TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/GEOMETRIC-R-SPIN-COLLAR-REVIEW.txt
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Inclusive original lines: 16-29
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000016 | 1. Global map and the old coefficient cocycle
000017 | Use exactly C: eta^2=1-w^6, z=eta/(1-w^3), omega=exp(2pi i/3),
000018 | rho=exp(i pi/3)=-omega^2. For c(w)=omega w, s(w)=-w,
000019 |   R=s c^2: w -> rho w,       pi R=iota pi, iota(z)=1/z,
000020 |   R^2=c, R^3=s, R^6=1.
000021 | The marked points are q_a=(-omega^a,0), p_a=(omega^a,0). The actual
000022 | normalized Kummer maps, already proved in the six-line completion, give
000023 |   R^*h_a^q=h_(a+1)^p, R^*h_a^p=h_(a+1)^q,
000024 |   c^*h_a^(q/p)=h_(a-1)^(q/p).                         (1)
000025 | Thus the q/p maps commute with the actual c cocycle. They are not a
000026 | constant symmetry asserted for the isolated original q Fuchs equation.
000027 | In its original holomorphic frame the connection really transforms as
000028 |   -z^-2 A_q(1/z)=A_q(z)^t-diag(2,1,1)/z.
000029 | The positive flat metric and the G frame must accompany this formula.