{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5DI33NKXUI657MBCCTVWRKPF3E","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":"726a632649443441b50a29de2297f66dd7b2a034030f946f97a6b2ee30d52636","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-04T03:47:28Z","title_canon_sha256":"7bbe1638a88ab5dc26f2272db61469ecffa45cb5bd59eb20ce5ad681908c07da"},"schema_version":"1.0","source":{"id":"1809.00788","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00788","created_at":"2026-05-18T00:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00788v1","created_at":"2026-05-18T00:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00788","created_at":"2026-05-18T00:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"5DI33NKXUI65","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5DI33NKXUI657MBC","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5DI33NKX","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:f0e39d0e58f6382b045b00ac0b5b78b4e3ccda0c0141d7adfcfff0fb6723ad9a","target":"graph","created_at":"2026-05-18T00:06:32Z","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":"Orlicz spaces are generalizations of Lebesgue spaces. The sufficient and necessary conditions for generalized H\\\"{o}lder's inequality in Lebesgue spaces and in weak Lebesgue spaces are well known. The aim of this paper is to present sufficient and necessary conditions for generalized H\\\"{o}lder's inequality in Orlicz spaces and in weak Orlicz spaces, which are obtained through estimates for characteristic functions of balls in $\\R^n$.","authors_text":"Al Azhary Masta, Hendra Gunawan, Ifronika, Muhammad Nur","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-04T03:47:28Z","title":"Generalized H\\\"{o}lder's Inequality in Orlicz Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00788","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":"sha256:28b21b0c8027d36233a104aac70d1ba641eedcef2ae63aff66325ae5dc9ead9d","target":"record","created_at":"2026-05-18T00:06:32Z","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":"726a632649443441b50a29de2297f66dd7b2a034030f946f97a6b2ee30d52636","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-04T03:47:28Z","title_canon_sha256":"7bbe1638a88ab5dc26f2272db61469ecffa45cb5bd59eb20ce5ad681908c07da"},"schema_version":"1.0","source":{"id":"1809.00788","kind":"arxiv","version":1}},"canonical_sha256":"e8d1bdb557a23ddfb02214eb68a9e5d926b507d0ffa2b512079f18c28294c97b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8d1bdb557a23ddfb02214eb68a9e5d926b507d0ffa2b512079f18c28294c97b","first_computed_at":"2026-05-18T00:06:32.492479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:32.492479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e4sVMM94qdyslmji+SC2SzIMcQQ3xRlqOPEIb8YsqaieNeZ8Ak9cL/AihjjPVAcwSAQsmuh+Xppq3a1ZVaTtAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:32.492901Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.00788","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28b21b0c8027d36233a104aac70d1ba641eedcef2ae63aff66325ae5dc9ead9d","sha256:f0e39d0e58f6382b045b00ac0b5b78b4e3ccda0c0141d7adfcfff0fb6723ad9a"],"state_sha256":"8600806c90094fbcd05177eff1d8a90d04c30bd540392a47018b7dfc49b3938b"}