{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:7RPNPP6MRPXWC4VOPMN5TY5KO2","short_pith_number":"pith:7RPNPP6M","canonical_record":{"source":{"id":"astro-ph/9501080","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"1995-01-22T17:53:44Z","cross_cats_sorted":[],"title_canon_sha256":"f55e7a9bbd45629915a2dc2c4186571ea04c36337a998b05ffc58e818949467f","abstract_canon_sha256":"2112bfd8eae5d961533719e9df82f0f53d3af93f227aee1b6244cb5f7ba21cd9"},"schema_version":"1.0"},"canonical_sha256":"fc5ed7bfcc8bef6172ae7b1bd9e3aa76bfb16f76071bfa167db620a51301b613","source":{"kind":"arxiv","id":"astro-ph/9501080","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9501080","created_at":"2026-05-18T01:07:42Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9501080v1","created_at":"2026-05-18T01:07:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9501080","created_at":"2026-05-18T01:07:42Z"},{"alias_kind":"pith_short_12","alias_value":"7RPNPP6MRPXW","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"7RPNPP6MRPXWC4VO","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"7RPNPP6M","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:7RPNPP6MRPXWC4VOPMN5TY5KO2","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/9501080","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"1995-01-22T17:53:44Z","cross_cats_sorted":[],"title_canon_sha256":"f55e7a9bbd45629915a2dc2c4186571ea04c36337a998b05ffc58e818949467f","abstract_canon_sha256":"2112bfd8eae5d961533719e9df82f0f53d3af93f227aee1b6244cb5f7ba21cd9"},"schema_version":"1.0"},"canonical_sha256":"fc5ed7bfcc8bef6172ae7b1bd9e3aa76bfb16f76071bfa167db620a51301b613","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:42.577807Z","signature_b64":"0UDBe9HhBzlj6cMfrqIDa4sJzvS68JMCGw77GX1WLwb2Z+2XVKnOz0Hta95MFLyuUFftw+sMeNrIFe64iLAaCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc5ed7bfcc8bef6172ae7b1bd9e3aa76bfb16f76071bfa167db620a51301b613","last_reissued_at":"2026-05-18T01:07:42.577300Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:42.577300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/9501080","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":"2026-05-18T01:07:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qao0la4/YdrvZfTs8co1QulHByf7drKd5Acj06k20LuNzXcx02kvLNFBvxyoDiMKOhb8LyG8eKtvwRBoz9oSDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:40:40.594704Z"},"content_sha256":"b4f03338b1bc122edc8697316c7702eb136089dd2ae6c1a01fd3537fed6f4445","schema_version":"1.0","event_id":"sha256:b4f03338b1bc122edc8697316c7702eb136089dd2ae6c1a01fd3537fed6f4445"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:7RPNPP6MRPXWC4VOPMN5TY5KO2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"STABILITY IN THE WEAK VARIATIONAL PRINCIPLE OF BAROTROPIC FLOWS","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Asher Yahalom","submitted_at":"1995-01-22T17:53:44Z","abstract_excerpt":"I find conditions under which the \"Weak Energy Principle\" of Katz, Inagaki and Yahalom (1993) gives necessary and sufficient conditions. My conclusion is that, necessary and sufficient conditions of stability are obtained when we have only two mode coupling in the gyroscopic terms of the perturbed Lagrangian. To illustrate the power of this new energy principle, I have calculated the stability limits of two dimensional configurations such as ordinary Maclaurin disk, an infinite self gravitating rotating sheet, and a two dimensional Rayleigh flow which has well known sufficient conditions of st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9501080","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":"2026-05-18T01:07:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zRfbpMCcluPogaTNNtxvUYEZCLlm2us/+97YiEEhdg1U5XPl7+X08LBnQEmPrkYXaIFgmiDonbZ725J6rDRhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:40:40.595405Z"},"content_sha256":"a6bf840f6c3632b31a4f354066169ca0443a29fec0bb43139e8847143196e526","schema_version":"1.0","event_id":"sha256:a6bf840f6c3632b31a4f354066169ca0443a29fec0bb43139e8847143196e526"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RPNPP6MRPXWC4VOPMN5TY5KO2/bundle.json","state_url":"https://pith.science/pith/7