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We find the optimal value ${\\bf{C}}_{n,p}$ such that the inequality $$\\|f-m_f\\|_p\\le {\\bf C}_{n,p}{\\rm Var}_{p}f$$ holds for every $f:V\\to \\mathbb{R},$ where ${\\rm Var}_p$ stands for the $p$-variation, and $m_f$ stands for the average value of $f$, for all $p\\in[1,3+\\delta^1_n)\\cup (3+\\delta^2_n,+\\infty)$, for $\\delta^1_n=\\frac{1}{2n^2\\log(n)}+O(1/n^3)$ and $\\delta^2_n=\\frac{2}{n}+O(1/n^2).$ Moreover, we characterize all the maximizer functions in that ca"},"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":"2411.12079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-11-18T21:44:33Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"173d549d0c2c9816d9e4b476ca544051183aca8dd28689425d71651bd26afce3","abstract_canon_sha256":"a10501262ebfc5a06533c6b5b85f5c3d873e4600d90e00e6a90eadb9839d89c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:37:15.814686Z","signature_b64":"PfvYgC7yXlYuHfnNbCN7x+GYLIIRpAFegomLzxZLsLNt4ZeiTinopm5btrL6+pbeUkmKXmrwYDSjBmlqhI78DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bcc7de99dede3f23b3d3346a040293b27e743c8e881a7c4a97738c76c38783e","last_reissued_at":"2026-07-05T09:37:15.814254Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:37:15.814254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp Poincare-Wirtinger inequalities on complete graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Cristian Gonz\\'alez-Riquelme, Jos\\'e Madrid","submitted_at":"2024-11-18T21:44:33Z","abstract_excerpt":"Let $K_n=(V,E)$ be the complete graph with $n\\geq 3$ vertices (here $V$ and $E$ denote the set of vertices and edges of $K_n$ respectively). We find the optimal value ${\\bf{C}}_{n,p}$ such that the inequality $$\\|f-m_f\\|_p\\le {\\bf C}_{n,p}{\\rm Var}_{p}f$$ holds for every $f:V\\to \\mathbb{R},$ where ${\\rm Var}_p$ stands for the $p$-variation, and $m_f$ stands for the average value of $f$, for all $p\\in[1,3+\\delta^1_n)\\cup (3+\\delta^2_n,+\\infty)$, for $\\delta^1_n=\\frac{1}{2n^2\\log(n)}+O(1/n^3)$ and $\\delta^2_n=\\frac{2}{n}+O(1/n^2).$ Moreover, we characterize all the maximizer functions in that ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12079","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.12079/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2411.12079","created_at":"2026-07-05T09:37:15.814312+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.12079v1","created_at":"2026-07-05T09:37:15.814312+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12079","created_at":"2026-07-05T09:37:15.814312+00:00"},{"alias_kind":"pith_short_12","alias_value":"TPGH32M55XR7","created_at":"2026-07-05T09:37:15.814312+00:00"},{"alias_kind":"pith_short_16","alias_value":"TPGH32M55XR7EOZ5","created_at":"2026-07-05T09:37:15.814312+00:00"},{"alias_kind":"pith_short_8","alias_value":"TPGH32M5","created_at":"2026-07-05T09:37:15.814312+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/TPGH32M55XR7EOZ5GNDKAQBJHM","json":"https://pith.science/pith/TPGH32M55XR7EOZ5GNDKAQBJHM.json","graph_json":"https://pith.science/api/pith-number/TPGH32M55XR7EOZ5GNDKAQBJHM/graph.json","events_json":"https://pith.science/api/pith-number/TPGH32M55XR7EOZ5GNDKAQBJHM/events.json","paper":"https://pith.science/paper/TPGH32M5"},"agent_actions":{"view_html":"https://pith.science/pith/TPGH32M55XR7EOZ5GNDKAQBJHM","download_json":"https://pith.science/pith/TPGH32M55XR7EOZ5GNDKAQBJHM.json","view_paper":"https://pith.science/paper/TPGH32M5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.12079&json=true","fetch_graph":"https://pith.science/api/pith-number/TPGH32M55XR7EOZ5GNDKAQBJHM/graph.json","fetch_events":"https://pith.science/api/pith-number/TPGH32M55XR7EOZ5GNDKAQBJHM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TPGH32M55XR7EOZ5GNDKAQBJHM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TPGH32M55XR7EOZ5GNDKAQBJHM/action/storage_attestation","attest_author":"https://pith.science/pith/TPGH32M55XR7EOZ5GNDKAQBJHM/action/author_attestation","sign_citation":"https://pith.science/pith/TPGH32M55XR7EOZ5GNDKAQBJHM/action/citation_signature","submit_replication":"https://pith.science/pith/TPGH32M55XR7EOZ5GNDKAQBJHM/action/replication_record"}},"created_at":"2026-07-05T09:37:15.814312+00:00","updated_at":"2026-07-05T09:37:15.814312+00:00"}