Follow a result back to its evidence.

the PILLOWCASE reduction of QGEO.SYM.01 (QGEO.PILLOW.01): the two separately-tracked open QGEO residuals — v180/QGEO.ISO.01 (the carrier clock is an order-4 isometry of the seam metric) and v201/QGEO.SUBPRIN.01 (the DtN sub-principal symbol is mark-local, the seam flat away from the μ4 marks) — are ONE statement, 'the seam carries the uniformising flat orbifold (pillowcase) metric', and the order-4 clock is DERIVED from cross-ratio 2 (v168), not assumed. A reduction + unification, NOT a closure. [E] χ_orb(S²(2,2,2,2))=2−4(1−1/2)=0 ⟹ flat (Troyanov cone-metric uniformisation, unique up to scale; Gauss–Bonnet four cone deficits π sum to 4π=2π·χ(S²) ⟹ ∫K_smooth=0, flat away from the marks). [E] NEW LINK: cross-ratio(μ4)=2 (v168) ⟹ j(λ)=256(λ²−λ+1)³/(λ²(λ−1)²) with j(2)=1728 (all six harmonic cross-ratios {2,−1,1/2} give 1728) ⟹ the square modulus, hence the order-4 clock, is a consequence of cross-ratio 2. [E]/[L] j=1728 ⟺ τ=i (square torus) ⟺ CM by ℤ[i] ⟺ Aut=ℤ/4 (only other exceptional modulus j=0 gives ℤ/6; generic ℤ/2). [E] explicit CM (x,y)→(−x,iy) on y²=x³−x has order 4 = z→iz. [E] negative control λ=3 ⟹ j=21952/9 ∉ {0,1728} ⟹ Aut=ℤ/2, no order-4 clock. [I] UNIFICATION: 'seam = uniformising flat pillowcase metric' implies BOTH v201 mark-locality AND v180 QGEO.ISO.01. [O] does NOT close QGEO.SYM.01 — the canonical constant-curvature-metric premise stays open, milder/more canonical than the bare isometry premise; net existence + full-cone RP remain v175's [E].

Linked claims

QGEO.PILLOW.01

Paper sections

Source section 1Source section 2Source section 3Source section 4Source section 5Source section 6Source section 7Source section 8Source section 9Source section 10Source section 11Source section 12Source section 13Source section 14Source section 15Source section 16Source section 17Source section 18Source section 19Source section 20Source section 21Source section 22Source section 23Source section 24Source section 25