Manuscript X-F-ST@1 · X-F-ST.tex · section · e71f03ef

Polynomial substitution is legitimate at fixed width

Free polynomial carrier and the scalar background identity › Polynomial substitution is legitimate at fixed width · lines 1333–1355

X-F-ST@1#eq:one-defect

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Consequently the scalar completed expression with an independent fixed free graviton has the defect

[ϕ (f) + κ A_{1} [h + r] + κ^{2} {Q [h + r, h + r] + A_{1} [k]}]^{'} - [\dots] \equiv - κ^{2} A_{1} [L_{ξ}^{c} r] (mod J, κ^{3}) .

Indeed the full second slot for $h + r$ would be $k^{'} + L_{ξ}^{c} r$ . Apply Lemma lem:scalaridentity, polarize, and subtract that missing affine term. This proves the X-E-ST truncation formula without an Einstein-shell shortcut XEST,XE.

Displayed formulas in this passage

X-F-ST@1#eq:one-defect · line 1337
$[ϕ (f) + κ A_{1} [h + r] + κ^{2} {Q [h + r, h + r] + A_{1} [k]}]^{'} - [\dots] \equiv - κ^{2} A_{1} [L_{ξ}^{c} r] (mod J, κ^{3}) .$

Nearby in this section

section: Polynomial substitution is legitimate at fixed width
lemma: Lemma: Admission of the finite scalar-completion forests