{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:IMVWCXTQFQDF53MXTTTZOS7LKV","short_pith_number":"pith:IMVWCXTQ","schema_version":"1.0","canonical_sha256":"432b615e702c065eed979ce7974beb5557b42ae62ff79692e7baf32d8fb3405e","source":{"kind":"arxiv","id":"1407.0757","version":4},"attestation_state":"computed","paper":{"title":"Spectral Asymptotics for Waveguides with Perturbed Periodic Twisting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Georgi Raikov","submitted_at":"2014-07-03T01:20:19Z","abstract_excerpt":"We consider the twisted waveguide $\\Omega_\\theta$, i.e. the domain obtained by the rotation of the bounded cross section $\\omega \\subset {\\mathbb R}^{2}$ of the straight tube $\\Omega : = \\omega \\times {\\mathbb R}$ at angle $\\theta$ which depends on the variable along the axis of $\\Omega$. We study the spectral properties of the Dirichlet Laplacian in $\\Omega_\\theta$, unitarily equivalent under the diffeomorphism $\\Omega_\\theta \\to \\Omega$ to the operator $H_{\\theta'}$, self-adjoint in ${\\rm L}^2(\\Omega)$. We assume that $\\theta' = \\beta - \\epsilon$ where $\\beta$ is a $2\\pi$-periodic function, "},"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":"1407.0757","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-07-03T01:20:19Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8378b3e16d5631e4253985624379c86eb06116893bbf5f8571b8e489d43bea71","abstract_canon_sha256":"b3a51c4a2ef9da8bd79c939d8a254e086342306dda47657efa700dfa74969faa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:08.161491Z","signature_b64":"Kv514VU65I/GazM2le4zCa8ZasuV1qOBywLHFsObGkSAUoMEEiUFUgJFakvViUIx7Rr3IfbxQ4WjwdytbAPyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"432b615e702c065eed979ce7974beb5557b42ae62ff79692e7baf32d8fb3405e","last_reissued_at":"2026-05-18T02:30:08.161011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:08.161011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral Asymptotics for Waveguides with Perturbed Periodic Twisting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Georgi Raikov","submitted_at":"2014-07-03T01:20:19Z","abstract_excerpt":"We consider the twisted waveguide $\\Omega_\\theta$, i.e. the domain obtained by the rotation of the bounded cross section $\\omega \\subset {\\mathbb R}^{2}$ of the straight tube $\\Omega : = \\omega \\times {\\mathbb R}$ at angle $\\theta$ which depends on the variable along the axis of $\\Omega$. We study the spectral properties of the Dirichlet Laplacian in $\\Omega_\\theta$, unitarily equivalent under the diffeomorphism $\\Omega_\\theta \\to \\Omega$ to the operator $H_{\\theta'}$, self-adjoint in ${\\rm L}^2(\\Omega)$. We assume that $\\theta' = \\beta - \\epsilon$ where $\\beta$ is a $2\\pi$-periodic function, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0757","kind":"arxiv","version":4},"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":"1407.0757","created_at":"2026-05-18T02:30:08.161081+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.0757v4","created_at":"2026-05-18T02:30:08.161081+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0757","created_at":"2026-05-18T02:30:08.161081+00:00"},{"alias_kind":"pith_short_12","alias_value":"IMVWCXTQFQDF","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"IMVWCXTQFQDF53MX","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"IMVWCXTQ","created_at":"2026-05-18T12:28:33.132498+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/IMVWCXTQFQDF53MXTTTZOS7LKV","json":"https://pith.science/pith/IMVWCXTQFQDF53MXTTTZOS7LKV.json","graph_json":"https://pith.science/api/pith-number/IMVWCXTQFQDF53MXTTTZOS7LKV/graph.json","events_json":"https://pith.science/api/pith-number/IMVWCXTQFQDF53MXTTTZOS7LKV/events.json","paper":"https://pith.science/paper/IMVWCXTQ"},"agent_actions":{"view_html":"https://pith.science/pith/IMVWCXTQFQDF53MXTTTZOS7LKV","download_json":"https://pith.science/pith/IMVWCXTQFQDF53MXTTTZOS7LKV.json","view_paper":"https://pith.science/paper/IMVWCXTQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.0757&json=true","fetch_graph":"https://pith.science/api/pith-number/IMVWCXTQFQDF53MXTTTZOS7LKV/graph.json","fetch_events":"https://pith.science/api/pith-number/IMVWCXTQFQDF53MXTTTZOS7LKV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IMVWCXTQFQDF53MXTTTZOS7LKV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IMVWCXTQFQDF53MXTTTZOS7LKV/action/storage_attestation","attest_author":"https://pith.science/pith/IMVWCXTQFQDF53MXTTTZOS7LKV/action/author_attestation","sign_citation":"https://pith.science/pith/IMVWCXTQFQDF53MXTTTZOS7LKV/action/citation_signature","submit_replication":"https://pith.science/pith/IMVWCXTQFQDF53MXTTTZOS7LKV/action/replication_record"}},"created_at":"2026-05-18T02:30:08.161081+00:00","updated_at":"2026-05-18T02:30:08.161081+00:00"}