λEnter Calculus CompanionRegistered manuscripts, kept distinct

Manuscript X-A-ST@1 · X-A-ST.tex · section · d9ccbde1

The prescribed host and the flat-completion ledger

The prescribed host and the flat-completion ledger · lines 236–258

X-A-ST@1#eq:host

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Fix $0 < δ_{c} < 2 π$ , $α_{c} = 1 - δ_{c} / (2 π)$ , and $c > 0$ . The regular host is

M^{\circ} = R_{T} \times C_{δ_{c}}^{\circ} \times R_{z}, G = - c^{2} d T^{2} + d r^{2} + α_{c}^{2} r^{2} d φ^{2} + d z^{2}, r > 0.

Its stipulated completion has singular set

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

Thus the defect is a worldsheet, not a worldline. The time orientation is increasing $T$ . These are I-B-type inputs IB.

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X-A-ST@1#eq:host · line 242
$M^{\circ} = R_{T} \times C_{δ_{c}}^{\circ} \times R_{z}, G = - c^{2} d T^{2} + d r^{2} + α_{c}^{2} r^{2} d φ^{2} + d z^{2}, r > 0.$
unlabeled · line 252
$W = R_{T} \times {o} \times R_{z} .$

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