Manuscript II@2 · II.tex · section · 50d64def

Blindness and analytic controls

Blindness and analytic controls · lines 1329–1386

Parity evenness is used in this proof. An arbitrary parity-odd class enlargement cannot inherit the blind row without a new argument.

Control	Specialization	Result and justification
$C_{1}$	One species, unit Einstein cubic, canonical Einstein quartic	Quartic $2$ , exchange sum $6 - 2 - 2 = 2$ ; response zero by the polarized Ward identity.
$C_{2}$	$a = e = 1, b = c = 0$ , species $1122$ , no extra contacts	All channel factors vanish at this point. For every associative product the orthogonal Einstein decomposition gives canonical cancellation.
$C_{3}$	$d_{I J K} = χ w_{I} w_{J} w_{K}$ , canonical reference	All channel factors equal $χ^{2} ∥ w ∥^{2} \prod_{i} w_{J_{i}}$ . The response is this scalar times one-sector zero. For $χ = 1, w = (1, 1)$ , it is $4 - 4 = 0$ .
$C_{4}$	Permute momenta, species, tensors, references, and insertion together	Coefficient extraction permutes all assignments and exchange partitions; the complete response is unchanged.
$C_{5}$	Compare each direct exchange with its Ward reduction	$X + W = (6, - 2, - 2) + (- 6, 2, 2) = 0$ . The channel identity holds throughout $X$ .
$C_{6}$	Rational and normalized blind seeds	All raw columns and the target vanish by Proposition prop:blind.

The associative and rank-one controls concern the canonical quartic, not arbitrary added contacts. The permutation control concerns complete data, not a tensor permutation with other labels held fixed. The exchange control uses conservation at the physical end before applying the inverse. These qualifications prevent weaker or differently normalized checks from being substituted for the stated identities.

Nearby in this section

proposition: Proposition: Complete blind identity