{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OBP5RXT37RNYZQ7UUFPNN57DEN","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":"d54b4f0942367e290eb90fabc5b22d62d395ced614e5667c2bb5f8f1b4db2e09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-05T18:58:15Z","title_canon_sha256":"fb60fb7ae0125ba2199abe43f0c2924b72b201024626ba40f318fc4cb88845f3"},"schema_version":"1.0","source":{"id":"1601.00938","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00938","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00938v1","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00938","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"OBP5RXT37RNY","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OBP5RXT37RNYZQ7U","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OBP5RXT3","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:60ffea49585c71aeaadcb237f01b23d42b5c070f3feba19e325661f0ed91881a","target":"graph","created_at":"2026-05-18T00:25:27Z","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":"Let $A_\\infty ^+$ denote the class of one-sided Muckenhoupt weights, namely all the weights $w$ for which $\\mathsf M^+:L^p(w)\\to L^{p,\\infty}(w)$ for some $p>1$, where $\\mathsf M^+$ is the forward Hardy-Littlewood maximal operator. We show that $w\\in A_\\infty ^+$ if and only if there exist numerical constants $\\gamma\\in(0,1)$ and $c>0$ such that $$ w(\\{x \\in \\mathbb{R} : \\, \\mathsf M ^+\\mathbf 1_E (x)>\\gamma\\})\\leq c w(E) $$ for all measurable sets $E\\subset \\mathbb R$. Furthermore, letting $$ \\mathsf C_w ^+(\\alpha):= \\sup_{0<w(E)<+\\infty} \\frac{1}{w(E)} w(\\{x\\in\\mathbb R:\\,\\mathsf M^+\\mathbf ","authors_text":"Ioannis Parissis, Olli Saari, Paul A. Hagelstein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-05T18:58:15Z","title":"Sharp inequalities for one-sided Muckenhoupt weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00938","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":"sha256:491a48212d3123b829e3fd6f722a74b6c64d326303badf9ae5f9f4d4544a3489","target":"record","created_at":"2026-05-18T00:25:27Z","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":"d54b4f0942367e290eb90fabc5b22d62d395ced614e5667c2bb5f8f1b4db2e09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-05T18:58:15Z","title_canon_sha256":"fb60fb7ae0125ba2199abe43f0c2924b72b201024626ba40f318fc4cb88845f3"},"schema_version":"1.0","source":{"id":"1601.00938","kind":"arxiv","version":1}},"canonical_sha256":"705fd8de7bfc5b8cc3f4a15ed6f7e323415e2aa152e915b4c8e4fbec14ea7bb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"705fd8de7bfc5b8cc3f4a15ed6f7e323415e2aa152e915b4c8e4fbec14ea7bb3","first_computed_at":"2026-05-18T00:25:27.329183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:27.329183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v5MdOkoe+3OF26fcBOvkkXjY6Lwj3RQ+XiZhk7InjtGR3M1E3trH4537D5Sr0xZD/wRzyOUz5s9Irco5U6raAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:27.329829Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.00938","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:491a48212d3123b829e3fd6f722a74b6c64d326303badf9ae5f9f4d4544a3489","sha256:60ffea49585c71aeaadcb237f01b23d42b5c070f3feba19e325661f0ed91881a"],"state_sha256":"8d0c1a481a0cb93eed592ed23a9d69a93dfbd6c1ddf5f9623f14accf24e202cb"}