Manuscript X-A-conv-ST@1 · X-A-conv-ST.tex · assumption · 8ca47088

Assumption: Retained host

Stage A: the unchanged host and the analytical completion · lines 248–285

X-A-conv-ST@1#ass:host, X-A-conv-ST@1#eq:signature

Retain the I-B/X-A-ST instance, including its deficit, time orientation, regular laboratory, developing chart, time calibration, operational permissions, and reserved finite transport tube.

Write its regular conical product as

M^{\circ} = R_{T} \times (C_{α} ∖ {o}) \times R_{z}, G = - c_{h}^{2} d T^{2} + d r^{2} + α^{2} r^{2} d φ^{2} + d z^{2},

where $c_{h} > 0$ and $0 < α < 1$ retain their inherited values. The completion defect is

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

It is a worldsheet.

The already declared analytical completion and chart are

M = R^{1 + 3}, η = diag (1, - 1, - 1, - 1), ι : L ⟶ M^{\circ},

with

ι^{*} G = - η, t = c_{h} (T - T_{Σ}) .

The chart is injective on its declared domain and the laboratory does not meet $W$ . No host-update map is added.

Displayed formulas in this passage

X-A-conv-ST@1#eq:signature · line 277
$ι^{*} G = - η, t = c_{h} (T - T_{Σ}) .$
unlabeled · line 256
$M^{\circ} = R_{T} \times (C_{α} ∖ {o}) \times R_{z}, G = - c_{h}^{2} d T^{2} + d r^{2} + α^{2} r^{2} d φ^{2} + d z^{2},$
unlabeled · line 265
$W = R_{T} \times {o} \times R_{z} .$
unlabeled · line 271
$M = R^{1 + 3}, η = diag (1, - 1, - 1, - 1), ι : L ⟶ M^{\circ},$

Assumption: Retained host

Displayed formulas in this passage

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