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

Theorem: Scalar-only negative closure

Stage C: readout closure of the retained coefficient › The encoding-independent statement · lines 1432–1450 · proof included or linked

X-A-conv-ST@1#thm:orbitclosure

Φ (Enc (λ c_{ε})) = Φ (Enc (0)) for all λ \in R,

then

Φ (Enc (a)) = Φ (Enc (0)) for all a \in R .

Proof. For any $a$ , choose $λ = a / c_{ε}$ . Theorem thm:positive guarantees that this is defined.

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