{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:AHSDSHD6G35KOX7ZZ3K43H57M4","short_pith_number":"pith:AHSDSHD6","schema_version":"1.0","canonical_sha256":"01e4391c7e36faa75ff9ced5cd9fbf67049942d917349c500f2715cf94f8166c","source":{"kind":"arxiv","id":"1105.3871","version":2},"attestation_state":"computed","paper":{"title":"The Probabilistic Method and large initial data for Generalized Navier-Stokes systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Jean C. Cortissoz","submitted_at":"2011-05-19T13:47:18Z","abstract_excerpt":"In this paper we introduce a probabilistic approach to show the existence of initial data with arbitrarily large $L^2(\\mathbb{R}^3)$, $\\dot{H}^{1/2}(\\mathbb{R}^3)$ and $\\mathcal{PM}^2$-norms for which a Generalized Navier-Stokes system generate a global regular solution. More precisely, we show that from a certain family of possible large initial data most of them give raise to global regular solutions to a given Generalized Navier-Stokes system."},"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":"1105.3871","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-19T13:47:18Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"3667a25bc89b585f5b78fe910ac6c68f2a124303236125cc849848d55ef6461f","abstract_canon_sha256":"4a03b861b10669946653c56d785d43bd515b40ae535336e494a6019cd28256c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:46.826338Z","signature_b64":"Ksv0F7tkvkne05/TFk7k7G5oGWNHyK7sQNh8HVmhsly9890R6SP6foU4sWKSGWeZap6u0/tJLZzA8HzSvZ7cDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01e4391c7e36faa75ff9ced5cd9fbf67049942d917349c500f2715cf94f8166c","last_reissued_at":"2026-05-18T04:13:46.825864Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:46.825864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Probabilistic Method and large initial data for Generalized Navier-Stokes systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Jean C. Cortissoz","submitted_at":"2011-05-19T13:47:18Z","abstract_excerpt":"In this paper we introduce a probabilistic approach to show the existence of initial data with arbitrarily large $L^2(\\mathbb{R}^3)$, $\\dot{H}^{1/2}(\\mathbb{R}^3)$ and $\\mathcal{PM}^2$-norms for which a Generalized Navier-Stokes system generate a global regular solution. More precisely, we show that from a certain family of possible large initial data most of them give raise to global regular solutions to a given Generalized Navier-Stokes system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3871","kind":"arxiv","version":2},"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":"1105.3871","created_at":"2026-05-18T04:13:46.825943+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.3871v2","created_at":"2026-05-18T04:13:46.825943+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3871","created_at":"2026-05-18T04:13:46.825943+00:00"},{"alias_kind":"pith_short_12","alias_value":"AHSDSHD6G35K","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"AHSDSHD6G35KOX7Z","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"AHSDSHD6","created_at":"2026-05-18T12:26:24.575870+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/AHSDSHD6G35KOX7ZZ3K43H57M4","json":"https://pith.science/pith/AHSDSHD6G35KOX7ZZ3K43H57M4.json","graph_json":"https://pith.science/api/pith-number/AHSDSHD6G35KOX7ZZ3K43H57M4/graph.json","events_json":"https://pith.science/api/pith-number/AHSDSHD6G35KOX7ZZ3K43H57M4/events.json","paper":"https://pith.science/paper/AHSDSHD6"},"agent_actions":{"view_html":"https://pith.science/pith/AHSDSHD6G35KOX7ZZ3K43H57M4","download_json":"https://pith.science/pith/AHSDSHD6G35KOX7ZZ3K43H57M4.json","view_paper":"https://pith.science/paper/AHSDSHD6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.3871&json=true","fetch_graph":"https://pith.science/api/pith-number/AHSDSHD6G35KOX7ZZ3K43H57M4/graph.json","fetch_events":"https://pith.science/api/pith-number/AHSDSHD6G35KOX7ZZ3K43H57M4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AHSDSHD6G35KOX7ZZ3K43H57M4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AHSDSHD6G35KOX7ZZ3K43H57M4/action/storage_attestation","attest_author":"https://pith.science/pith/AHSDSHD6G35KOX7ZZ3K43H57M4/action/author_attestation","sign_citation":"https://pith.science/pith/AHSDSHD6G35KOX7ZZ3K43H57M4/action/citation_signature","submit_replication":"https://pith.science/pith/AHSDSHD6G35KOX7ZZ3K43H57M4/action/replication_record"}},"created_at":"2026-05-18T04:13:46.825943+00:00","updated_at":"2026-05-18T04:13:46.825943+00:00"}