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Following Gishboliner, Glock, and Sgueglia \\cite{GishbolinerGlockSgueglia2025}, the bulk of the recent work on this quantity has been on lower bounds for $r \\ge 3$ (proving $\\delta_r(n) = \\Ome"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.00492","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-01T08:02:38Z","cross_cats_sorted":[],"title_canon_sha256":"d2d8276a6c8bcaf648628abf6d558739c50a55789afc2f0e126c068d363c7045","abstract_canon_sha256":"d9705e14f49e5a5c11fb435b73a09612e724f72cc36767d09eac5b424caf71bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:55.490682Z","signature_b64":"yiAKNlcyVLM/JWNwatpO3++Jb1HpstEEjICbovgF7q29eZNsFsFUDbQVcoHPM3GA8xvnG8Xf+6gkjt1EoWJuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b45775ec17e1ee8162f86f28e17837409b03db67bcda456626af9a4d142b4630","last_reissued_at":"2026-06-19T16:10:55.490221Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:55.490221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An exact small-$n$ computation of the minimum 2-coloring discrepancy of $K_n^{(3)}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"For n ≡ 1 or 3 mod 6 up to 21, the minimum 2-coloring discrepancy of Steiner triple systems equals min over x of |x(n-x)/2 - n(n-1)/12|.","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tong Niu","submitted_at":"2026-05-01T08:02:38Z","abstract_excerpt":"For an integer $r \\ge 2$ and an order $n \\equiv 1, 3 \\pmod{6}$, write $\\delta_r(n)$ for the minimum, over all $r$-colourings $\\chi : \\binom{[n]}{3} \\to [r]$, of $\\max_{\\mathcal{S}} \\mathrm{disc}(\\mathcal{S}, \\chi)$, where the maximum is over labelled Steiner triple systems $\\mathcal{S}$ of order $n$ and $\\mathrm{disc}(\\mathcal{S}, \\chi) = \\max_c |\\#\\{T \\in \\mathcal{S} : \\chi(T) = c\\} - |\\mathcal{S}|/r|$. Following Gishboliner, Glock, and Sgueglia \\cite{GishbolinerGlockSgueglia2025}, the bulk of the recent work on this quantity has been on lower bounds for $r \\ge 3$ (proving $\\delta_r(n) = \\Ome"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"An exact value of δ₂(n) for each such n, matching the formula δ₂(n) = min_{x ∈ [0,n] ∩ Z} |x(n-x)/2 - n(n-1)/12| obtained by optimising the GGS Example 1.1 family.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That simulated annealing finds the global minimum for n=13,15,19,21 and that the conjectural formula continues to hold for all larger n ≡1,3 mod 6.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Exact values of δ₂(n) for n=7,9,13,15,19,21 match the min over x of |x(n-x)/2 - n(n-1)/12|, with a conjecture that this holds for all n ≡1,3 mod 6.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"For n ≡ 1 or 3 mod 6 up to 21, the minimum 2-coloring discrepancy of Steiner triple systems equals min over x of |x(n-x)/2 - 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