{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GCJ6CH56AP5KF4HFDLSHDY3YWQ","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":"5e9c52b241903b0cf486a767b27eb0b697c86f5c91b7e131861ab4aed718bce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-25T11:35:04Z","title_canon_sha256":"2023de785adba280278747bd55cf2259adf14dccc2d147255e520683f12cccf7"},"schema_version":"1.0","source":{"id":"1701.07270","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07270","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07270v1","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07270","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"GCJ6CH56AP5K","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GCJ6CH56AP5KF4HF","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GCJ6CH56","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:842c839ab7f7c484badd161585181e0a30fdc2b8ed5cc6e99d2996951f5348b6","target":"graph","created_at":"2026-05-18T00:07:12Z","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":"This paper studies the global existence of classical solutions to the two-dimensional incompressible magneto-hydrodynamical (MHD) system with only magnetic diffusion on the periodic domain. The approach is based on a time-weighted energy estimate, under the assumptions that the initial magnetic field is close enough to an equilibrium state and the initial data have reflection symmetry.","authors_text":"Yi Zhou, Yi Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-25T11:35:04Z","title":"Global classical solutions of 2D MHD system with only magnetic diffusion on periodic domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07270","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:ccba3ff6ecf07c373ec3d3a765d516339815901bd00df19de1171b066bb469d8","target":"record","created_at":"2026-05-18T00:07:12Z","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":"5e9c52b241903b0cf486a767b27eb0b697c86f5c91b7e131861ab4aed718bce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-25T11:35:04Z","title_canon_sha256":"2023de785adba280278747bd55cf2259adf14dccc2d147255e520683f12cccf7"},"schema_version":"1.0","source":{"id":"1701.07270","kind":"arxiv","version":1}},"canonical_sha256":"3093e11fbe03faa2f0e51ae471e378b400d98a976c9812c52dad30aa29db634e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3093e11fbe03faa2f0e51ae471e378b400d98a976c9812c52dad30aa29db634e","first_computed_at":"2026-05-18T00:07:12.410212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:12.410212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J6IcB96x/X96MNowAMwpXQyYaFh2pPGmXbcamS7UGLXkI4N2PckDGv2REsjq4UlP5t7eBOD5vAg31OJskElVDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:12.410904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.07270","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccba3ff6ecf07c373ec3d3a765d516339815901bd00df19de1171b066bb469d8","sha256:842c839ab7f7c484badd161585181e0a30fdc2b8ed5cc6e99d2996951f5348b6"],"state_sha256":"4486f6ca9c282f70cbbed1583a3f50eb5883163245ea4048dea7d6866bfc35ee"}