Manuscript XXII-E@1 · XXII-E.tex · assumption · 51c99d2f

Model specification: Conditional kinematic input

Conditional operational input › Conditional extraction and transport · lines 253–291

XXII-E@1#spec:kinematic, XXII-E@1#eq:faithful, XXII-E@1#eq:span, XXII-E@1#eq:generated, XXII-E@1#eq:lorentz

Fix $m \geq 3$ . For a datum $D$ , suppose a successful predeclared extraction has provided

(V_{D}, ι_{D}, K_{D}, T_{D}), T_{D} : V_{D} ⟶ R^{m}

with $T_{D}$ invertible, $K_{D}$ proper, and

p ⪯_{D} q V_{D} K_{D} T_{D} (K_{D}) ⟺ ι_{D} (q) - ι_{D} (p) \in K_{D}, = span {ι_{D} (q) - ι_{D} (p) : p, q \in E_{D}}, = cone {ι_{D} (q) - ι_{D} (p) : p ⪯_{D} q, p \neq = q}, = L_{m} = {(t, x) : t \geq ∥ x ∥_{2}} .

Suppose also that a separately justified realization $B_{D}$ meets the compatible transport contract of XXII-D on a declared nonempty target family.

If a revised carrier or access model is used, its maps, faithfulness, composition validity, and compatibility with (eq:generated) must be stated. No nonempty joint domain satisfying these conditions is exhibited in this note.

Displayed formulas in this passage

XXII-E@1#eq:faithful · line 264
$p ⪯_{D} q V_{D} K_{D} T_{D} (K_{D}) ⟺ ι_{D} (q) - ι_{D} (p) \in K_{D}, = span {ι_{D} (q) - ι_{D} (p) : p, q \in E_{D}}, = cone {ι_{D} (q) - ι_{D} (p) : p ⪯_{D} q, p \neq = q}, = L_{m} = {(t, x) : t \geq ∥ x ∥_{2}} .$
XXII-E@1#eq:span · line 264
$p ⪯_{D} q V_{D} K_{D} T_{D} (K_{D}) ⟺ ι_{D} (q) - ι_{D} (p) \in K_{D}, = span {ι_{D} (q) - ι_{D} (p) : p, q \in E_{D}}, = cone {ι_{D} (q) - ι_{D} (p) : p ⪯_{D} q, p \neq = q}, = L_{m} = {(t, x) : t \geq ∥ x ∥_{2}} .$
XXII-E@1#eq:generated · line 264
$p ⪯_{D} q V_{D} K_{D} T_{D} (K_{D}) ⟺ ι_{D} (q) - ι_{D} (p) \in K_{D}, = span {ι_{D} (q) - ι_{D} (p) : p, q \in E_{D}}, = cone {ι_{D} (q) - ι_{D} (p) : p ⪯_{D} q, p \neq = q}, = L_{m} = {(t, x) : t \geq ∥ x ∥_{2}} .$
XXII-E@1#eq:lorentz · line 264
$p ⪯_{D} q V_{D} K_{D} T_{D} (K_{D}) ⟺ ι_{D} (q) - ι_{D} (p) \in K_{D}, = span {ι_{D} (q) - ι_{D} (p) : p, q \in E_{D}}, = cone {ι_{D} (q) - ι_{D} (p) : p ⪯_{D} q, p \neq = q}, = L_{m} = {(t, x) : t \geq ∥ x ∥_{2}} .$
unlabeled · line 258
$(V_{D}, ι_{D}, K_{D}, T_{D}), T_{D} : V_{D} ⟶ R^{m}$

Nearby in this section

section: Conditional extraction and transport