Manuscript X-A-conv-ST@1 · X-A-conv-ST.tex · proposition · 8ca47088

Proposition: Exact matching requirement

Stage D: the conditional relational alternative · lines 1777–1797 · proof included or linked

X-A-conv-ST@1#prop:matching, X-A-conv-ST@1#eq:matching

The combination

I_{rel} = r_{ε} a - c_{ε} r

is invariant on the stated witness orbit. Its charge vanishes on the whole declared coefficient algebra exactly when

r_{ε} q_{a} (ξ) - c_{ε} q_{r} (ξ) = 0 (ξ \in g_{C}) .

Proof. The witness $λ$ -coefficient cancels. For a general direction, the charge of the combination is exactly the left side of (eq:matching).

Displayed formulas in this passage

X-A-conv-ST@1#eq:matching · line 1786
$r_{ε} q_{a} (ξ) - c_{ε} q_{r} (ξ) = 0 (ξ \in g_{C}) .$
unlabeled · line 1780
$I_{rel} = r_{ε} a - c_{ε} r$