Manuscript XV-B@2 · XV-B.tex · section · 4d3f12e8

Application boundary and numbering

Introduction and scope › Application boundary and numbering · lines 253–283

XV-B@2#eq:targetmap, XV-B@2#eq:admission

The retained application asks for a map

M : K_{int} ⟶ D^{'} (W; E_{res})

for the full joint characteristic target inherited from XIV-I and XIV-J CheungXIVI,CheungXIVJ. Here $W$ is the attachment domain and $E_{res}$ is the residual-species bundle.

A successful construction must agree with canonical composition on its proved domain, act on tests meeting the characteristic locus, retain every branch and prescribed tensor operation, respect reconstruction, and satisfy the complete-graph microlocal bounds.

In this paper, XV-B denotes the technical continuation studying these obligations. The predecessor phrase “XV-B remains closed” concerns its earlier downstream admission contract, not the nonexistence of a technical continuation. The admission condition

Q_{H} R_{1}^{(1)} \in E_{H}

is not established here. Changing the manuscript convention neither proves (eq:admission) nor supplies a free quantum BV carrier. In particular, the model-and-domain audit cited as XV-A below is not identified with the differently described free-carrier prerequisite appearing under that label in older passages CheungXVA,CheungXIVI,CheungXIVJ.

Displayed formulas in this passage

XV-B@2#eq:targetmap · line 256
$M : K_{int} ⟶ D^{'} (W; E_{res})$
XV-B@2#eq:admission · line 273
$Q_{H} R_{1}^{(1)} \in E_{H}$