{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JHM4WW5RYEKWA5M6BHNBBTP3AP","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":"096285f3634e500c55d6bcee6ffbd4226c3280cc8a09951fb663ab1c95e94cd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2018-08-29T03:31:32Z","title_canon_sha256":"1317c74e6b01eee1bb48e66496f3638af34b58c926e19676f03c130159ab6cbc"},"schema_version":"1.0","source":{"id":"1808.09622","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09622","created_at":"2026-05-18T00:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09622v1","created_at":"2026-05-18T00:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09622","created_at":"2026-05-18T00:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"JHM4WW5RYEKW","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JHM4WW5RYEKWA5M6","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JHM4WW5R","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:ac27df3b63aed11f5593c421061b805685e0b3115458701c40692d431fea7d53","target":"graph","created_at":"2026-05-18T00:06:54Z","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":"Starting from hydrodynamic equations, we have established a set of hydrodynamic equations for average flow and a set of dynamic equations of auto- and cross-correlations of turbulent velocity and temperature fluctuations, following the classic Reynold's treatment of turbulence. The combination of the two sets of equations leads to a complete and self-consistent mathematical expressions ready for the calculations of stellar structure and oscillations. In this paper, non-locality and anisotropy of turbulent convection are concisely presented, together with defining and calibrating of the three c","authors_text":"C. Zhang, D. R. Xiong, L. Deng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2018-08-29T03:31:32Z","title":"Turbulent convection and pulsation stability of stars - I. Basic equations for calculations of stellar structure and oscillations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09622","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:b573f38975c287f7b48415b8f0b6ccc08c29c2526acdb050b52e0b7630dcf523","target":"record","created_at":"2026-05-18T00:06:54Z","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":"096285f3634e500c55d6bcee6ffbd4226c3280cc8a09951fb663ab1c95e94cd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2018-08-29T03:31:32Z","title_canon_sha256":"1317c74e6b01eee1bb48e66496f3638af34b58c926e19676f03c130159ab6cbc"},"schema_version":"1.0","source":{"id":"1808.09622","kind":"arxiv","version":1}},"canonical_sha256":"49d9cb5bb1c11560759e09da10cdfb03ce3a75cd8f812999f8492190f3549277","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49d9cb5bb1c11560759e09da10cdfb03ce3a75cd8f812999f8492190f3549277","first_computed_at":"2026-05-18T00:06:54.988242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:54.988242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6sWe6S0WockDTg9eNuliHTT6PW1i7a9PbcNzhO0B/f2995Tt8PGmwUXMkdNjGoP3//1Q7dESM8Mo+2cUgKUCBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:54.988680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.09622","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b573f38975c287f7b48415b8f0b6ccc08c29c2526acdb050b52e0b7630dcf523","sha256:ac27df3b63aed11f5593c421061b805685e0b3115458701c40692d431fea7d53"],"state_sha256":"7409ca71732540aef99e3eb9490cb95c5564bba00164ff516a3fcce4afba0358"}