{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZKQSFNTWV5ITMKWD7XCNNLPFJZ","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":"d0593d64f670be64924f1b591e79dcaf516818f1ee39430375eacb12428b3781","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-18T03:53:13Z","title_canon_sha256":"ffece36ad343fe27953186b77513692a48ff2cf9a31ae14699e8e32c9537186c"},"schema_version":"1.0","source":{"id":"2606.19764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19764","created_at":"2026-06-19T16:12:34Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19764v1","created_at":"2026-06-19T16:12:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19764","created_at":"2026-06-19T16:12:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZKQSFNTWV5IT","created_at":"2026-06-19T16:12:34Z"},{"alias_kind":"pith_short_16","alias_value":"ZKQSFNTWV5ITMKWD","created_at":"2026-06-19T16:12:34Z"},{"alias_kind":"pith_short_8","alias_value":"ZKQSFNTW","created_at":"2026-06-19T16:12:34Z"}],"graph_snapshots":[{"event_id":"sha256:c2a98accfd21ae577f5d7e475d98563e83c5b1d52cffe00cddc1a3efaa103d46","target":"graph","created_at":"2026-06-19T16:12:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.19764/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a second-order approximation to the compressible atmospheric Euler equations with gravity that is invariant domain preserving and well-balanced with respect to rest states. The approximation is built upon discrete auxiliary states derived from a hydrostatic reconstruction of the density. These auxiliary states, together with an affine shift of the numerical state, provide local bounds needed for maintaining well-balancing and invariant domain preserving properties of the method. The numerical method is then verified and validated with analytic solutions, well-balancing tests, and ","authors_text":"Crystal Farris, Eric J. Tovar, Matthias Maier","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-18T03:53:13Z","title":"Well-balanced second-order approximation of the compressible atmospheric Euler equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19764","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:bc37effc074d5dae22303cc3a4ce72c3e70c2a0a06b501e8971dad6e83eb2817","target":"record","created_at":"2026-06-19T16:12:34Z","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":"d0593d64f670be64924f1b591e79dcaf516818f1ee39430375eacb12428b3781","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-18T03:53:13Z","title_canon_sha256":"ffece36ad343fe27953186b77513692a48ff2cf9a31ae14699e8e32c9537186c"},"schema_version":"1.0","source":{"id":"2606.19764","kind":"arxiv","version":1}},"canonical_sha256":"caa122b676af51362ac3fdc4d6ade54e7e52130016ca5432a4906ac87677f03c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"caa122b676af51362ac3fdc4d6ade54e7e52130016ca5432a4906ac87677f03c","first_computed_at":"2026-06-19T16:12:34.508196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:34.508196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PwP17+ahXIyI+ghkW4UaM3xz1qMY0+/V2qj31zQPptQsj9pT5iWSWEAd7lS7w2nWXT5crQJ53H+eo/m4iYlPCg==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:34.508542Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc37effc074d5dae22303cc3a4ce72c3e70c2a0a06b501e8971dad6e83eb2817","sha256:c2a98accfd21ae577f5d7e475d98563e83c5b1d52cffe00cddc1a3efaa103d46"],"state_sha256":"6a9bb6c2bfc6bbecda74482d70d60594d49880ef04f24c53051f6b0689af04b9"}