A finite two-temperature lower bound for the GHR sum-difference constant
The Gyarmati-Hennecart-Ruzsa constant C₃ₐ is the supremum of real exponents theta for which every K > 1 admits a positive constant c and arbitrarily large nonempty finite integer sets X with nonempty partners Y satisfying |X+Y| 60709/50000 = 1.21418. A finite type at depth 10^13, separate difference and sum tilts, cyclic compression, and a proved finite-set principle supply the bound. The result concerns extremal sumset and difference-set growth in additive combinatorics. The paper's general limiting theorem is outside the formalized claim.
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