{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Q5NNGR44DQRW7ATDRWO7LIJBDE","short_pith_number":"pith:Q5NNGR44","canonical_record":{"source":{"id":"1412.6317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-19T12:39:24Z","cross_cats_sorted":[],"title_canon_sha256":"b0e72e79af6c6ca4078c5013a9da86a394f1898f27e2cf3fe91f8262302b567f","abstract_canon_sha256":"3530c348400411b0746a19a5ee9a1ef2d4eea3e9e902e891d4ed580299df9b0c"},"schema_version":"1.0"},"canonical_sha256":"875ad3479c1c236f82638d9df5a1211916fbc743566edb149242ae36f3a74f89","source":{"kind":"arxiv","id":"1412.6317","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6317","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6317v1","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6317","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"pith_short_12","alias_value":"Q5NNGR44DQRW","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q5NNGR44DQRW7ATD","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q5NNGR44","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Q5NNGR44DQRW7ATDRWO7LIJBDE","target":"record","payload":{"canonical_record":{"source":{"id":"1412.6317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-19T12:39:24Z","cross_cats_sorted":[],"title_canon_sha256":"b0e72e79af6c6ca4078c5013a9da86a394f1898f27e2cf3fe91f8262302b567f","abstract_canon_sha256":"3530c348400411b0746a19a5ee9a1ef2d4eea3e9e902e891d4ed580299df9b0c"},"schema_version":"1.0"},"canonical_sha256":"875ad3479c1c236f82638d9df5a1211916fbc743566edb149242ae36f3a74f89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:53.817948Z","signature_b64":"X8ca1A4wR5KR8VHMbEjzOYjmHVCOoFltUSDOgoNE10fa53dd25kBFnKTRa39C8txXSewcOFqoKKjjwIP+grKBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"875ad3479c1c236f82638d9df5a1211916fbc743566edb149242ae36f3a74f89","last_reissued_at":"2026-05-18T02:30:53.817264Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:53.817264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.6317","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":"2026-05-18T02:30:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QTTOk2gyuTwRUdS/QuMEUoDZ2MIsCMIMx2MvuJlAOvS6A8ni2rbKxbBNmWpx+64t2dywaX5i0ST/ciAH41jPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:25:28.844869Z"},"content_sha256":"fb1b20f2783abb208b0386715d683b0a0da4eefe3ab318d3d1543493c1986ca9","schema_version":"1.0","event_id":"sha256:fb1b20f2783abb208b0386715d683b0a0da4eefe3ab318d3d1543493c1986ca9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Q5NNGR44DQRW7ATDRWO7LIJBDE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Instability of Planetary Flows using Riemann Curvature: a Numerical Study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Richard Blender","submitted_at":"2014-12-19T12:39:24Z","abstract_excerpt":"The instability of ideal non-divergent zonal flows on the sphere is determined numerically by the instability criterion of Arnol'd (1966) for the sectional curvature. Zonal flows are unstable for all perturbations besides for a small set which are in approximate resonance. The sectional curvature scales with $m/\\ell$ for large total and zonal wave numbers $\\ell$ and $m$ of the perturbations. The planetary rotation is stable and the presence of rotation reduces the instability of perturbations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6317","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":"2026-05-18T02:30:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XuXESDgIq/Q6rZ8nD7zQnpMjPV3dTFHYWXHExjxdw8RJL6SlVvpc1oOk+//h9Uf8onrkkah2frIhhc3aBY6CAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:25:28.845571Z"},"content_sha256":"1050a8b644f43c1fd7394b087cc0705615fedc179cc6a6d3f2901292845fa358","schema_version":"1.0","event_id":"sha256:1050a8b644f43c1fd7394b087cc0705615fedc179cc6a6d3f2901292845fa358"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q5NNGR44DQRW7ATDRWO7LIJBDE/bundle.json","state_url":"https://pith.science/pith/Q5NNGR44DQRW7ATDRWO7LIJBDE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q5NNGR44DQRW7ATDRWO7LIJBDE/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":"2026-06-12T03:25:28Z","links":{"resolver":"https://pith.science/pith/Q5NNGR44DQRW7ATDRWO7LIJBDE","bundle":"https://pith.science/pith/Q5NNGR44DQRW7ATDRWO7LIJBDE/bundle.json","state":"https://pith.science/pith/Q5NNGR44DQRW7ATDRWO7LIJBDE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q5NNGR44DQRW7ATDRWO7LIJBDE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q5NNGR44DQRW7ATDRWO7LIJBDE","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":"3530c348400411b0746a19a5ee9a1ef2d4eea3e9e902e891d4ed580299df9b0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-19T12:39:24Z","title_canon_sha256":"b0e72e79af6c6ca4078c5013a9da86a394f1898f27e2cf3fe91f8262302b567f"},"schema_version":"1.0","source":{"id":"1412.6317","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6317","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6317v1","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6317","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"pith_short_12","alias_value":"Q5NNGR44DQRW","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q5NNGR44DQRW7ATD","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q5NNGR44","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:1050a8b644f43c1fd7394b087cc0705615fedc179cc6a6d3f2901292845fa358","target":"graph","created_at":"2026-05-18T02:30:53Z","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 instability of ideal non-divergent zonal flows on the sphere is determined numerically by the instability criterion of Arnol'd (1966) for the sectional curvature. Zonal flows are unstable for all perturbations besides for a small set which are in approximate resonance. The sectional curvature scales with $m/\\ell$ for large total and zonal wave numbers $\\ell$ and $m$ of the perturbations. The planetary rotation is stable and the presence of rotation reduces the instability of perturbations.","authors_text":"Richard Blender","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-19T12:39:24Z","title":"Instability of Planetary Flows using Riemann Curvature: a Numerical Study"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6317","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:fb1b20f2783abb208b0386715d683b0a0da4eefe3ab318d3d1543493c1986ca9","target":"record","created_at":"2026-05-18T02:30:53Z","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":"3530c348400411b0746a19a5ee9a1ef2d4eea3e9e902e891d4ed580299df9b0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-19T12:39:24Z","title_canon_sha256":"b0e72e79af6c6ca4078c5013a9da86a394f1898f27e2cf3fe91f8262302b567f"},"schema_version":"1.0","source":{"id":"1412.6317","kind":"arxiv","version":1}},"canonical_sha256":"875ad3479c1c236f82638d9df5a1211916fbc743566edb149242ae36f3a74f89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"875ad3479c1c236f82638d9df5a1211916fbc743566edb149242ae36f3a74f89","first_computed_at":"2026-05-18T02:30:53.817264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:53.817264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X8ca1A4wR5KR8VHMbEjzOYjmHVCOoFltUSDOgoNE10fa53dd25kBFnKTRa39C8txXSewcOFqoKKjjwIP+grKBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:53.817948Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.6317","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb1b20f2783abb208b0386715d683b0a0da4eefe3ab318d3d1543493c1986ca9","sha256:1050a8b644f43c1fd7394b087cc0705615fedc179cc6a6d3f2901292845fa358"],"state_sha256":"301e513f1e79269ebe9bb411aeade965311a94da16924a4d0b4ab3ae24b6a0c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yNjIs7mT5/blL6/c8s0CjWvDfagoSze+jkhf8ASEIJyvhgE2CqF1SzKfyuTwn5+dIkR8umcAtAslDAdK/lmWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:25:28.849711Z","bundle_sha256":"613407a7af4e390f92bf6346b1537355f3e98ef0a7c35f30491a886d153bb325"}}