{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:C5YZNP5DJ3CS5YK3JB7J2PXWU7","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":"e458f0f1e1c749cb746da4b462019babce3da58cff37b709000b622b9230e961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-28T20:43:13Z","title_canon_sha256":"e09fd9f398b43aaa1bafb22d89f141ccf10eacf2d62175b335c1267a0ceebca9"},"schema_version":"1.0","source":{"id":"1203.6376","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6376","created_at":"2026-05-18T03:59:02Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6376v1","created_at":"2026-05-18T03:59:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6376","created_at":"2026-05-18T03:59:02Z"},{"alias_kind":"pith_short_12","alias_value":"C5YZNP5DJ3CS","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C5YZNP5DJ3CS5YK3","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C5YZNP5D","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:c512f0c768f6b7709ae5b8382b485606d4f3adbca301d166c3b0e2fdae0bd28d","target":"graph","created_at":"2026-05-18T03:59:02Z","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":"The initial value problem of the Zakharov system on two-dimensional torus with general period is considered in this paper. We apply the $I$-method with some 'resonant decomposition' to show global well-posedness results for small-in-$L^2$ initial data belonging to some spaces weaker than the energy class. We also consider an application of our ideas to the initial value problem on $\\mathbb{R}^2$ and give an improvement of the best known result by Pecher (2012).","authors_text":"Nobu Kishimoto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-28T20:43:13Z","title":"Resonant decomposition and the $I$-method for the two-dimensional Zakharov system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6376","kind":"arxiv","version":1},"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:f682697fc94cb0bb158014f81dae4c93b46939f8adc537735c2325789c8df439","target":"record","created_at":"2026-05-18T03:59:02Z","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":"e458f0f1e1c749cb746da4b462019babce3da58cff37b709000b622b9230e961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-28T20:43:13Z","title_canon_sha256":"e09fd9f398b43aaa1bafb22d89f141ccf10eacf2d62175b335c1267a0ceebca9"},"schema_version":"1.0","source":{"id":"1203.6376","kind":"arxiv","version":1}},"canonical_sha256":"177196bfa34ec52ee15b487e9d3ef6a7fbc3945d73dd34465f36c6154fc121ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"177196bfa34ec52ee15b487e9d3ef6a7fbc3945d73dd34465f36c6154fc121ae","first_computed_at":"2026-05-18T03:59:02.687383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:02.687383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w7Ah3/5qxU6iM7H7wLqUkYZb01Z72ZXEeNIwXEAHoi93BPiiwlImmcn/sH458aG11uZpHDWy37ayib1bZDd3BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:02.687940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6376","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f682697fc94cb0bb158014f81dae4c93b46939f8adc537735c2325789c8df439","sha256:c512f0c768f6b7709ae5b8382b485606d4f3adbca301d166c3b0e2fdae0bd28d"],"state_sha256":"ac7ab2d35463fe60c8dc56092a1abfeea9d045fa9629c9901af9d02346afacbb"}