Certified SAT/LRAT exclusion of all groups of order 114 for degree-13 diameter-2 Cayley graphs (Nc(13,2) ≠114)

This deposit supports the following theorem: Nc(13,2) ≠ 114 — there is no Cayley graph of degree 13 and diameter 2 on any group of order 114. Structure of the proof: there are exactly six isomorphism classes ofgroups of order 114 (completeness follows from Hölder's classification,cross-checked by two independent enumerations and by GAPNumberSmallGroups(114) = 6). · Class 1 (abelian, Z_114): abelian counting bound |G| ≤ ⌊d²/2⌋ + d + 1 = 98 < 114; · Class 4 (dihedral, D_114): direct corollary of Erskine (Discrete Math. 338(6), 2015), Lemma 2 (d ≥ 2√57 − 1 ≈ 14.1 ⟹ d ≥ 15 > 13); · Classes 2, 3, 5, 6: UNSAT by SAT encoding, with LRAT machine certificates, all verified by the independent checker lrat-check.The full argument is given in the accompanying paper"Nc(13,2) ≠ 114: No Cayley Graph of Degree 13 and Diameter 2 on AnyGroup of Order 114" (PDF included).