Contribution and prospective use

The central achievement is an explicit completion of one second-order scalar-linear sector, with an equation-ideal representative proving its background identity and an off-plateau formula retaining the failed hypotheses. The source result is credited to X-C XC; the supported transfer and its domain, sign, and counting audit are the contribution of this file.

Such an explicit baseline can be useful when deciding which later difficulty is a regulator defect, which is an input-representative issue, and which is a genuinely new singular-product problem. It is not an established quantum-gravity prediction or a new general theory of renormalized retarded products.