Braid phase reference and correction ledger

For the fixed Fibonacci convention, write $\rho (b)$ for the physical braid matrix and $B(b)$ for the normalized word matrix obtained by removing the common exchange scalar $R_1$ from each Artin generator, as in The braid phase is a common scalar character. If $e(b)$ is exponent sum, then $\rho (b)=R_1^{e(b)}B(b)\mathrm{.}$ On the three-anyon total-$\tau$ block the SK alphabet instead uses the special-unitary lifts $z{B}_j$ with $z=e^{3\pi i\mathrm{/}10}$, so a word of exponent sum $k$ satisfies $\rho (b)=(R_1{z}^{-1}{)}^k\widehat{B}(b),\widehat{B}(b)=z^{k}B(b)\mathrm{.}$ A phase reference record stores the exact generator scalar, exponent sum, which normalized convention was compiled, the resulting scalar on each coherently used branch, and any correction operation and its declared cost under Circuit-family and computation cost model. A standalone fixed-sector computation may report its output projectively using the metric of Projective braid gate and operator metric. In coherent control the active branch scalar is relative to the inactive branch and must remain in the record. No phase correction is assigned zero cost unless its interface says so. This ledger distinguishes the common $R_1^{e(b)}$ phase from the additional $z^{-e(b)}$ needed when the compiled alphabet is the SU(2) lift.