Exact Finite-Field Constructions Saturating the Knipfer Bipartite Magic Conjecture ($5 \le d \le 113$) - RJW

Optimizing quantum non-stabilizerness is traditionally treated as a continuous variational problem. Recent work by Knipfer et al. (arXiv:2607.07197) conjectured a maximal bipartite stabilizer Rényi entropy (magic) bound of $M_2^*(d) = \ln(d^4/(2d^2-1))$. In this work, we provide explicit analytical constructions that successfully saturate this open conjecture. Through 1,000-digit precision verification across all 28 prime dimensions from $d=5$ to $d=113$, we introduce two distinct families of $\mathrm{GF}(d^2)$ trace generators that achieve this exact limit. Crucially, this construction reveals a massive degeneracy in the magic-saturation landscape. We verify that our symmetric trace family ("Family A") yields an exact, quantized half-rank bipartite Schmidt spectrum, demonstrating that maximal magic does not require maximal entanglement. Conversely, our Golden-Lucas trace family ("Family B") achieves the same exact magic saturation while maintaining full or near-full Schmidt rank, governed strictly by a $d \pmod 3$ selection rule. Finally, we outline a purely algebraic consequence of the bounds: the infinite product of the complementary magic purity over our evaluated prime ladder converges precisely to $\pi^2/9$ via the Euler-Basel identity. By relying strictly on reproducible finite-field arithmetic and exact Weyl-Heisenberg operators, this dataset provides a deterministic foundation for qudit magic state generation.Authors note: Thank you for reading. I have a request. run the math. Check the math. I do not think it will disapoint. It passee multiple AI reviews and it should be solid. I appreciate your efforts to check and validate it again. May your path to elegance be amazing. Mine sure has. Take care. RJW