Manuscript XVIII-A@2 · XVIII-A-v2.tex · section · 0f4336ec

Documentary normalization, not a reconstructed model

The frozen specification contract › Documentary normalization, not a reconstructed model · lines 387–432

XVIII-A@2#eq:docnormalization, XVIII-A@2#eq:docsource, XVIII-A@2#eq:docsign, XVIII-A@2#eq:doclayer

For comparison only, the supplied XVI-A convention records

S_{EH} S_{grav, D} r = - \frac{2}{κ ^{2}} \int - q R, = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3}, = - u_{D}, G_{gr}^{R} J_{D} (P a)_{μν} = - P E_{0}^{R}, = σ_{ε} J_{3} + D_{σ}, = a_{μν} - \frac{1}{2} η_{μν} tr_{η} a .

Here $q$ is the source's metric notation, $R$ its curvature scalar, and $ℓ_{3}$ its fixed unintegrated cubic density. These displayed conventions are not a definition here of the full cubic component arrays or gauge complex CheungXVIA,CheungXIIC.

The cubic-only density weight matters: weighting the entire Einstein–Hilbert density would alter lower orders and would not preserve the same frozen specification CheungXIIC. For a time-only weight, the documentary source residual is

D_{σ}^{μν} = 2 C_{2}^{μν 00} σ_{ε}^{''} - 2 M_{2}^{μν 0} σ_{ε}^{'} .

The arrays $C_{2}, M_{2}$ are source-defined coefficients, not derived from their names in this paper.

Nor are these conventions equated with the X-track inverse $- 4 P E_{0}^{R}$ . Comparing the two normalizations requires an explicit transport of fields, vertices, products, and observables CheungXE,CheungXF.

Displayed formulas in this passage

XVIII-A@2#eq:docnormalization · line 390
$S_{EH} S_{grav, D} r = - \frac{2}{κ ^{2}} \int - q R, = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3}, = - u_{D}, G_{gr}^{R} J_{D} (P a)_{μν} = - P E_{0}^{R}, = σ_{ε} J_{3} + D_{σ}, = a_{μν} - \frac{1}{2} η_{μν} tr_{η} a .$
XVIII-A@2#eq:docsource · line 390
$S_{EH} S_{grav, D} r = - \frac{2}{κ ^{2}} \int - q R, = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3}, = - u_{D}, G_{gr}^{R} J_{D} (P a)_{μν} = - P E_{0}^{R}, = σ_{ε} J_{3} + D_{σ}, = a_{μν} - \frac{1}{2} η_{μν} tr_{η} a .$
XVIII-A@2#eq:docsign · line 390
$S_{EH} S_{grav, D} r = - \frac{2}{κ ^{2}} \int - q R, = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3}, = - u_{D}, G_{gr}^{R} J_{D} (P a)_{μν} = - P E_{0}^{R}, = σ_{ε} J_{3} + D_{σ}, = a_{μν} - \frac{1}{2} η_{μν} tr_{η} a .$
XVIII-A@2#eq:doclayer · line 418
$D_{σ}^{μν} = 2 C_{2}^{μν 00} σ_{ε}^{''} - 2 M_{2}^{μν 0} σ_{ε}^{'} .$