from pathlib import Path from html import escape OUT=Path(__file__).resolve().parent def text(x,y,s,size=22,weight='normal',fill='#203c50'): return f'{escape(s)}' def rect(x,y,w,h,fill): return f'' parts=['', 'Intrinsic fibre rationality depends on the base', 'The intrinsic presentation has invariant coordinates I j equals exp minus p times w j. The original derivative rational invariant field consists of the ratios w j over w 2. In the slice x equals u equals w equals p equals z equals zero, the exact points w 2,w 3 equals one,one and two,two have equal ratio but different intrinsic invariant coordinates and different H orbits.', '', text(30,42,'An intrinsic action: the base fixes the rational coefficient class',26,'bold'), rect(25,65,1150,255,'#edf3fb'), text(45,105,'Equation uₓₓ=0; free function w(x). Intrinsic base M′=E¹.',24,'bold'), text(45,146,'p=uₓ, z=wₓ, b=u−px. On M′: bₓ=pₓ=0, wₓ=z.',23), text(45,189,'x′=x+s, b′=b+h, p′=p+a, z′=eᵃz+c, w′=eᵃw+cx+d.',23), text(45,232,'Iⱼ=e⁻ᵖwⱼ (j≥2), DIⱼ=Iⱼ₊₁. All fixed-point jet groups are trivial.',23), text(45,278,'In (x,u,w), u′=u+ax+sp+as+h depends on the derivative p when s≠0.',22), rect(25,340,555,440,'#f2f8f5'), text(45,380,'Exact original third-order slice',24,'bold'), text(45,416,'x=u=w=p=z=0; w₂≠0',21), '', text(445,727,'w₂',23),text(62,455,'w₃',23), '', text(310,505,'r₃=1',22), '', '', text(171,749,'1',19),text(261,749,'2',19),text(66,637,'1',19),text(66,547,'2',19), text(193,655,'P=(1,1)',20,fill='#187e75'),text(282,563,'Q=(2,2)',20,fill='#a44f2a'), rect(605,340,570,440,'#fff6eb'), text(627,380,'Two different invariant fields',24,'bold'), text(627,427,'Intrinsic S² over M′:',23,'bold'), text(627,464,'ℝ(I₂,I₃), q₂(P)=(1,1),',23), text(627,501,'q₂(Q)=(2,2). Full H-orbits differ.',23), text(627,555,'Original derivative-rational class:',23,'bold'), text(627,593,'ℝ(r₃), r₃=w₃/w₂. Both values are 1.',22), text(627,639,'δ=∂ₚ+t∂ₜ on ℝ(p,t,r₃), t=w₂.',22), text(627,676,'Its rational constants are ℝ(r₃).',22), text(627,723,'The dashed ray is not one H-orbit.',22,'bold'), text(45,820,'Example 4.41: full normalization and affine quotient tower, (4.109)–(4.111).',22), text(45,856,'Lemma 4.42 and Proposition 4.43: the rational constant field and failure of orbit separation.',21), text(45,895,'Scope context: Kruglikov–Lychagin, arXiv:1111.5480v3 §0.1. GPT-6.1 Sol (OpenAI). CC0 1.0.',17), ''] svg='\n'.join(parts)+'\n' if __name__=='__main__': (OUT/'intrinsic-coefficient-classes.svg').write_bytes(svg.encode('utf-8')) print(str(OUT/'intrinsic-coefficient-classes.svg'))