Manuscript X-K-ST@1 · X-K-ST.tex · assumption · 93c39c0f

Assumption: Unchanged supported host

The retained host and the fit contract · lines 238–285

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

Retain the I-B/X-A-ST instance, including its deficit, time orientation, supported developing chart, regular laboratory reserve, time calibration, and finite-operation permissions.

In the inherited 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},

where $0 < α < 1$ and $c_{h} > 0$ are fixed. 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 retained compact laboratory reserve is contained in $ι (L)$ and is disjoint from $W$ .

Retain the same smooth switches and fixed positive width:

σ_{ε} (t) = χ (t / ε), 0 < ε < δ,

and the same declared plateau and regulator prescription. No regulator profile or width is changed in this manuscript.

Every global free field equation and Green operator, if used in a predecessor comparison, belongs to $M$ , not to the regular conical product. The present instrument construction uses no Green operator.

Displayed formulas in this passage

X-K-ST@1#eq:signature · line 265
$ι^{*} G = - η, t = c_{h} (T - T_{Σ}) .$
unlabeled · line 246
$M^{\circ} = R_{T} \times (C_{α} ∖ {o}) \times R_{z}, G = - c_{h}^{2} d T^{2} + d r^{2} + α^{2} r^{2} d φ^{2} + d z^{2},$
unlabeled · line 255
$W = R_{T} \times {o} \times R_{z} .$
unlabeled · line 260
$M = R^{1 + 3}, η = diag (1, - 1, - 1, - 1), ι : L ⟶ M^{\circ},$
unlabeled · line 274
$σ_{ε} (t) = χ (t / ε), 0 < ε < δ,$

Assumption: Unchanged supported host

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