{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:ITTOZLWKQ7RJW7GFOXSJTHSKL5","short_pith_number":"pith:ITTOZLWK","schema_version":"1.0","canonical_sha256":"44e6ecaeca87e29b7cc575e4999e4a5f4c4a86019abc7d62375ab9db755fe9ac","source":{"kind":"arxiv","id":"0806.1183","version":1},"attestation_state":"computed","paper":{"title":"Analytic structure of the four-wave mixing model in photorefractive materials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"nlin.PS","authors_text":"Kiev), Robert Conte (CEA Saclay), Svetlana Bugaychuk (Institute of physics","submitted_at":"2008-06-06T15:07:28Z","abstract_excerpt":"In order to later find explicit analytic solutions, we investigate the singularity structure of a fundamental model of nonlinear optics, the four-wave mixing model in one space variable z. This structure is quite similar, and this is not a surprise, to that of the cubic complex Ginzburg-Landau equation. The main result is that, in order to be single valued, time-dependent solutions should depend on the space-time coordinates through the reduced variable xi=\\sqrt{z} exp(-t / tau), in which tau is the relaxation time."},"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":"0806.1183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2008-06-06T15:07:28Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"ff278d68f9c2032555b4c904a78a4dc30b8deb5526dfa04f0fe92a65f9bfb85b","abstract_canon_sha256":"d49c68cae464d755cfe855e35e4fcf2813a9b0133ab427b8d210dd946c39d143"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:00.469185Z","signature_b64":"VWUIFus+UycjIZywjJSrYRgEBKeF2Ny7nEgWQkabwGLWVy0PWITXDW45mpUAigNXnoRG0dk/ePohsPsRBLtKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44e6ecaeca87e29b7cc575e4999e4a5f4c4a86019abc7d62375ab9db755fe9ac","last_reissued_at":"2026-05-18T00:33:00.468586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:00.468586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic structure of the four-wave mixing model in photorefractive materials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"nlin.PS","authors_text":"Kiev), Robert Conte (CEA Saclay), Svetlana Bugaychuk (Institute of physics","submitted_at":"2008-06-06T15:07:28Z","abstract_excerpt":"In order to later find explicit analytic solutions, we investigate the singularity structure of a fundamental model of nonlinear optics, the four-wave mixing model in one space variable z. This structure is quite similar, and this is not a surprise, to that of the cubic complex Ginzburg-Landau equation. The main result is that, in order to be single valued, time-dependent solutions should depend on the space-time coordinates through the reduced variable xi=\\sqrt{z} exp(-t / tau), in which tau is the relaxation time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.1183","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":"0806.1183","created_at":"2026-05-18T00:33:00.468679+00:00"},{"alias_kind":"arxiv_version","alias_value":"0806.1183v1","created_at":"2026-05-18T00:33:00.468679+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.1183","created_at":"2026-05-18T00:33:00.468679+00:00"},{"alias_kind":"pith_short_12","alias_value":"ITTOZLWKQ7RJ","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"ITTOZLWKQ7RJW7GF","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"ITTOZLWK","created_at":"2026-05-18T12:25:57.157939+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/ITTOZLWKQ7RJW7GFOXSJTHSKL5","json":"https://pith.science/pith/ITTOZLWKQ7RJW7GFOXSJTHSKL5.json","graph_json":"https://pith.science/api/pith-number/ITTOZLWKQ7RJW7GFOXSJTHSKL5/graph.json","events_json":"https://pith.science/api/pith-number/ITTOZLWKQ7RJW7GFOXSJTHSKL5/events.json","paper":"https://pith.science/paper/ITTOZLWK"},"agent_actions":{"view_html":"https://pith.science/pith/ITTOZLWKQ7RJW7GFOXSJTHSKL5","download_json":"https://pith.science/pith/ITTOZLWKQ7RJW7GFOXSJTHSKL5.json","view_paper":"https://pith.science/paper/ITTOZLWK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0806.1183&json=true","fetch_graph":"https://pith.science/api/pith-number/ITTOZLWKQ7RJW7GFOXSJTHSKL5/graph.json","fetch_events":"https://pith.science/api/pith-number/ITTOZLWKQ7RJW7GFOXSJTHSKL5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ITTOZLWKQ7RJW7GFOXSJTHSKL5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ITTOZLWKQ7RJW7GFOXSJTHSKL5/action/storage_attestation","attest_author":"https://pith.science/pith/ITTOZLWKQ7RJW7GFOXSJTHSKL5/action/author_attestation","sign_citation":"https://pith.science/pith/ITTOZLWKQ7RJW7GFOXSJTHSKL5/action/citation_signature","submit_replication":"https://pith.science/pith/ITTOZLWKQ7RJW7GFOXSJTHSKL5/action/replication_record"}},"created_at":"2026-05-18T00:33:00.468679+00:00","updated_at":"2026-05-18T00:33:00.468679+00:00"}