The golden family's boundary at n = 3: general-n theorems for x^n = x + 1
Kernel-checked general-n theorems for the golden family — the ladder of trinomials x^n - x - 1, whose unique real root r_n > 1 descends from the golden ratio (n = 2) through the plastic number (n = 3) toward 1. The family's structural boundary falls at n = 3; this entry proves the morphic half unconditionally at general n and holds the Pisot half as the measure⟺Pisot equivalence, the unconditional n = 4 non-Pisot statement, and the Siegel-conditional strict excess for n >= 4, from the family's own arithmetic, with no per-degree case check above the boundary. Eleven compared statements carry…
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