{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:DYUTJQP2MG4RDV5NQT4BRVELO2","short_pith_number":"pith:DYUTJQP2","schema_version":"1.0","canonical_sha256":"1e2934c1fa61b911d7ad84f818d48b7692f1b0e8a57311bc6e81861e0e8cb470","source":{"kind":"arxiv","id":"2607.13287","version":1},"attestation_state":"computed","paper":{"title":"Exactly Solvable Diffraction-Grating Scattering Problems for TE and TM waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"physics.optics","authors_text":"Ali Mostafazadeh, Farhang Loran","submitted_at":"2026-07-14T21:49:56Z","abstract_excerpt":"In J.~Phys.~A {\\bf 31}, 3493 (1998), Berry provides an analytic solution of the problem of determining the diffracted beam intensities for atoms incident upon a grating given by the potential, $v(x,y):=iV_0(e^{i\\mathfrak{K}\\,y}-1)$ for $0\\leq x\\leq\\ell$ and $v(x,y):=0$ otherwise, where $V_0, \\mathfrak{K}$, and $\\ell$ are positive real parameters. This result, which relies on the paraxial approximation, readily applies to the diffraction of transverse electric (TE) waves by the nonmagnetic optical grating given by the relative permittivity, $\\hat\\varepsilon(x,y):=1-v(x,y)/k^2$, where $k$ is the"},"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":"2607.13287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2026-07-14T21:49:56Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"aa7f96f4f5fb5eccb88b2b843e985daddcf018e97c5744878fdd240b8795ed37","abstract_canon_sha256":"fa7291aa1568016bf45e040b4a45fd50ec8ab93981baa651078a469a6618501f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T00:22:07.782685Z","signature_b64":"OVe2HS76WAdZV6cgfuEGeqZWpJUeccvI7vuArmXl/mt5Fl6MrJJ/l4JeXsoV8t91q32F3GC2BmWSf87OPXTRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e2934c1fa61b911d7ad84f818d48b7692f1b0e8a57311bc6e81861e0e8cb470","last_reissued_at":"2026-07-16T00:22:07.781865Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T00:22:07.781865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exactly Solvable Diffraction-Grating Scattering Problems for TE and TM waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"physics.optics","authors_text":"Ali Mostafazadeh, Farhang Loran","submitted_at":"2026-07-14T21:49:56Z","abstract_excerpt":"In J.~Phys.~A {\\bf 31}, 3493 (1998), Berry provides an analytic solution of the problem of determining the diffracted beam intensities for atoms incident upon a grating given by the potential, $v(x,y):=iV_0(e^{i\\mathfrak{K}\\,y}-1)$ for $0\\leq x\\leq\\ell$ and $v(x,y):=0$ otherwise, where $V_0, \\mathfrak{K}$, and $\\ell$ are positive real parameters. This result, which relies on the paraxial approximation, readily applies to the diffraction of transverse electric (TE) waves by the nonmagnetic optical grating given by the relative permittivity, $\\hat\\varepsilon(x,y):=1-v(x,y)/k^2$, where $k$ is the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13287","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.13287/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.13287","created_at":"2026-07-16T00:22:07.782290+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.13287v1","created_at":"2026-07-16T00:22:07.782290+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13287","created_at":"2026-07-16T00:22:07.782290+00:00"},{"alias_kind":"pith_short_12","alias_value":"DYUTJQP2MG4R","created_at":"2026-07-16T00:22:07.782290+00:00"},{"alias_kind":"pith_short_16","alias_value":"DYUTJQP2MG4RDV5N","created_at":"2026-07-16T00:22:07.782290+00:00"},{"alias_kind":"pith_short_8","alias_value":"DYUTJQP2","created_at":"2026-07-16T00:22:07.782290+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/DYUTJQP2MG4RDV5NQT4BRVELO2","json":"https://pith.science/pith/DYUTJQP2MG4RDV5NQT4BRVELO2.json","graph_json":"https://pith.science/api/pith-number/DYUTJQP2MG4RDV5NQT4BRVELO2/graph.json","events_json":"https://pith.science/api/pith-number/DYUTJQP2MG4RDV5NQT4BRVELO2/events.json","paper":"https://pith.science/paper/DYUTJQP2"},"agent_actions":{"view_html":"https://pith.science/pith/DYUTJQP2MG4RDV5NQT4BRVELO2","download_json":"https://pith.science/pith/DYUTJQP2MG4RDV5NQT4BRVELO2.json","view_paper":"https://pith.science/paper/DYUTJQP2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.13287&json=true","fetch_graph":"https://pith.science/api/pith-number/DYUTJQP2MG4RDV5NQT4BRVELO2/graph.json","fetch_events":"https://pith.science/api/pith-number/DYUTJQP2MG4RDV5NQT4BRVELO2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DYUTJQP2MG4RDV5NQT4BRVELO2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DYUTJQP2MG4RDV5NQT4BRVELO2/action/storage_attestation","attest_author":"https://pith.science/pith/DYUTJQP2MG4RDV5NQT4BRVELO2/action/author_attestation","sign_citation":"https://pith.science/pith/DYUTJQP2MG4RDV5NQT4BRVELO2/action/citation_signature","submit_replication":"https://pith.science/pith/DYUTJQP2MG4RDV5NQT4BRVELO2/action/replication_record"}},"created_at":"2026-07-16T00:22:07.782290+00:00","updated_at":"2026-07-16T00:22:07.782290+00:00"}