The Five Cut Cycles Are Free Derived H1 Not Five Physical Sections
Entry 535 isolated five rational top-degree survivors of the carrier differential on cellwise Cut-Čech (H^1). This entry completes the integral test and corrects the interpretation of that group.
Each of the four induced carrier matrices admits a complete reduction by unimodular row and column operations using only (pm1) pivots. The unit-pivot counts equal the rational ranks
Consequently every nonzero Smith factor is one. Images are primitive, all intermediate zero rational homology groups vanish integrally, and the top kernel is free:
in top carrier degree, with zero homology in the other degrees. There is no finite torsion and no hidden index in the induced differentials.
Interpretation correction
The five classes live in Čech degree one. They are ambient derived (H^1)-classes of the full loaded chart system, not five distinct global physical sections. The distinguished physical section constructed in Entries 441, 446, and 533 lies in Čech degree zero. Entry 445 already proves that its combined sheet/conductor/log-Thom transport is (+1) on every edge and hence (+1) around all five Wagner cycles. Its additive edge cocycle is therefore zero.
Thus the correct statement is
Whether this (mathbb Z^5) acts as a deformation space requires a separately typed shift or mapping-complex action. It cannot be called a torsor of physical sections merely because it is (H^1). The next gate is to compute the relative endomorphism/deformation complex of the framed physical line inside the totalized Cut object. Its degree-zero homology, with the eight local boundary values fixed, is the actual uniqueness group.
The executable audit is
research/voevodsky/check_n8_cut_cech_h1_carrier_homology.py.