":"https://pith.science/api/pith-number/PID6FL7Q2UTDE6J6TK5XXNXDVQ/graph.json","fetch_events":"https://pith.science/api/pith-number/PID6FL7Q2UTDE6J6TK5XXNXDVQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PID6FL7Q2UTDE6J6TK5XXNXDVQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PID6FL7Q2UTDE6J6TK5XXNXDVQ/action/storage_attestation","attest_author":"https://pith.science/pith/PID6FL7Q2UTDE6J6TK5XXNXDVQ/action/author_attestation","sign_citation":"https://pith.science/pith/PID6FL7Q2UTDE6J6TK5XXNXDVQ/action/citation_signature","submit_replication":"https://pith.science/pith/PID6FL7Q2UTDE6J6TK5XXNXDVQ/action/replication_record"}},"created_at":"2026-05-18T04:23:11.531433+00:00","updated_at":"2026-05-18T04:23:11.531433+00:00"}