{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6G2SW3MDUKHVJWMEYDCJUQCUCP","short_pith_number":"pith:6G2SW3MD","canonical_record":{"source":{"id":"1207.1966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-07-09T06:48:46Z","cross_cats_sorted":["physics.ao-ph"],"title_canon_sha256":"b3600063e732d7a9c7bf5533b34200391aac174dd3f2b0fc294529b41610f895","abstract_canon_sha256":"fb393f49d4a3d13bb2f457df87d1101e412cc08713bfbb8a07382501857b8990"},"schema_version":"1.0"},"canonical_sha256":"f1b52b6d83a28f54d984c0c49a405413fb4a51e63fc396c056b57c9ab1fd7052","source":{"kind":"arxiv","id":"1207.1966","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1966","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1966v1","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1966","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"6G2SW3MDUKHV","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6G2SW3MDUKHVJWME","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6G2SW3MD","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6G2SW3MDUKHVJWMEYDCJUQCUCP","target":"record","payload":{"canonical_record":{"source":{"id":"1207.1966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-07-09T06:48:46Z","cross_cats_sorted":["physics.ao-ph"],"title_canon_sha256":"b3600063e732d7a9c7bf5533b34200391aac174dd3f2b0fc294529b41610f895","abstract_canon_sha256":"fb393f49d4a3d13bb2f457df87d1101e412cc08713bfbb8a07382501857b8990"},"schema_version":"1.0"},"canonical_sha256":"f1b52b6d83a28f54d984c0c49a405413fb4a51e63fc396c056b57c9ab1fd7052","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:24.854003Z","signature_b64":"P4691LINym/kxHOCqLZZO0G6oFglCmfMTE1gMYKwgvptaTUPDorDNRyMcEhnuwQiU15t9Ew0jEHYB/ZJv4j+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1b52b6d83a28f54d984c0c49a405413fb4a51e63fc396c056b57c9ab1fd7052","last_reissued_at":"2026-05-18T03:51:24.853205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:24.853205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.1966","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":"2026-05-18T03:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vln7Fsz+Wr5Mq5ZS0QwbYOJl//Qtdt0rTWmZa8nsVwto/DnLmf9xAJGCPsgLUZU+VWBTBDAEI3m/F1qM9XIkAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:12:41.036830Z"},"content_sha256":"f69eb995e3a356379792b026cd0856bc4c42aa4ecc00cbdc18f81dbc2deccb4a","schema_version":"1.0","event_id":"sha256:f69eb995e3a356379792b026cd0856bc4c42aa4ecc00cbdc18f81dbc2deccb4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6G2SW3MDUKHVJWMEYDCJUQCUCP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A complete theory of low-energy phase diagrams for two-dimensional turbulence steady states and equilibria","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.ao-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Freddy Bouchet (Phys-ENS), Marianne Corvellec (Phys-ENS)","submitted_at":"2012-07-09T06:48:46Z","abstract_excerpt":"For the 2D Euler equations and related models of geophysical flows, minima of energy--Casimir variational problems are stable steady states of the equations (Arnol'd theorems). The same variational problems also describe sets of statistical equilibria of the equations. In this paper, we make use of Lyapunov--Schmidt reduction in order to study the bifurcation diagrams for these variational problems, in the limit of small energy or, equivalently, of small departure from quadratic Casimir functionals. We show a generic occurrence of phase transitions, either continuous or discontinuous. We deriv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1966","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":"2026-05-18T03:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ftS8U+c0t5Ekdi35BjaboQaDEHkM0p2NEbBH8sOV9cHzF6Hw/Ev6Ilobue8ToVRL/xeKplhEFYgvwKFJOtdQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:12:41.037186Z"},"content_sha256":"87ac4b44fd2c9ef703ec329741434afc010fc0d6efc9fe52fb6693ed44fa1547","schema_version":"1.0","event_id":"sha256:87ac4b44fd2c9ef703ec329741434afc010fc0d6efc9fe52fb6693ed44fa1547"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6G2SW3MDUKHVJWMEYDCJUQCUCP/bundle.json","state_url":"https://pith.science