Improve C1a lower bound to 1.292#89
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Three-scale arcsine kernel with reoptimized Fejer majorant applied to the Matolcsi-Vinuesa master inequality; analytic reduction formalized in Lean 4 (sorry-free), numerical anchors certified by flint.arb interval arithmetic. AI-assisted. Code and certificates: https://github.com/AndreiPiterbarg/sidon-autocorrelation
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This updates the lower bound for the Sidon autocorrelation constant$C_{1a}$ to 1.292.
The bound is obtained from a three-scale arcsine kernel combined with a reoptimized Fejér-side majorant, applied to the Matolcsi–Vinuesa master inequality. The analytic argument — including the reduction from the full nonnegative$L^1$ class — is formalized in Lean 4, and the numerical anchors (the kernel's $L^2$ norm, the gain functional, the majorant minimum, and lattice positivity) are certified by
flint.arbinterval arithmetic at 256-bit precision.Full details, the Lean formalization, and the certificates are available in the repository: https://github.com/AndreiPiterbarg/sidon-autocorrelation
This submission was prepared with AI assistance; all references and results have been reviewed and verified by the authors.