{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4OEMXC3DEO33MAYO4DEJQ62TMC","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":"1b91b4dbe8ff1214031281b3221f468359dd2ad2658a77f05414f895b9e63767","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-10T22:05:35Z","title_canon_sha256":"4fb1cd5411b5c600c811c534dbb43a7a431441eb17190c0078897a53b4aef5c3"},"schema_version":"1.0","source":{"id":"1103.2151","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2151","created_at":"2026-05-18T02:02:54Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2151v1","created_at":"2026-05-18T02:02:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2151","created_at":"2026-05-18T02:02:54Z"},{"alias_kind":"pith_short_12","alias_value":"4OEMXC3DEO33","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4OEMXC3DEO33MAYO","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4OEMXC3D","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:4856b9247d61fe67912666df6633d62b775b9fc04a8135a0a99e23f1c62171eb","target":"graph","created_at":"2026-05-18T02:02:54Z","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":"Gaussian measures of Gibbsian type are associated with some shell models of 3D turbulence; they are constructed by means of the energy, a conserved quantity for the 3D inviscid and unforced shell model. We prove the existence of a unique global flow for a stochastic viscous shell model and a global flow for the deterministic inviscid shell model, with the property that these Gibbs measures are invariant for these flows.","authors_text":"Benedetta Ferrario, Hakima Bessaih","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-10T22:05:35Z","title":"Invariant Gibbs measures of the energy for shell models of turbulence; the inviscid and viscous cases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2151","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":"sha256:5c84767969fee68db49724d6537180f8d65de1fda7ea8be378c4bbf024002d0c","target":"record","created_at":"2026-05-18T02:02:54Z","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":"1b91b4dbe8ff1214031281b3221f468359dd2ad2658a77f05414f895b9e63767","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-10T22:05:35Z","title_canon_sha256":"4fb1cd5411b5c600c811c534dbb43a7a431441eb17190c0078897a53b4aef5c3"},"schema_version":"1.0","source":{"id":"1103.2151","kind":"arxiv","version":1}},"canonical_sha256":"e388cb8b6323b7b6030ee0c8987b53609959d6282734104d43546d05a1f13ee9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e388cb8b6323b7b6030ee0c8987b53609959d6282734104d43546d05a1f13ee9","first_computed_at":"2026-05-18T02:02:54.857399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:54.857399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FunQ5WqmpKMrcpL5wBb8yBLyCynFWQn/kIpZCwmO87iI9CoBQ7Clqw+wiaZTxygXnjlzuBZgpL5Pe4tT26aeBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:54.857878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2151","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c84767969fee68db49724d6537180f8d65de1fda7ea8be378c4bbf024002d0c","sha256:4856b9247d61fe67912666df6633d62b775b9fc04a8135a0a99e23f1c62171eb"],"state_sha256":"e78a83dd5c645056d37649e80b3fc139d96f8d5dbd0f202e9e96c42d2b5fc3cf"}