{"id":"palomar/PALOMAR-2026-10-19-000017","url":"https://github.com/JD-Jones-ASES/continued-fraction-bounds/tree/a7657a01aec49be60f36a2cda8e6c6bfcd3840c3","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-19-000017-v1.json","repo":"https://github.com/JD-Jones-ASES/continued-fraction-bounds","tags":["math.NT","msc:11J70","msc:11A55","msc:26D07","continued-fractions","diophantine-approximation","inequalities"],"score":0,"title":"Sharp continued-fraction bounds from exact digit runs","trust":"high","domain":"math.NT","source":"palomar","authors":["JD Jones"],"reviews":0,"subject":"math.NT","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-19","reactions":{},"formalized":true}