Manuscript VIII-B@3 · VIII-B-v3.tex · section · 3aa6baa1

Charts and words

Reference specialization at mu0=pi/2 › Charts and words · lines 2639–2696

The reference gradients are

g_{h} = (2/3, 2/3)^{T}, g_{-} = (0, 3/5)^{T}, g_{+} = (3/5, 0)^{T} .

Their boosts are

B_{h} = 3 - 2 - 2 - 2 21 - 2 12, B_{x} = 5/4 - 3/4 0 - 3/4 5/4 0 001, B_{y} = 5/4 0 - 3/4 010 - 3/4 0 5/4 .

Thus

A_{V_{i}} (z) A_{U_{i}^{-}} (z) A_{U_{i}^{+}} (z) = O_{i} B_{h} O_{i}^{- 1} z - 3 s t, = O_{i} B_{y} O_{i}^{- 1} z - \frac{5}{2} s t, = O_{i} B_{x} O_{i}^{- 1} z - \frac{5}{2} s t, O_{i} = diag (1, Rot (iπ /2)) .

Resting charts are identities.

The core and collar loops remain $ρ = 29/10$ and $ρ = 15/4$ . Their winding marks are one; the core and star words are (eq:core-word) and (eq:star-word) with $J = J_{0}$ . The intrinsic audit specializes to

θ_{h} = arccos (- 4/5), θ_{k} = arctan (4/5), v \in int K_{s} \sum κ_{v} = π /2.

Hence the source-off specialization includes the complete displayed graph, cell pattern, vertices, times, lengths, one-sided slopes, areas, adapted charts, seam, primitive words, collar, worldline, rest data, and intrinsic audit.

Displayed formulas in this passage

unlabeled · line 2642
$g_{h} = (2/3, 2/3)^{T}, g_{-} = (0, 3/5)^{T}, g_{+} = (3/5, 0)^{T} .$
unlabeled · line 2648
$B_{h} = 3 - 2 - 2 - 2 21 - 2 12, B_{x} = 5/4 - 3/4 0 - 3/4 5/4 0 001, B_{y} = 5/4 0 - 3/4 010 - 3/4 0 5/4 .$
unlabeled · line 2671
$A_{V_{i}} (z) A_{U_{i}^{-}} (z) A_{U_{i}^{+}} (z) = O_{i} B_{h} O_{i}^{- 1} z - 3 s t, = O_{i} B_{y} O_{i}^{- 1} z - \frac{5}{2} s t, = O_{i} B_{x} O_{i}^{- 1} z - \frac{5}{2} s t, O_{i} = diag (1, Rot (iπ /2)) .$
unlabeled · line 2686
$θ_{h} = arccos (- 4/5), θ_{k} = arctan (4/5), v \in int K_{s} \sum κ_{v} = π /2.$