{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:4OEMXC3DEO33MAYO4DEJQ62TMC","short_pith_number":"pith:4OEMXC3D","schema_version":"1.0","canonical_sha256":"e388cb8b6323b7b6030ee0c8987b53609959d6282734104d43546d05a1f13ee9","source":{"kind":"arxiv","id":"1103.2151","version":1},"attestation_state":"computed","paper":{"title":"Invariant Gibbs measures of the energy for shell models of turbulence; the inviscid and viscous cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Benedetta Ferrario, Hakima Bessaih","submitted_at":"2011-03-10T22:05:35Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1103.2151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-10T22:05:35Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"4fb1cd5411b5c600c811c534dbb43a7a431441eb17190c0078897a53b4aef5c3","abstract_canon_sha256":"1b91b4dbe8ff1214031281b3221f468359dd2ad2658a77f05414f895b9e63767"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:54.857878Z","signature_b64":"FunQ5WqmpKMrcpL5wBb8yBLyCynFWQn/kIpZCwmO87iI9CoBQ7Clqw+wiaZTxygXnjlzuBZgpL5Pe4tT26aeBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e388cb8b6323b7b6030ee0c8987b53609959d6282734104d43546d05a1f13ee9","last_reissued_at":"2026-05-18T02:02:54.857399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:54.857399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant Gibbs measures of the energy for shell models of turbulence; the inviscid and viscous cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Benedetta Ferrario, Hakima Bessaih","submitted_at":"2011-03-10T22:05:35Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2151","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1103.2151","created_at":"2026-05-18T02:02:54.857474+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.2151v1","created_at":"2026-05-18T02:02:54.857474+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2151","created_at":"2026-05-18T02:02:54.857474+00:00"},{"alias_kind":"pith_short_12","alias_value":"4OEMXC3DEO33","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"4OEMXC3DEO33MAYO","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"4OEMXC3D","created_at":"2026-05-18T12:26:20.644004+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4OEMXC3DEO33MAYO4DEJQ62TMC","json":"https://pith.science/pith/4OEMXC3DEO33MAYO4DEJQ62TMC.json","graph_json":"https://pith.science/api/pith-number/4OEMXC3DEO33MAYO4DEJQ62TMC/graph.json","events_json":"https://pith.science/api/pith-number/4OEMXC3DEO33MAYO4DEJQ62TMC/events.json","paper":"https://pith.science/paper/4OEMXC3D"},"agent_actions":{"view_html":"https://pith.science/pith/4OEMXC3DEO33MAYO4DEJQ62TMC","download_json":"https://pith.science/pith/4OEMXC3DEO33MAYO4DEJQ62TMC.json","view_paper":"https://pith.science/paper/4OEMXC3D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.2151&json=true","fetch_graph":"https://pith.science/api/pith-number/4OEMXC3DEO33MAYO4DEJQ62TMC/graph.json","fetch_events":"https://pith.science/api/pith-number/4OEMXC3DEO33MAYO4DEJQ62TMC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4OEMXC3DEO33MAYO4DEJQ62TMC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4OEMXC3DEO33MAYO4DEJQ62TMC/action/storage_attestation","attest_author":"https://pith.science/pith/4OEMXC3DEO33MAYO4DEJQ62TMC/action/author_attestation","sign_citation":"https://pith.science/pith/4OEMXC3DEO33MAYO4DEJQ62TMC/action/citation_signature","submit_replication":"https://pith.science/pith/4OEMXC3DEO33MAYO4DEJQ62TMC/action/replication_record"}},"created_at":"2026-05-18T02:02:54.857474+00:00","updated_at":"2026-05-18T02:02:54.857474+00:00"}