Manuscript IX-E-2@1 · IX-E-2.tex · section · e70d9077

Other inherited boundaries

Explicit inherited inputs and their limits › Other inherited boundaries · lines 460–491

V's externally retarded object

R_{1, 1} = i (T_{2} - V ϕ), u_{f} = - G_{A} f, q_{g, h, f} = Q_{g h} u_{f}

belongs to its compactly switched minimal vertex problem. Its linear coefficient, finite-mode oscillator coefficient, and cubic Newton–wave Wick form remain different objects. In particular, V does not supply $T_{2} (V, V)$ or the sharp map sought here.

VI's first-order compact-switch defect and VII-A's restricted plateau intertwining statement are retained. The expression

O^{(2)} + R_{1} (V_{1}; O^{(1)}) + R_{1} (V_{2}; O^{(0)}) + \frac{1}{2} R_{2} (V_{1}, V_{1}; O^{(0)})

is an obligation list, not a construction imported into this paper.

VII-E/F and VIII-A–C supply their stated observation, exchange, particle-link, affine-matching, packet, and scheduling certificates. No supplied map identifies those outputs with $B_{f}$ , $W_{g}$ , a triangle finite part, or an element of $D_{2}$ . VIII-C's token policy supplies a semantic promise, not an acquired expectation.

Displayed formulas in this passage

unlabeled · line 463
$R_{1, 1} = i (T_{2} - V ϕ), u_{f} = - G_{A} f, q_{g, h, f} = Q_{g h} u_{f}$
unlabeled · line 477
$O^{(2)} + R_{1} (V_{1}; O^{(1)}) + R_{1} (V_{2}; O^{(0)}) + \frac{1}{2} R_{2} (V_{1}, V_{1}; O^{(0)})$