{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AXXBLOMDRAT5HCI6D4JWSXCOKX","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":"8c2fe2546d4d7c37dcd78b46a8191f57823d9ca37632cb13858a48021606b1ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-20T13:06:46Z","title_canon_sha256":"558912abd499a13ba7830d0e88f9557c195938dba8ac0903b336e4ac46a4f92a"},"schema_version":"1.0","source":{"id":"1401.4885","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4885","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4885v2","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4885","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"AXXBLOMDRAT5","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AXXBLOMDRAT5HCI6","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AXXBLOMD","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:d1dde9a5a6dd45960fe792b1dc4f3799b45a3af5b9dd4967b7aee891ade4cc30","target":"graph","created_at":"2026-05-18T00:53:40Z","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":"We prove a version of the negative norm theorem in Orlicz-Sobolev spaces. A study of continuity properties of the Bogovskii -operator between Orlicz spaces is a crucial step, of independent interest, in our approach. Applications to the problem of pressure reconstruction for Non-Newtonian fluids governed by constitutive laws, which are not necessarily power type, are presented. A key inequality for a numerical analysis of the underlying elliptic system is also derived.","authors_text":"Andrea Cianchi, Dominic Breit","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-20T13:06:46Z","title":"Negative Orlicz-Sobolev norms and strongly nonlinear systems in fluid mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4885","kind":"arxiv","version":2},"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":"sha256:7dc2d9c59e9bc99e425c9738daf2f3993ad1a0b30ddddf625aaa3cb26f363e93","target":"record","created_at":"2026-05-18T00:53:40Z","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":"8c2fe2546d4d7c37dcd78b46a8191f57823d9ca37632cb13858a48021606b1ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-20T13:06:46Z","title_canon_sha256":"558912abd499a13ba7830d0e88f9557c195938dba8ac0903b336e4ac46a4f92a"},"schema_version":"1.0","source":{"id":"1401.4885","kind":"arxiv","version":2}},"canonical_sha256":"05ee15b9838827d3891e1f13695c4e55f9667272f418c57b5491115be15cf7ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05ee15b9838827d3891e1f13695c4e55f9667272f418c57b5491115be15cf7ee","first_computed_at":"2026-05-18T00:53:40.851772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:40.851772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wbCNRUrooTGQdeViVuPw6LA+wn4xpgUofMrIirX0nBnCO7H0KqF0gQljqnNTisFuEwoXUQAODDZYRzHO7YKBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:40.852173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.4885","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7dc2d9c59e9bc99e425c9738daf2f3993ad1a0b30ddddf625aaa3cb26f363e93","sha256:d1dde9a5a6dd45960fe792b1dc4f3799b45a3af5b9dd4967b7aee891ade4cc30"],"state_sha256":"6d68dfa20c1a2ef9869b3096d5b01d85feb0f2dc6504af8d9a276c3420f2b914"}