Original ledger status
DIAMOND.AXIS.01
DIAMOND.AXIS.01
DIAMOND AXIS CURVATURE LEMMA (2026-06-15): along the two canonical axes of the centered cross (C center, U winding, V sheet, v95) the Sheet-Diamond determinant is LINEAR on the winding axis and QUADRATIC on the sheet axis: det(C+xU)=14+6x (flat, slope 6=|R^+(A_3)|), det(C+yV)=14+14y+4y^2 (2nd difference 8=rank E_8); the anchor block satisfies det B(C+xU)=28+12x=2 det(C+xU) and det B(C+yV)=28+21y+3y^2 (2nd difference 6=|R^+(A_3)|). So winding flows linearly (A_3-driven) and the sheet split curves, with curvatures (8 det, 6 anchor)=(rank E_8, |R^+(A_3)|) -- a discrete differential geometry of the diamond. Exact identity UPDATE (2026-07-31, v566, DIAMOND.PARA.SELFCODE.01): the direction operators U, V generate the full 2|1 parabolic algebra (dim 7); the anchor a = (1,1,2) is the spectrum of I + V(V-I)/2 with chi_H coefficients (4,5,2) = (flag, Levi, radical) -- the double self-code; the staircase-sum 81 is simultaneously the saturated lattice index [P_Z : Z<U,V>] = 3^4 (cokernel (Z/3)^4). Markers unchanged.
Recorded status: Identity (exact)
Dependencies, status detail and source
Canonical status: [E] det(C+xU)=14+6x linear, det(C+yV)=14+14y+4y^2 quadratic; curvatures (8,6)=(rank E_8, |R^+(A_3)|)
Dependencies: v94_sheet_diamond.py; v95_centered_diamond.py
Scripts: v218_diamond_axis_geometry.py
Location: tfpt_2_standard_model
Original CSV, line 303