{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RNQXV5MXLEGAKQ73FYX23XMBXR","short_pith_number":"pith:RNQXV5MX","canonical_record":{"source":{"id":"1006.2606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-06-14T06:56:33Z","cross_cats_sorted":[],"title_canon_sha256":"cd4c99fbceb49931262587353457443f5b0694e2a63a9dbd4b98f7f01c27bb6e","abstract_canon_sha256":"08eeec680eaf91d5a1dbcb364671e0a318ff0d375fd7c6659264f1c90e0bba6b"},"schema_version":"1.0"},"canonical_sha256":"8b617af597590c0543fb2e2faddd81bc4c23d40dd72f04f888e59a4f2a456055","source":{"kind":"arxiv","id":"1006.2606","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2606","created_at":"2026-05-18T02:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2606v1","created_at":"2026-05-18T02:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2606","created_at":"2026-05-18T02:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"RNQXV5MXLEGA","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RNQXV5MXLEGAKQ73","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RNQXV5MX","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RNQXV5MXLEGAKQ73FYX23XMBXR","target":"record","payload":{"canonical_record":{"source":{"id":"1006.2606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-06-14T06:56:33Z","cross_cats_sorted":[],"title_canon_sha256":"cd4c99fbceb49931262587353457443f5b0694e2a63a9dbd4b98f7f01c27bb6e","abstract_canon_sha256":"08eeec680eaf91d5a1dbcb364671e0a318ff0d375fd7c6659264f1c90e0bba6b"},"schema_version":"1.0"},"canonical_sha256":"8b617af597590c0543fb2e2faddd81bc4c23d40dd72f04f888e59a4f2a456055","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:06:54.003236Z","signature_b64":"r/2RK4dNPC8MdMVyk+b8gQnXv3bZWqgg6QAF5VAV7QSyvuvLiSQUYT+iUKbpmAa75vCs50is3jVE9KZttGO9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b617af597590c0543fb2e2faddd81bc4c23d40dd72f04f888e59a4f2a456055","last_reissued_at":"2026-05-18T02:06:54.002474Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:06:54.002474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.2606","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xG8ex98duPxdGmT1jjvModLjk8Mq4gqMaIVLW/hNyzQOdYNXGQPfDTP+H9NyXpdcjMNnMu5vFxxFthHYXzL1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:43:01.094171Z"},"content_sha256":"38f3a37e58df69c62ad2b5dc1c3d3681ed66d9e493c2ad549186d786392077da","schema_version":"1.0","event_id":"sha256:38f3a37e58df69c62ad2b5dc1c3d3681ed66d9e493c2ad549186d786392077da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RNQXV5MXLEGAKQ73FYX23XMBXR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compressible primitive equation: formal derivation and stability of weak solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"LANI), Mamadou Sy (LANI), Mehmet Ersoy (LAMA), Timack Ngom (LAMA","submitted_at":"2010-06-14T06:56:33Z","abstract_excerpt":"We present a formal derivation of a simplified version of Compressible Primitive Equations (CPEs) for atmosphere modeling. They are obtained from $3$-D compressible Navier-Stokes equations with an \\emph{anisotropic viscous stress tensor} where viscosity depends on the density. We then study the stability of the weak solutions of this model by using an intermediate model, called model problem, which is more simple and practical, to achieve the main result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2606","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZToonof9E1h3Dswr8TS5jpPFgRrWufgEoVuhJ2G0Q/W/hQ0wP9zybeyBWnh48aYhvol6+6dgENQOnYKtBNKFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:43:01.094702Z"},"content_sha256":"ea8294b832387292e82c07e455ba9da53e2ed573bad979ceebbaaf1843b1cd6e","schema_version":"1.0","event_id":"sha256:ea8294b832387292e82c07e455ba9da53e2ed573bad979ceebbaaf1843b1cd6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RNQXV5MXLEGAKQ73FYX23XMBXR/bundle.json","state_url":"https://pith.science/pith/RNQXV5MXLEGAKQ73FYX23XMBXR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