/pith/6G2SW3MDUKHVJWMEYDCJUQCUCP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6G2SW3MDUKHVJWMEYDCJUQCUCP/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":"2026-06-03T08:12:41Z","links":{"resolver":"https://pith.science/pith/6G2SW3MDUKHVJWMEYDCJUQCUCP","bundle":"https://pith.science/pith/6G2SW3MDUKHVJWMEYDCJUQCUCP/bundle.json","state":"https://pith.science/pith/6G2SW3MDUKHVJWMEYDCJUQCUCP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6G2SW3MDUKHVJWMEYDCJUQCUCP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6G2SW3MDUKHVJWMEYDCJUQCUCP","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":"fb393f49d4a3d13bb2f457df87d1101e412cc08713bfbb8a07382501857b8990","cross_cats_sorted":["physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-07-09T06:48:46Z","title_canon_sha256":"b3600063e732d7a9c7bf5533b34200391aac174dd3f2b0fc294529b41610f895"},"schema_version":"1.0","source":{"id":"1207.1966","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1966","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1966v1","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1966","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"6G2SW3MDUKHV","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6G2SW3MDUKHVJWME","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6G2SW3MD","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:87ac4b44fd2c9ef703ec329741434afc010fc0d6efc9fe52fb6693ed44fa1547","target":"graph","created_at":"2026-05-18T03:51:24Z","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":"For the 2D Euler equations and related models of geophysical flows, minima of energy--Casimir variational problems are stable steady states of the equations (Arnol'd theorems). The same variational problems also describe sets of statistical equilibria of the equations. In this paper, we make use of Lyapunov--Schmidt reduction in order to study the bifurcation diagrams for these variational problems, in the limit of small energy or, equivalently, of small departure from quadratic Casimir functionals. We show a generic occurrence of phase transitions, either continuous or discontinuous. We deriv","authors_text":"Freddy Bouchet (Phys-ENS), Marianne Corvellec (Phys-ENS)","cross_cats":["physics.ao-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-07-09T06:48:46Z","title":"A complete theory of low-energy phase diagrams for two-dimensional turbulence steady states and equilibria"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1966","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:f69eb995e3a356379792b026cd0856bc4c42aa4ecc00cbdc18f81dbc2deccb4a","target":"record","created_at":"2026-05-18T03:51:24Z","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":"fb393f49d4a3d13bb2f457df87d1101e412cc08713bfbb8a07382501857b8990","cross_cats_sorted":["physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-07-09T06:48:46Z","title_canon_sha256":"b3600063e732d7a9c7bf5533b34200391aac174dd3f2b0fc294529b41610f895"},"schema_version":"1.0","source":{"id":"1207.1966","kind":"arxiv","version":1}},"canonical_sha256":"f1b52b6d83a28f54d984c0c49a405413fb4a51e63fc396c056b57c9ab1fd7052","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1b52b6d83a28f54d984c0c49a405413fb4a51e63fc396c056b57c9ab1fd7052","first_computed_at":"2026-05-18T03:51:24.853205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:24.853205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P4691LINym/kxHOCqLZZO0G6oFglCmfMTE1gMYKwgvptaTUPDorDNRyMcEhnuwQiU15t9Ew0jEHYB/ZJv4j+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:24.854003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1966","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f69eb995e3a356379792b026cd0856bc4c42aa4ecc00cbdc18f81dbc2deccb4a","sha256:87ac4b44fd2c9ef703ec329741434afc010fc0d6efc9fe52fb6693ed44fa1547"],"state_sha256":"ed2aa0f474de0abd0eba10ce6f1093130cb99702c6ababcdc374a787b337e7be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FCsito8daxEF74s02w7pawnbQZ/di8gKDd9U8J8bjlySIPsA5BYXco7cY7I7IkSxnm31RsHcKRw2uxtxxOpjCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:12:41.039160Z","bundle_sha256":"5ea4eefd2f3a09dddc3f4f56c1163c87f98acd3bedd39fcd870fd9388c20a0f3"}}