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We study the inverse problem consisting in the determination of $V$, through the boundary spectral data of the operator $u\\mapsto Au := -\\Delta u + Vu$, acting on $L^2(\\omega\\times(0,2\\pi))$, with quasi-periodic and Dirichlet boundary conditions. More precisely we show that if for two potentials $V_{1}$ and $V_{2}$ we denote by $(\\lambda_{1,k})_{k}$ and $(\\lambda_{2,k})_{k}$ the eigenvalues as"},"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":"1504.04267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-16T15:08:09Z","cross_cats_sorted":[],"title_canon_sha256":"de628ba748c8eda58ee071860eb742b696e5016f8b5e8b38af29d85c62e85a94","abstract_canon_sha256":"649e41cb55a9c100c745cc7cad27f699162ba12b15efbfa473ecd660ff2cbc75"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:41.831457Z","signature_b64":"rq/81iUNrmta0MmT6ikAtDFcp2/ckaxNPSdgZr2agAPZ9L0kTgxqmPe8JlMfuhphgr12+JlOU6PepCAvUyl2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1734c56ae00075b159bc6b198f039308bca2291b9cedfc104ad15d2cfe34266c","last_reissued_at":"2026-05-18T01:21:41.830967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:41.830967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness and stability results for an inverse spectral problem in a periodic waveguide","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eric Soccorsi, Otared Kavian, Yavar Kian","submitted_at":"2015-04-16T15:08:09Z","abstract_excerpt":"Let $\\Omega =\\omega\\times\\mathbb R$ where $\\omega\\subset \\mathbb R^2$ be a bounded domain, and $V : \\Omega \\to\\mathbb R$ a bounded potential which is $2\\pi$-periodic in the variable $x_{3}\\in \\mathbb R$. We study the inverse problem consisting in the determination of $V$, through the boundary spectral data of the operator $u\\mapsto Au := -\\Delta u + Vu$, acting on $L^2(\\omega\\times(0,2\\pi))$, with quasi-periodic and Dirichlet boundary conditions. More precisely we show that if for two potentials $V_{1}$ and $V_{2}$ we denote by $(\\lambda_{1,k})_{k}$ and $(\\lambda_{2,k})_{k}$ the eigenvalues as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04267","kind":"arxiv","version":1},"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":"1504.04267","created_at":"2026-05-18T01:21:41.831039+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.04267v1","created_at":"2026-05-18T01:21:41.831039+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04267","created_at":"2026-05-18T01:21:41.831039+00:00"},{"alias_kind":"pith_short_12","alias_value":"C42MK2XAAB23","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"C42MK2XAAB23CWN4","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"C42MK2XA","created_at":"2026-05-18T12:29:14.074870+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/C42MK2XAAB23CWN4NMMY6A4TBC","json":"https://pith.science/pith/C42MK2XAAB23CWN4NMMY6A4TBC.json","graph_json":"https://pith.science/api/pith-number/C42MK2XAAB23CWN4NMMY6A4TBC/graph.json","events_json":"https://pith.science/api/pith-number/C42MK2XAAB23CWN4NMMY6A4TBC/events.json","paper":"https://pith.science/paper/C42MK2XA"},"agent_actions":{"view_html":"https://pith.science/pith/C42MK2XAAB23CWN4NMMY6A4TBC","download_json":"https://pith.science/pith/C42MK2XAAB23CWN4NMMY6A4TBC.json","view_paper":"https://pith.science/paper/C42MK2XA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.04267&json=true","fetch_graph":"https://pith.science/api/pith-number/C42MK2XAAB23CWN4NMMY6A4TBC/graph.json","fetch_events":"https://pith.science/api/pith-number/C42MK2XAAB23CWN4NMMY6A4TBC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C42MK2XAAB23CWN4NMMY6A4TBC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C42MK2XAAB23CWN4NMMY6A4TBC/action/storage_attestation","attest_author":"https://pith.science/pith/C42MK2XAAB23CWN4NMMY6A4TBC/action/author_attestation","sign_citation":"https://pith.science/pith/C42MK2XAAB23CWN4NMMY6A4TBC/action/citation_signature","submit_replication":"https://pith.science/pith/C42MK2XAAB23CWN4NMMY6A4TBC/action/replication_record"}},"created_at":"2026-05-18T01:21:41.831039+00:00","updated_at":"2026-05-18T01:21:41.831039+00:00"}