{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2YOWZIIGGIZUBUEKFPQ73RVSRF","short_pith_number":"pith:2YOWZIIG","schema_version":"1.0","canonical_sha256":"d61d6ca106323340d08a2be1fdc6b2894dac8fcccc41632cccc1b1061fdae787","source":{"kind":"arxiv","id":"1812.04836","version":4},"attestation_state":"computed","paper":{"title":"Analytic solutions of nonlinear elliptic equations on rectangular tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Yunfeng Shi","submitted_at":"2018-12-12T07:48:32Z","abstract_excerpt":"In this paper, we consider the nonlinear elliptic equations on rectangular tori. Using methods in the study of KAM theory and Anderson localization, we prove that these equations admit many analytic solutions."},"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":"1812.04836","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-12T07:48:32Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"d0cd1cf50d6b52dd21c2b524ce8c7df39c76caa67640be4f5dece844bd203f45","abstract_canon_sha256":"f6d6cb3b708b8c475d0a69072712fbc11c2738b9ba311d98e4897ccf8c47f09f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:56.762631Z","signature_b64":"5pPfiLCGUG86NZmv1JeIsrTx3CPuEKPdt3xbZJ9c+5dBtd3fuKbOLi3o4JovAFVJ2xxTBHixIfENclCBEaNQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d61d6ca106323340d08a2be1fdc6b2894dac8fcccc41632cccc1b1061fdae787","last_reissued_at":"2026-05-17T23:57:56.762094Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:56.762094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic solutions of nonlinear elliptic equations on rectangular tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Yunfeng Shi","submitted_at":"2018-12-12T07:48:32Z","abstract_excerpt":"In this paper, we consider the nonlinear elliptic equations on rectangular tori. Using methods in the study of KAM theory and Anderson localization, we prove that these equations admit many analytic solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04836","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":"1812.04836","created_at":"2026-05-17T23:57:56.762176+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.04836v4","created_at":"2026-05-17T23:57:56.762176+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04836","created_at":"2026-05-17T23:57:56.762176+00:00"},{"alias_kind":"pith_short_12","alias_value":"2YOWZIIGGIZU","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2YOWZIIGGIZUBUEK","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2YOWZIIG","created_at":"2026-05-18T12:32:02.567920+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/2YOWZIIGGIZUBUEKFPQ73RVSRF","json":"https://pith.science/pith/2YOWZIIGGIZUBUEKFPQ73RVSRF.json","graph_json":"https://pith.science/api/pith-number/2YOWZIIGGIZUBUEKFPQ73RVSRF/graph.json","events_json":"https://pith.science/api/pith-number/2YOWZIIGGIZUBUEKFPQ73RVSRF/events.json","paper":"https://pith.science/paper/2YOWZIIG"},"agent_actions":{"view_html":"https://pith.science/pith/2YOWZIIGGIZUBUEKFPQ73RVSRF","download_json":"https://pith.science/pith/2YOWZIIGGIZUBUEKFPQ73RVSRF.json","view_paper":"https://pith.science/paper/2YOWZIIG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.04836&json=true","fetch_graph":"https://pith.science/api/pith-number/2YOWZIIGGIZUBUEKFPQ73RVSRF/graph.json","fetch_events":"https://pith.science/api/pith-number/2YOWZIIGGIZUBUEKFPQ73RVSRF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2YOWZIIGGIZUBUEKFPQ73RVSRF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2YOWZIIGGIZUBUEKFPQ73RVSRF/action/storage_attestation","attest_author":"https://pith.science/pith/2YOWZIIGGIZUBUEKFPQ73RVSRF/action/author_attestation","sign_citation":"https://pith.science/pith/2YOWZIIGGIZUBUEKFPQ73RVSRF/action/citation_signature","submit_replication":"https://pith.science/pith/2YOWZIIGGIZUBUEKFPQ73RVSRF/action/replication_record"}},"created_at":"2026-05-17T23:57:56.762176+00:00","updated_at":"2026-05-17T23:57:56.762176+00:00"}