{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:O2IXEIESUGRH5XY6SIE7OV564C","short_pith_number":"pith:O2IXEIES","canonical_record":{"source":{"id":"1408.3680","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2014-08-15T23:43:34Z","cross_cats_sorted":[],"title_canon_sha256":"991982722a0161b1bdfa1c3f0c12a5248948289b92044fbd4d00c95989ffc32f","abstract_canon_sha256":"ce1411321b1b15bc53663e6ef52d2ca1fcdec7e16dae9e1a4a33e57cefc86bfd"},"schema_version":"1.0"},"canonical_sha256":"7691722092a1a27edf1e9209f757bee0a504675199a3b222131e9769ea7a4ef0","source":{"kind":"arxiv","id":"1408.3680","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3680","created_at":"2026-05-18T01:42:18Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3680v1","created_at":"2026-05-18T01:42:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3680","created_at":"2026-05-18T01:42:18Z"},{"alias_kind":"pith_short_12","alias_value":"O2IXEIESUGRH","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O2IXEIESUGRH5XY6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O2IXEIES","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:O2IXEIESUGRH5XY6SIE7OV564C","target":"record","payload":{"canonical_record":{"source":{"id":"1408.3680","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2014-08-15T23:43:34Z","cross_cats_sorted":[],"title_canon_sha256":"991982722a0161b1bdfa1c3f0c12a5248948289b92044fbd4d00c95989ffc32f","abstract_canon_sha256":"ce1411321b1b15bc53663e6ef52d2ca1fcdec7e16dae9e1a4a33e57cefc86bfd"},"schema_version":"1.0"},"canonical_sha256":"7691722092a1a27edf1e9209f757bee0a504675199a3b222131e9769ea7a4ef0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:18.374355Z","signature_b64":"K0oGDXxwFnXbUDwmdkzj0rKyU3J9xiWsJMGQEGJQpw7Revf3FSqw0s/7CRLu2XgnqYsH5+U6p7ZFB9e0lQt6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7691722092a1a27edf1e9209f757bee0a504675199a3b222131e9769ea7a4ef0","last_reissued_at":"2026-05-18T01:42:18.373644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:18.373644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.3680","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":"2026-05-18T01:42:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S0kzQMrqY0BwbrP49FJTqp5BKGQ53cbzggsNyMq09qyJtNn9g42jPsSUMouIiXd8YMkkVwj7Cp2nyy/4I9YZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:58:17.443826Z"},"content_sha256":"7616d549aaceabf1e0c462d36c2d195ae9a479c7a7473fbb7f603246c7adf52d","schema_version":"1.0","event_id":"sha256:7616d549aaceabf1e0c462d36c2d195ae9a479c7a7473fbb7f603246c7adf52d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:O2IXEIESUGRH5XY6SIE7OV564C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large Scale Quasi-geostrophic Magnetohydrodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"Alexander M. Balk","submitted_at":"2014-08-15T23:43:34Z","abstract_excerpt":"We consider the ideal magnetohydrodynamics (MHD) of a shallow fluid layer on a rapidly rotating planet or star. The presence of a background toroidal magnetic field is assumed, and the \"shallow water\" beta-plane approximation is used. We derive a single equation for the slow large length scale dynamics. The range of validity of this equation fits the MHD of the lighter fluid at the top of Earth's outer core. The form of this equation is similar to the quasi-geostrophic (Q-G) equation (for usual ocean or atmosphere), but the parameters are essentially different. Our equation also implies the in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3680","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":"2026-05-18T01:42:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RnTEfdjvzNC/eXv35wkH01xIDsxV+qZeZ2Xch2QO/iZBmPw2WFpbT8VxIuO0KIrcwtJSiN4K3b7Db5oeYDeqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:58:17.444170Z"},"content_sha256":"bcf18671945267099f533a4a3fe3b1aeb4f23ffeb898b78beaa0e402e71af713","schema_version":"1.0","event_id":"sha256:bcf18671945267099f533a4a3fe3b1aeb4f23ffeb898b78beaa0e402e71af713"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O2IXEIESUGRH5XY6SIE7OV564C/bundle.json","state_url":"https://pith.science/pith/O2IXEIESUGRH5XY6SIE7OV564C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O2IXEIESUGRH5XY6SIE7OV564C/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":"2026-06-01T23:58:17Z","links":{"resolver":"https://pith.science/pith/O2IXEIESUGRH5XY6SIE7OV564C","bundle":"https://pith.science/pith/O2IXEIESUGRH5XY6SIE7OV564C/bundle.json","state":"https://pith.science/pith/O2IXEIESUGRH5XY6SIE7OV564C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O2IXEIESUGRH5XY6SIE7OV564C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O2IXEIESUGRH5XY6SIE7OV564C","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":"ce1411321b1b15bc53663e6ef52d2ca1fcdec7e16dae9e1a4a33e57cefc86bfd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2014-08-15T23:43:34Z","title_canon_sha256":"991982722a0161b1bdfa1c3f0c12a5248948289b92044fbd4d00c95989ffc32f"},"schema_version":"1.0","source":{"id":"1408.3680","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3680","created_at":"2026-05-18T01:42:18Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3680v1","created_at":"2026-05-18T01:42:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3680","created_at":"2026-05-18T01:42:18Z"},{"alias_kind":"pith_short_12","alias_value":"O2IXEIESUGRH","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O2IXEIESUGRH5XY6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O2IXEIES","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:bcf18671945267099f533a4a3fe3b1aeb4f23ffeb898b78beaa0e402e71af713","target":"graph","created_at":"2026-05-18T01:42:18Z","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 consider the ideal magnetohydrodynamics (MHD) of a shallow fluid layer on a rapidly rotating planet or star. The presence of a background toroidal magnetic field is assumed, and the \"shallow water\" beta-plane approximation is used. We derive a single equation for the slow large length scale dynamics. The range of validity of this equation fits the MHD of the lighter fluid at the top of Earth's outer core. The form of this equation is similar to the quasi-geostrophic (Q-G) equation (for usual ocean or atmosphere), but the parameters are essentially different. Our equation also implies the in","authors_text":"Alexander M. Balk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2014-08-15T23:43:34Z","title":"Large Scale Quasi-geostrophic Magnetohydrodynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3680","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":"sha256:7616d549aaceabf1e0c462d36c2d195ae9a479c7a7473fbb7f603246c7adf52d","target":"record","created_at":"2026-05-18T01:42:18Z","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":"ce1411321b1b15bc53663e6ef52d2ca1fcdec7e16dae9e1a4a33e57cefc86bfd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2014-08-15T23:43:34Z","title_canon_sha256":"991982722a0161b1bdfa1c3f0c12a5248948289b92044fbd4d00c95989ffc32f"},"schema_version":"1.0","source":{"id":"1408.3680","kind":"arxiv","version":1}},"canonical_sha256":"7691722092a1a27edf1e9209f757bee0a504675199a3b222131e9769ea7a4ef0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7691722092a1a27edf1e9209f757bee0a504675199a3b222131e9769ea7a4ef0","first_computed_at":"2026-05-18T01:42:18.373644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:18.373644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K0oGDXxwFnXbUDwmdkzj0rKyU3J9xiWsJMGQEGJQpw7Revf3FSqw0s/7CRLu2XgnqYsH5+U6p7ZFB9e0lQt6AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:18.374355Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3680","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7616d549aaceabf1e0c462d36c2d195ae9a479c7a7473fbb7f603246c7adf52d","sha256:bcf18671945267099f533a4a3fe3b1aeb4f23ffeb898b78beaa0e402e71af713"],"state_sha256":"4753279ab26f69ccf4477a7c8243bd7fdb4f8d962dbc926a3bf2e43bbdf86661"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A06kkQckmoOpwzk7sxjEldKHNVm/ZOUC22L/prGKcovt9h7+1xOQ8BGtvdbhy3L/EWZeiWkZje1+UbMZXmKsDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T23:58:17.446311Z","bundle_sha256":"8e55315d19a85224c87fd6e428a25b90ec9343e58f858c7c51c4336a0018c9b6"}}