RPNPP6MRPXWC4VOPMN5TY5KO2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RPNPP6MRPXWC4VOPMN5TY5KO2/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":"2026-06-08T04:40:40Z","links":{"resolver":"https://pith.science/pith/7RPNPP6MRPXWC4VOPMN5TY5KO2","bundle":"https://pith.science/pith/7RPNPP6MRPXWC4VOPMN5TY5KO2/bundle.json","state":"https://pith.science/pith/7RPNPP6MRPXWC4VOPMN5TY5KO2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RPNPP6MRPXWC4VOPMN5TY5KO2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:7RPNPP6MRPXWC4VOPMN5TY5KO2","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":"2112bfd8eae5d961533719e9df82f0f53d3af93f227aee1b6244cb5f7ba21cd9","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"1995-01-22T17:53:44Z","title_canon_sha256":"f55e7a9bbd45629915a2dc2c4186571ea04c36337a998b05ffc58e818949467f"},"schema_version":"1.0","source":{"id":"astro-ph/9501080","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9501080","created_at":"2026-05-18T01:07:42Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9501080v1","created_at":"2026-05-18T01:07:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9501080","created_at":"2026-05-18T01:07:42Z"},{"alias_kind":"pith_short_12","alias_value":"7RPNPP6MRPXW","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"7RPNPP6MRPXWC4VO","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"7RPNPP6M","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:a6bf840f6c3632b31a4f354066169ca0443a29fec0bb43139e8847143196e526","target":"graph","created_at":"2026-05-18T01:07:42Z","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":"I find conditions under which the \"Weak Energy Principle\" of Katz, Inagaki and Yahalom (1993) gives necessary and sufficient conditions. My conclusion is that, necessary and sufficient conditions of stability are obtained when we have only two mode coupling in the gyroscopic terms of the perturbed Lagrangian. To illustrate the power of this new energy principle, I have calculated the stability limits of two dimensional configurations such as ordinary Maclaurin disk, an infinite self gravitating rotating sheet, and a two dimensional Rayleigh flow which has well known sufficient conditions of st","authors_text":"Asher Yahalom","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"1995-01-22T17:53:44Z","title":"STABILITY IN THE WEAK VARIATIONAL PRINCIPLE OF BAROTROPIC FLOWS"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9501080","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:b4f03338b1bc122edc8697316c7702eb136089dd2ae6c1a01fd3537fed6f4445","target":"record","created_at":"2026-05-18T01:07:42Z","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":"2112bfd8eae5d961533719e9df82f0f53d3af93f227aee1b6244cb5f7ba21cd9","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"1995-01-22T17:53:44Z","title_canon_sha256":"f55e7a9bbd45629915a2dc2c4186571ea04c36337a998b05ffc58e818949467f"},"schema_version":"1.0","source":{"id":"astro-ph/9501080","kind":"arxiv","version":1}},"canonical_sha256":"fc5ed7bfcc8bef6172ae7b1bd9e3aa76bfb16f76071bfa167db620a51301b613","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc5ed7bfcc8bef6172ae7b1bd9e3aa76bfb16f76071bfa167db620a51301b613","first_computed_at":"2026-05-18T01:07:42.577300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:42.577300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0UDBe9HhBzlj6cMfrqIDa4sJzvS68JMCGw77GX1WLwb2Z+2XVKnOz0Hta95MFLyuUFftw+sMeNrIFe64iLAaCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:42.577807Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/9501080","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4f03338b1bc122edc8697316c7702eb136089dd2ae6c1a01fd3537fed6f4445","sha256:a6bf840f6c3632b31a4f354066169ca0443a29fec0bb43139e8847143196e526"],"state_sha256":"39e85fc3ccd4047c2dd72d6517211aad51ba15342a387c32c8d89a0e6e822e08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iUqr2TCZTxD26Is7VtsfxEe9l5fysYBjyCf6G+bM8Kz5ZXukMp3/p107HZEGL0WwwrEx3ra81nLfLhL1tAU4DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T04:40:40.600311Z","bundle_sha256":"120ad507bdf41a9857089e7812aaaad639c03d0a31c467efcd50b0491ba66498"}}