RNQXV5MXLEGAKQ73FYX23XMBXR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T23:43:01Z","links":{"resolver":"https://pith.science/pith/RNQXV5MXLEGAKQ73FYX23XMBXR","bundle":"https://pith.science/pith/RNQXV5MXLEGAKQ73FYX23XMBXR/bundle.json","state":"https://pith.science/pith/RNQXV5MXLEGAKQ73FYX23XMBXR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RNQXV5MXLEGAKQ73FYX23XMBXR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RNQXV5MXLEGAKQ73FYX23XMBXR","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":"08eeec680eaf91d5a1dbcb364671e0a318ff0d375fd7c6659264f1c90e0bba6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-06-14T06:56:33Z","title_canon_sha256":"cd4c99fbceb49931262587353457443f5b0694e2a63a9dbd4b98f7f01c27bb6e"},"schema_version":"1.0","source":{"id":"1006.2606","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2606","created_at":"2026-05-18T02:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2606v1","created_at":"2026-05-18T02:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2606","created_at":"2026-05-18T02:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"RNQXV5MXLEGA","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RNQXV5MXLEGAKQ73","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RNQXV5MX","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:ea8294b832387292e82c07e455ba9da53e2ed573bad979ceebbaaf1843b1cd6e","target":"graph","created_at":"2026-05-18T02:06:54Z","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":"We present a formal derivation of a simplified version of Compressible Primitive Equations (CPEs) for atmosphere modeling. They are obtained from $3$-D compressible Navier-Stokes equations with an \\emph{anisotropic viscous stress tensor} where viscosity depends on the density. We then study the stability of the weak solutions of this model by using an intermediate model, called model problem, which is more simple and practical, to achieve the main result.","authors_text":"LANI), Mamadou Sy (LANI), Mehmet Ersoy (LAMA), Timack Ngom (LAMA","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-06-14T06:56:33Z","title":"Compressible primitive equation: formal derivation and stability of weak solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2606","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":"sha256:38f3a37e58df69c62ad2b5dc1c3d3681ed66d9e493c2ad549186d786392077da","target":"record","created_at":"2026-05-18T02:06:54Z","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":"08eeec680eaf91d5a1dbcb364671e0a318ff0d375fd7c6659264f1c90e0bba6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-06-14T06:56:33Z","title_canon_sha256":"cd4c99fbceb49931262587353457443f5b0694e2a63a9dbd4b98f7f01c27bb6e"},"schema_version":"1.0","source":{"id":"1006.2606","kind":"arxiv","version":1}},"canonical_sha256":"8b617af597590c0543fb2e2faddd81bc4c23d40dd72f04f888e59a4f2a456055","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b617af597590c0543fb2e2faddd81bc4c23d40dd72f04f888e59a4f2a456055","first_computed_at":"2026-05-18T02:06:54.002474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:06:54.002474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r/2RK4dNPC8MdMVyk+b8gQnXv3bZWqgg6QAF5VAV7QSyvuvLiSQUYT+iUKbpmAa75vCs50is3jVE9KZttGO9Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:06:54.003236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.2606","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38f3a37e58df69c62ad2b5dc1c3d3681ed66d9e493c2ad549186d786392077da","sha256:ea8294b832387292e82c07e455ba9da53e2ed573bad979ceebbaaf1843b1cd6e"],"state_sha256":"4369d9e8132a0083558b70d67acde1375b0b77494832e09c1737a96817f1c44b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o0nLiQeup70xdJ3n/2bNC8/sOMVEImIA2KpmzBn7hupRiW894C6A+md/iGsE+eKAafWTjrey6g7iL7RjogCjDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:43:01.097856Z","bundle_sha256":"bac679b49a23a6c35199a8a02738dbd5003601f3134bc401a41987cc6f5e3a94"}}