{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KGFRVVA4EZXW6YB3V6VQIYCAI5","short_pith_number":"pith:KGFRVVA4","canonical_record":{"source":{"id":"1405.6631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-26T16:23:50Z","cross_cats_sorted":[],"title_canon_sha256":"bcbfb4ac2565b27a20411376ca36623368efd055c4ba9621f4a1cf58bdcd8bfe","abstract_canon_sha256":"a7d60dc1ed0d563f2a70da62e30b272d15087ddd351ca3ff68542a0aac2583c3"},"schema_version":"1.0"},"canonical_sha256":"518b1ad41c266f6f603bafab0460404774d371e954ed0b97782b4018be66d185","source":{"kind":"arxiv","id":"1405.6631","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6631","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6631v2","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6631","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"KGFRVVA4EZXW","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KGFRVVA4EZXW6YB3","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KGFRVVA4","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KGFRVVA4EZXW6YB3V6VQIYCAI5","target":"record","payload":{"canonical_record":{"source":{"id":"1405.6631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-26T16:23:50Z","cross_cats_sorted":[],"title_canon_sha256":"bcbfb4ac2565b27a20411376ca36623368efd055c4ba9621f4a1cf58bdcd8bfe","abstract_canon_sha256":"a7d60dc1ed0d563f2a70da62e30b272d15087ddd351ca3ff68542a0aac2583c3"},"schema_version":"1.0"},"canonical_sha256":"518b1ad41c266f6f603bafab0460404774d371e954ed0b97782b4018be66d185","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:27.482329Z","signature_b64":"PSjMsMItanqano9bOAKAGmJJb0iDXaJngSlVF6hyuFWOYCVHMy3/uFuvVbW2bp4nDcl2yyKF5CfB6PEb0lF5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"518b1ad41c266f6f603bafab0460404774d371e954ed0b97782b4018be66d185","last_reissued_at":"2026-05-18T00:25:27.481664Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:27.481664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.6631","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xDRyG/y/dI91yyMhAi3acihdU8et5n3zIAqjACwrjZnTZDjHXWBSIUoHKlQ+Hy+cIMaIEg1DcODWQNKBHXprAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:02:25.404683Z"},"content_sha256":"ade903e3c3e5b48bc09b63bf43c82e0a4c617741f3c2fd0b70f6a4c30c25345b","schema_version":"1.0","event_id":"sha256:ade903e3c3e5b48bc09b63bf43c82e0a4c617741f3c2fd0b70f6a4c30c25345b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KGFRVVA4EZXW6YB3V6VQIYCAI5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted Solyanik Estimates for the Hardy-Littlewood maximal operator and embedding of $A_\\infty$ into $A_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ioannis Parissis, Paul A. Hagelstein","submitted_at":"2014-05-26T16:23:50Z","abstract_excerpt":"Let $w$ denote a weight in $\\mathbb{R}^n$ which belongs to the Muckenhoupt class $A_\\infty$ and let $\\mathsf{M}_w$ denote the uncentered Hardy-Littlewood maximal operator defined with respect to the measure $w(x)dx$. The \\emph{sharp Tauberian constant} of $\\mathsf M_w$ with respect to $\\alpha$, denoted by $\\mathsf{C}_w (\\alpha)$, is defined by \\[ \\mathsf{C}_w (\\alpha) := \\sup_{E:\\, 0 < w(E) < \\infty}w(E)^{-1}w\\big(\\big\\{x \\in \\mathbb{R}^n:\\, \\mathsf{M}_w \\chi_E (x) > \\alpha\\big\\}\\big). \\] In this paper, we show that the Solyanik estimate \\[ \\lim_{\\alpha \\rightarrow 1^-}\\mathsf{C}_w(\\alpha) = 