{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZXKBXHYFFQMFNJPHSOQAIASZH2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1fa811ddf9680b40203757abf9ad2888a6a7425c39aff26496a659d969942870","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-07T09:08:41Z","title_canon_sha256":"a5f4c8ddd90d98bbc9d79b279134ef1427e0c43dfba1a02817262ebb2d95c2d3"},"schema_version":"1.0","source":{"id":"1102.1248","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1248","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1248v2","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1248","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZXKBXHYFFQMF","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZXKBXHYFFQMFNJPH","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZXKBXHYF","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:fbd5a64c36c6e138837762882da1097dff64d108560c655ba01bbf7f308a9040","target":"graph","created_at":"2026-05-18T01:37:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We construct time quasi-periodic solutions to nonlinear wave equations on the torus in arbitrary dimensions. All previously known results (in the case of zero or a multiplicative potential) seem to be limited to the circle. This generalizes the method developed in the limit-elliptic setting of NLS to the hyperbolic setting. The additional ingredient is a Diophantine property of algebraic numbers.","authors_text":"Wei-Min Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-07T09:08:41Z","title":"Quasi-periodic solutions for nonlinear wave equations (announcement)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1248","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e5ae618e22c00547ea9d3c8f3ace1b7ad86d6a0ab4d5a4fac89b90992911b336","target":"record","created_at":"2026-05-18T01:37:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1fa811ddf9680b40203757abf9ad2888a6a7425c39aff26496a659d969942870","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-07T09:08:41Z","title_canon_sha256":"a5f4c8ddd90d98bbc9d79b279134ef1427e0c43dfba1a02817262ebb2d95c2d3"},"schema_version":"1.0","source":{"id":"1102.1248","kind":"arxiv","version":2}},"canonical_sha256":"cdd41b9f052c1856a5e793a00402593e9c3e9bdca2f29104d4276157f6e2dc20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdd41b9f052c1856a5e793a00402593e9c3e9bdca2f29104d4276157f6e2dc20","first_computed_at":"2026-05-18T01:37:06.075271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:06.075271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mIaaNvrYiCJO5lluFpvs7kbpX9DS6hvYgY9Mr7ghQhWDuxAS9W6LeqINGX8phjguoFsCSYUhpxu8QOY2SUKrDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:06.075979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1248","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5ae618e22c00547ea9d3c8f3ace1b7ad86d6a0ab4d5a4fac89b90992911b336","sha256:fbd5a64c36c6e138837762882da1097dff64d108560c655ba01bbf7f308a9040"],"state_sha256":"2a2e6fab6cddc7c5bbe56d99e90090cf930ff7e370ace9c1fa8d4ad3745cd792"}