Manuscript X-H-ST@1 · X-H-ST.tex · proposition · 943aa27e

Proposition: Conditional quantum cancellation criterion

Stage D: the first quantum correction remains conditional › A conditional first-order consistency equation · lines 1736–1760 · proof included or linked

X-H-ST@1#prop:quantumcriterion, X-H-ST@1#eq:quantumcriterion

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Under Definition def:quantuminterface, a permitted counterterm cancels the first-order residual exactly when

Q^{[2]} C_{1} - A_{1} = 0 (mod κ^{3}) .

Existence is an exact-image question in the specified permitted counterterm space. It is not implied by the closedness of $A_{1}$ .

Proof. This is the change law (Q3). Condition (Q4) is necessary for (eq:quantumcriterion) because $(Q^{[2]})^{2} = 0$ , but a closed element need not be in the image of the differential. No vanishing theorem for the relevant ghost-number-one cohomology or permitted counterterm image has been proved here.

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X-H-ST@1#eq:quantumcriterion · line 1741
$Q^{[2]} C_{1} - A_{1} = 0 (mod κ^{3}) .$

Proposition: Conditional quantum cancellation criterion

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