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Sharp continued-fraction bounds from exact digit runs

JD Jones

Palomar Registrypalomar/PALOMAR-2026-10-19-000017Oct 19, 2026math.NTscore 0

Proves sharp bounds for both extrema of three consecutive ordinary continued-fraction approximation coefficients. Exact finite runs of every integer central digit at least two have rational four-corner constants, unique coordinate extremizers, strict actual inequalities, and optimality within the prescribed digit classes. The project also proves exact clipping on every closed unit-square rectangle for every real parameter at least one; sharp inverse stability for both extrema for every real parameter at least two, including their equality loci and actual-convergent optimality; fixed-word…

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