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We prove that $G$ contains at least $n^{(\\frac{1}{4} - o(1))\\log n}$ monochromatic complete subgraphs of size $r$, where \\[ 0.3\\log n < r < 0.7\\log n. \\] The previously known lower bound on the total number of monochromatic complete subgraphs, due to Sz\\'{e}kely was $n^{0.1576\\log n}$. We also prove that $G$ contains at least $n^{\\frac{1}{7} \\log n} $ monochromatic complete subgraphs of size $\\frac{1}{2}\\log n$.\n  If furthermore one assumes that the largest monochromatic complete subgraph in $G$ is of si"},"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":"1703.09682","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-28T17:32:56Z","cross_cats_sorted":[],"title_canon_sha256":"f0fedc925c3373897d5713b5ad17528feb1664582d0edfbd29bb4d14434fe8ce","abstract_canon_sha256":"8f2d5aa2aa7a1c47ce1c7999490e5343b546ccd9dc21d87438ca9a9e28e08676"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:56.020940Z","signature_b64":"n5aCIDzS1U4OJdlhDE0GUlKUHlfEBWqWVFdtxETxLGt4ofl2RtnN333dUmuFVXpCCqCdPbuW20PC6z0XPPOPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c6609e0208097c090b73a5dfceb1f8a0dc6ea2a97b914f214c62b4e0a0b5fc9","last_reissued_at":"2026-05-17T23:56:56.020272Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:56.020272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Profile of Multiplicities of Complete Subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anne Kenyon, Shimon Kogan, Uriel Feige","submitted_at":"2017-03-28T17:32:56Z","abstract_excerpt":"Let $G$ be a $2$-coloring of a complete graph on $n$ vertices, for sufficiently large $n$. 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