{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KC35B255PAQZKIZQYDUYQHNBW3","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":"76ba1d3e3ea2eddac369456728b1863eacff3efe155a3afa43311a201f7079a4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2015-11-11T10:57:07Z","title_canon_sha256":"f0b0a664433123ac5853092e9244c8eee59d4870ccde7ad02e96bdd03d299b3f"},"schema_version":"1.0","source":{"id":"1511.03448","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03448","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03448v2","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03448","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"KC35B255PAQZ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KC35B255PAQZKIZQ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KC35B255","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:19f2b7c5d94181758e9ad1e3c904d379d7e513ffd719f487d4f4ffd5261834e9","target":"graph","created_at":"2026-05-18T01:25:46Z","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 Boussingesq equations was introduced in understanding the coupling nature of the thermodynamics and the fluid dynamics. We show the existence of continuous periodic weak solutions of the Boussinesq equations which satisfies the prescribed kinetic energy or some other prescribed property. Our results represent the conversions between internal energy and mechanical energy.","authors_text":"Liqun Zhang, Tao Tao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2015-11-11T10:57:07Z","title":"On The Continuous Periodic Weak Slution of Boussinesq Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03448","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:fd10450a6f329025731dfbf14c3e9de8da97e504fac53a3ebcf6cc3c56f46a27","target":"record","created_at":"2026-05-18T01:25:46Z","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":"76ba1d3e3ea2eddac369456728b1863eacff3efe155a3afa43311a201f7079a4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2015-11-11T10:57:07Z","title_canon_sha256":"f0b0a664433123ac5853092e9244c8eee59d4870ccde7ad02e96bdd03d299b3f"},"schema_version":"1.0","source":{"id":"1511.03448","kind":"arxiv","version":2}},"canonical_sha256":"50b7d0ebbd7821952330c0e9881da1b6cfbdbd25de101e29e63c955dbd1f436e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50b7d0ebbd7821952330c0e9881da1b6cfbdbd25de101e29e63c955dbd1f436e","first_computed_at":"2026-05-18T01:25:46.502010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:46.502010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tlpS3vxhVCUvCwxcHfIyarLxH/wqXe3vHNCzCqldYtqNfinpdnmELpKdm/zeTiwKEVKicPJHbK9RCeUPjk1eBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:46.502593Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03448","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd10450a6f329025731dfbf14c3e9de8da97e504fac53a3ebcf6cc3c56f46a27","sha256:19f2b7c5d94181758e9ad1e3c904d379d7e513ffd719f487d4f4ffd5261834e9"],"state_sha256":"6cea3340706980eb0f368bb0191a86a3c3003790a9ab20e9d1dc5dd5b1ac8b5f"}