Manuscript X-J-ST@1 · X-J-ST.tex · assumption · 8f0d1a36

Assumption: Retained I-B/X-A-ST host

The unchanged host and its finite operational reserve · lines 305–349

X-J-ST@1#ass:host

Retain the same conical product, supported chart, width, time orientation, and finite operational permissions as in X-I-ST. In regular conical coordinates,

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},

with the inherited $0 < α < 1$ and $c_{h} > 0$ . The completion defect is the worldsheet

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

The independent analytical completion and supported chart are

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

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

The chart is injective on the retained domain, and its laboratory reserve is disjoint from $W$ .

Retain a nonempty relatively compact plateau

U ⋐ L, g = σ_{ε} = 1 near U, ε > 0

with the same positive width as before.

Any finite experiment released below must fit the already supplied time, space, register, and control reserve. Register allocation is charged; no enlargement of the chart or change of $ε$ is inferred.

Displayed formulas in this passage

unlabeled · line 310
$M^{\circ} = R_{T} \times (C_{α} ∖ {o}) \times R_{z}, G = - c_{h}^{2} d T^{2} + d r^{2} + α^{2} r^{2} d φ^{2} + d z^{2},$
unlabeled · line 319
$W = R_{T} \times {o} \times R_{z} .$
unlabeled · line 324
$M = R^{1 + 3}, η = diag (1, - 1, - 1, - 1), ι : L ⟶ M^{\circ},$
unlabeled · line 329
$ι^{*} G = - η, t = c_{h} (T - T_{Σ}) .$
unlabeled · line 337
$U ⋐ L, g = σ_{ε} = 1 near U, ε > 0$

Assumption: Retained I-B/X-A-ST host

Displayed formulas in this passage

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