Manuscript XXII-D@1 · XXII-D.tex · section · 17889d18

Null targets and a frozen-carrier obstruction

Null targets and a frozen-carrier obstruction · lines 450–483

XXII-D@1#eq:null-pairs, XXII-D@1#eq:source-differences

Define the formal future-null set

N_{D} = \partial K_{D} ∖ {0} .

A formal anchored target is

ζ = (a, v), a \in ι_{D} (E_{D}), v \in N_{D} .

Its target endpoint is $a + v$ , which need not lie in $ι_{D} (E_{D})$ .

The represented null-pair set is instead

N_{D}^{pair} = {(p, q) : p \neq = q, ι_{D} (q) - ι_{D} (p) \in N_{D}} .

It may be empty. Even a member of (eq:null-pairs) is a represented comparison, not an identity-transmission protocol.

For a fixed source $p$ , put

F_{p} = {ι_{D} (q) - ι_{D} (p) : p ⪯_{D} q, q \neq = p} .

Displayed formulas in this passage

unlabeled · line 453
$N_{D} = \partial K_{D} ∖ {0} .$
unlabeled · line 457
$ζ = (a, v), a \in ι_{D} (E_{D}), v \in N_{D} .$
XXII-D@1#eq:null-pairs · line 465
$N_{D}^{pair} = {(p, q) : p \neq = q, ι_{D} (q) - ι_{D} (p) \in N_{D}} .$
XXII-D@1#eq:source-differences · line 477
$F_{p} = {ι_{D} (q) - ι_{D} (p) : p ⪯_{D} q, q \neq = p} .$