Manuscript XV-F-patch@1 · XV-F-patch.tex · section · 6d6ef16d

The coefficient displays actually available

Assembled ledger, debugging, and the revised F0 verdict › The coefficient displays actually available · lines 2016–2100

XV-F-patch@1#eq:Q, XV-F-patch@1#eq:T, XV-F-patch@1#eq:K8, XV-F-patch@1#eq:K9

The proposed outline places $K_{8}$ and $K_{9}$ wholly outside the input set. That is not correct for the supplied texts. XIV-I and XIV-J copy their formulas explicitly. Their upstream owner may be XIV-H, but the copied displays are available as premises of the four-sheet patch, with their copied scope.

{Defines the copied response formulas. XIV-I.tex; input:Hresponse, eq:Q, eq:T, eq:K8, eq:K9; reported lines 257–321, with formulas reported at lines 285–310.}

Those displays are

Q^{L, I, J} (v; a, z) = ∣ α ∣ + ∣ β ∣ \leq 2 \sum q_{α β}^{L, I, J} (v) \partial_{v}^{α} δ^{(4)} (v - z) \partial_{v}^{β} δ^{(4)} (v - a),

T^{L, I, J} (b; a, z) = P^{L}_{M} \int R (b - v) Q^{M, I, J} (v; a, z) d^{4} v,

and

K_{8}^{I, J} (a, b, z) = - \partial_{b^{μ}} [f (b) A^{α μ}_{L} P^{L}_{M} \partial_{b^{α}} \int B (b - v) Q^{M, I, J} (v; a, z) d^{4} v],

K_{9}^{I, J} (a, b, z) = - \partial_{b^{ν}} [g (b) \partial_{b^{μ}} F (b) A^{μν}_{L} T^{L, I, J} (b; a, z)] - m^{2} g (b) F (b) b_{L} T^{L, I, J} (b; a, z), F = E_{m}^{A} f .

The source indices and maps are retained. In particular, the copied source uses $P$ and $b$ in these displays. This patch does not identify those symbols with differently styled maps in the XV-F retrieval account.

The coefficients $q_{α β}^{L, I, J}$ are specified by role as the actual differentiated-source coefficients. They are not expanded in these displays. The functions and fiber maps also remain inherited inputs rather than newly chosen coefficients. Thus the formulas are available, while their complete instantiation is still missing.

Likewise, the supplied sheets display

L^{μ, I} (s, a) = σ_{ε} (a) A^{λ μ, I} \partial_{a^{λ}} R (s - a),

and define the role of the constant bilinear map by

a_{2} ˙^{α μ} [G; h] = D^{α μ, I, J} h_{I} G_{J} .

These equations define dependencies. They do not expand $a_{1}$ , $a_{2}$ , $a ˙_{2}$ , the graph source, or all inherited switches and observations.

The exact correction to D0.13–D0.14 is therefore not “the formulas are unavailable.” It is “the formulas are copied, but the frozen coefficient ingredients are not completely recovered from the permitted inputs.”

Displayed formulas in this passage

XV-F-patch@1#eq:Q · line 2029
$Q^{L, I, J} (v; a, z) = ∣ α ∣ + ∣ β ∣ \leq 2 \sum q_{α β}^{L, I, J} (v) \partial_{v}^{α} δ^{(4)} (v - z) \partial_{v}^{β} δ^{(4)} (v - a),$
XV-F-patch@1#eq:T · line 2037
$T^{L, I, J} (b; a, z) = P^{L}_{M} \int R (b - v) Q^{M, I, J} (v; a, z) d^{4} v,$
XV-F-patch@1#eq:K8 · line 2044
$K_{8}^{I, J} (a, b, z) = - \partial_{b^{μ}} [f (b) A^{α μ}_{L} P^{L}_{M} \partial_{b^{α}} \int B (b - v) Q^{M, I, J} (v; a, z) d^{4} v],$
XV-F-patch@1#eq:K9 · line 2055
$K_{9}^{I, J} (a, b, z) = - \partial_{b^{ν}} [g (b) \partial_{b^{μ}} F (b) A^{μν}_{L} T^{L, I, J} (b; a, z)] - m^{2} g (b) F (b) b_{L} T^{L, I, J} (b; a, z), F = E_{m}^{A} f .$
unlabeled · line 2081
$L^{μ, I} (s, a) = σ_{ε} (a) A^{λ μ, I} \partial_{a^{λ}} R (s - a),$
unlabeled · line 2087
$a_{2} ˙^{α μ} [G; h] = D^{α μ, I, J} h_{I} G_{J} .$