1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6631","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o+kZMsWmx1nYc0vQ6mDWXye2NGUxf98Zm8suTuPgHF4tl4g/bzeFYAikyhnxTegl0Wf053cF6utQp3L7BY2/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:02:25.405027Z"},"content_sha256":"7abed07e553b3b972003c86c26579e07ed192f8250c6aef41d9d659e859859e9","schema_version":"1.0","event_id":"sha256:7abed07e553b3b972003c86c26579e07ed192f8250c6aef41d9d659e859859e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KGFRVVA4EZXW6YB3V6VQIYCAI5/bundle.json","state_url":"https://pith.science/pith/KGFRVVA4EZXW6YB3V6VQIYCAI5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KGFRVVA4EZXW6YB3V6VQIYCAI5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T10:02:25Z","links":{"resolver":"https://pith.science/pith/KGFRVVA4EZXW6YB3V6VQIYCAI5","bundle":"https://pith.science/pith/KGFRVVA4EZXW6YB3V6VQIYCAI5/bundle.json","state":"https://pith.science/pith/KGFRVVA4EZXW6YB3V6VQIYCAI5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KGFRVVA4EZXW6YB3V6VQIYCAI5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KGFRVVA4EZXW6YB3V6VQIYCAI5","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":"a7d60dc1ed0d563f2a70da62e30b272d15087ddd351ca3ff68542a0aac2583c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-26T16:23:50Z","title_canon_sha256":"bcbfb4ac2565b27a20411376ca36623368efd055c4ba9621f4a1cf58bdcd8bfe"},"schema_version":"1.0","source":{"id":"1405.6631","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6631","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6631v2","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6631","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"KGFRVVA4EZXW","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KGFRVVA4EZXW6YB3","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KGFRVVA4","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:7abed07e553b3b972003c86c26579e07ed192f8250c6aef41d9d659e859859e9","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 $w$ denote a weight in $\\mathbb{R}^n$ which belongs to the Muckenhoupt class $A_\\infty$ and let $\\mathsf{M}_w$ denote the uncentered Hardy-Littlewood maximal operator defined with respect to the measure $w(x)dx$. The \\emph{sharp Tauberian constant} of $\\mathsf M_w$ with respect to $\\alpha$, denoted by $\\mathsf{C}_w (\\alpha)$, is defined by \\[ \\mathsf{C}_w (\\alpha) := \\sup_{E:\\, 0 < w(E) < \\infty}w(E)^{-1}w\\big(\\big\\{x \\in \\mathbb{R}^n:\\, \\mathsf{M}_w \\chi_E (x) > \\alpha\\big\\}\\big). \\] In this paper, we show that the Solyanik estimate \\[ \\lim_{\\alpha \\rightarrow 1^-}\\mathsf{C}_w(\\alpha) = 1","authors_text":"Ioannis Parissis, Paul A. Hagelstein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-26T16:23:50Z","title":"Weighted Solyanik Estimates for the Hardy-Littlewood maximal operator and embedding of $A_\\infty$ into $A_p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6631","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:ade903e3c3e5b48bc09b63bf43c82e0a4c617741f3c2fd0b70f6a4c30c25345b","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":"a7d60dc1ed0d563f2a70da62e30b272d15087ddd351ca3ff68542a0aac2583c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-26T16:23:50Z","title_canon_sha256":"bcbfb4ac2565b27a20411376ca36623368efd055c4ba9621f4a1cf58bdcd8bfe"},"schema_version":"1.0","source":{"id":"1405.6631","kind":"arxiv","version":2}},"canonical_sha256":"518b1ad41c266f6f603bafab0460404774d371e954ed0b97782b4018be66d185","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"518b1ad41c266f6f603bafab0460404774d371e954ed0b97782b4018be66d185","first_computed_at":"2026-05-18T00:25:27.481664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:27.481664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PSjMsMItanqano9bOAKAGmJJb0iDXaJngSlVF6hyuFWOYCVHMy3/uFuvVbW2bp4nDcl2yyKF5CfB6PEb0lF5Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:27.482329Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6631","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ade903e3c3e5b48bc09b63bf43c82e0a4c617741f3c2fd0b70f6a4c30c25345b","sha256:7abed07e553b3b972003c86c26579e07ed192f8250c6aef41d9d659e859859e9"],"state_sha256":"0318e048645d5af6fba450014dd5d0f4b0415479652cd2633329ab54f5509e04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qs4AZ0IH+nHgoOUfN7rGl6646aksKLWoaDTL7hGuD7nvC/1/Evafxm0sObSkzxi4dtfoxH3G8i5rHbmlnJkCDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:02:25.406939Z","bundle_sha256":"9874ee676653386a18e0af4eed4ce019812177f6df9f5546597f4c578c6b4c68"}}