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It is shown in this paper that if $C_2=2/e$, then the best possible $C_1$ is $C_1= \\frac{1}{2}e^{4/e}$."},"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":"1303.3310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-13T23:20:58Z","cross_cats_sorted":[],"title_canon_sha256":"bcbf53d42bfd32b5db29433a580dc5cc11c374a0ca24e3ff3b20d2b3b4208a6f","abstract_canon_sha256":"2935375468dc0fc53b5dcff96fc83336408371d08ffd20d5df0f313116e9ecfa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:55.835860Z","signature_b64":"mHwPDDh6eLxSPlZ+qwbpIY52et/AeR2Ht4Q7cPlOUUZvI1i+blXkG2lP5AoXcJdEYS9V6pzqNblwsIH4sn+gCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95af53c6e8e08e23911c361fa668793bbe9d15ddb02b37a5978a6a14ceeb5547","last_reissued_at":"2026-05-18T03:30:55.835154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:55.835154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The John-Nirenberg inequality with sharp constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andrei K. Lerner","submitted_at":"2013-03-13T23:20:58Z","abstract_excerpt":"We consider the one-dimensional John-Nirenberg inequality: $$ |\\{x\\in I_0:|f(x)-f_{I_0}|>\\a\\}|\\le C_1|I_0|\\exp\\Big(-\\frac{C_2}{\\|f\\|_{*}}\\a\\Big). $$ A. Korenovskii found that the sharp $C_2$ here is $C_2=2/e$. It is shown in this paper that if $C_2=2/e$, then the best possible $C_1$ is $C_1= \\frac{1}{2}e^{4/e}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3310","kind":"arxiv","version":1},"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":"1303.3310","created_at":"2026-05-18T03:30:55.835281+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.3310v1","created_at":"2026-05-18T03:30:55.835281+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3310","created_at":"2026-05-18T03:30:55.835281+00:00"},{"alias_kind":"pith_short_12","alias_value":"SWXVHRXI4CHC","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SWXVHRXI4CHCHEI4","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SWXVHRXI","created_at":"2026-05-18T12:27:59.945178+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/SWXVHRXI4CHCHEI4GYP2M2DZHO","json":"https://pith.science/pith/SWXVHRXI4CHCHEI4GYP2M2DZHO.json","graph_json":"https://pith.science/api/pith-number/SWXVHRXI4CHCHEI4GYP2M2DZHO/graph.json","events_json":"https://pith.science/api/pith-number/SWXVHRXI4CHCHEI4GYP2M2DZHO/events.json","paper":"https://pith.science/paper/SWXVHRXI"},"agent_actions":{"view_html":"https://pith.science/pith/SWXVHRXI4CHCHEI4GYP2M2DZHO","download_json":"https://pith.science/pith/SWXVHRXI4CHCHEI4GYP2M2DZHO.json","view_paper":"https://pith.science/paper/SWXVHRXI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.3310&json=true","fetch_graph":"https://pith.science/api/pith-number/SWXVHRXI4CHCHEI4GYP2M2DZHO/graph.json","fetch_events":"https://pith.science/api/pith-number/SWXVHRXI4CHCHEI4GYP2M2DZHO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SWXVHRXI4CHCHEI4GYP2M2DZHO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SWXVHRXI4CHCHEI4GYP2M2DZHO/action/storage_attestation","attest_author":"https://pith.science/pith/SWXVHRXI4CHCHEI4GYP2M2DZHO/action/author_attestation","sign_citation":"https://pith.science/pith/SWXVHRXI4CHCHEI4GYP2M2DZHO/action/citation_signature","submit_replication":"https://pith.science/pith/SWXVHRXI4CHCHEI4GYP2M2DZHO/action/replication_record"}},"created_at":"2026-05-18T03:30:55.835281+00:00","updated_at":"2026-05-18T03:30:55.835281+00:00"}