Manuscript Em02-A@6 · Em02-A-v6.tex · section · cb2f0a9a

Where the core substitution is valid

Route B: geometry, support zeros, and the contribution ledger › Where the core substitution is valid · lines 755–780

The identity

(β - α) q_{1} + α q_{2} = 4 α (β - α) u - β ∣ ξ ∣^{2}

implies, on the fixed compact chart,

q_{R}, q_{1}, q_{2} = O (δ) ⟹ u, v = O (δ), ξ = O (δ) .

Thus the $00$ sector permits $(u, v, ξ) = (δ u_{*}, δ v_{*}, δ X)$ . The translated equations, including their higher-order terms, are retained in Appendix app:geometry.

Neither this implication nor simultaneous crossed cones forces $r = O (δ)$ . Moreover, the $5 z$ support admits $q_{1} = q_{2} = 0$ with $q_{R} > 0$ fixed; see Proposition prop:counterexample. The $0 R$ sector therefore cannot be removed by the core argument.

Displayed formulas in this passage

unlabeled · line 758
$(β - α) q_{1} + α q_{2} = 4 α (β - α) u - β ∣ ξ ∣^{2}$
unlabeled · line 764
$q_{R}, q_{1}, q_{2} = O (δ) ⟹ u, v = O (δ), ξ = O (δ) .$