{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:VHYHAE6PZVFOYDBBUVWLFU46WE","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":"f08980b764991e31898e887b4b766024d498ffbec10846231090762bdb8c629a","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2006-09-06T15:36:06Z","title_canon_sha256":"d2d956a25e946c4962d2ea1c5e2c151d0eff36690f3388c7ef3c852e0ef2159a"},"schema_version":"1.0","source":{"id":"astro-ph/0609164","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0609164","created_at":"2026-07-04T16:59:21Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0609164v1","created_at":"2026-07-04T16:59:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0609164","created_at":"2026-07-04T16:59:21Z"},{"alias_kind":"pith_short_12","alias_value":"VHYHAE6PZVFO","created_at":"2026-07-04T16:59:21Z"},{"alias_kind":"pith_short_16","alias_value":"VHYHAE6PZVFOYDBB","created_at":"2026-07-04T16:59:21Z"},{"alias_kind":"pith_short_8","alias_value":"VHYHAE6P","created_at":"2026-07-04T16:59:21Z"}],"graph_snapshots":[{"event_id":"sha256:544770df80acf3deecd57e16d8e12bf90ae650b261580746cd8adeb8403dd318","target":"graph","created_at":"2026-07-04T16:59:21Z","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/astro-ph/0609164/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Irregular structure in planetary rings is often attributed to the intrinsic instabilities of a homogeneous state undergoing Keplerian shear. Previously these have been analysed with simple hydrodynamic models. We instead employ a kinetic theory, in which we solve the linearised moment equations derived in Shu and Stewart 1985 for a dilute ring. This facilitates an examination of velocity anisotropy and non-Newtonian stress, and their effects on the viscous and viscous/gravitational instabilities thought to occur in Saturn's rings. Because we adopt a dilute gas model, the applicability of our r","authors_text":"Gordon I. Ogilvie, Henrik N. Latter","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2006-09-06T15:36:06Z","title":"The linear stability of dilute particulate rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0609164","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":"sha256:7df9be7b39484e4e46f941d37143e788909fb2b309b47af8d9dcbbecb8ff6758","target":"record","created_at":"2026-07-04T16:59:21Z","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":"f08980b764991e31898e887b4b766024d498ffbec10846231090762bdb8c629a","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2006-09-06T15:36:06Z","title_canon_sha256":"d2d956a25e946c4962d2ea1c5e2c151d0eff36690f3388c7ef3c852e0ef2159a"},"schema_version":"1.0","source":{"id":"astro-ph/0609164","kind":"arxiv","version":1}},"canonical_sha256":"a9f07013cfcd4aec0c21a56cb2d39eb125e91a778637555d1d542a00e88a715f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9f07013cfcd4aec0c21a56cb2d39eb125e91a778637555d1d542a00e88a715f","first_computed_at":"2026-07-04T16:59:21.766036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:59:21.766036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Imf1hdzxrrBcZxOCVB0pPEECGDhBNQwgHJjzU7bX5HWN6vOWxMHhYXAQxddId9mY4MfwtQQFpI/3Q+ST5J62Cg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:59:21.766428Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0609164","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7df9be7b39484e4e46f941d37143e788909fb2b309b47af8d9dcbbecb8ff6758","sha256:544770df80acf3deecd57e16d8e12bf90ae650b261580746cd8adeb8403dd318"],"state_sha256":"175131a448f3fae78e50a5b71c957a7d147b6a6d39242595adaf5396437915e2"}