Fröberg's conjecture through degree 2d in sufficiently many variables
For every positive generating degree d, there is a variable threshold depending only on d such that, over every infinite field and for every number of general degree-d generators, the quotient polynomial ring has Fröberg's predicted Hilbert function through degree 2d. The threshold is independent of both the field and the number of generators. The prediction uses positive truncation at the first nonpositive coefficient of (1-t^d)^r/(1-t)^n. The development includes a direct construction for d at least three and a separate quadratic argument in arbitrary characteristic.
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