Manuscript X-Enter-ST@1 · X-Enter-ST.tex · section · f76acc1f

Unchanged geometric presentation

Stage A: the inherited host and the frozen coefficient › Unchanged geometric presentation · lines 291–327

In I-B's coordinates, the prescribed regular metric is locally represented by

G = - c_{host}^{2} d T^{2} + d r^{2} + α^{2} r^{2} d φ^{2} + d z^{2}, α = 1 - \frac{μ}{2 π}, 0 < μ < 2 π .

The completion locus is

W = R_{T} \times {o} \times R_{z},

a worldsheet. A fixed- $z$ section is a worldline; it is not the whole defect IB.

The coordinate formula describes the retained instance. It does not select a new deficit or update its metric. There is no second cone, no host-update map, and no global conical inverse.

For comparison with the inherited ramp, retain a fixed positive width and plateau:

0 < ε < δ, σ_{ε}^{R} (t) = χ (t / ε), U_{R} ⋐ L \cap int {g_{R} = 1} \cap {ε < t < T_{*}},

g_{R} = C_{c}^{\infty} (U_{R}; T M) .

The profile $χ$ is smooth, zero before zero, one after one, and flat at the endpoints. Its width is not removed.

Displayed formulas in this passage

unlabeled · line 295
$G = - c_{host}^{2} d T^{2} + d r^{2} + α^{2} r^{2} d φ^{2} + d z^{2}, α = 1 - \frac{μ}{2 π}, 0 < μ < 2 π .$
unlabeled · line 302
$W = R_{T} \times {o} \times R_{z},$
unlabeled · line 315
$0 < ε < δ, σ_{ε}^{R} (t) = χ (t / ε), U_{R} ⋐ L \cap int {g_{R} = 1} \cap {ε < t < T_{*}},$
unlabeled · line 322
$g_{R} = C_{c}^{\infty} (U_{R}; T M) .$

Nearby in this section

assumption: Assumption: Retained I-B/X-A-ST instance