Manuscript Psy03-D@1 · Psy03-D-v1.tex · theorem · 3e18951d

Theorem: Per-tensor multiplier cancellation

Score allocation and recurrent-protection counterexamples · lines 1479–1498 · proof included or linked

Psy03-D@1#thm:cancel

Let $s_{i}$ be scores in one tensor, let $s_{(k)}$ be its $k$ -th ascending order statistic, and let $c > 0$ . Then

{i : c s_{i} > c s_{(k)}} = {i : s_{i} > s_{(k)}} .

The same retained support is obtained by a consistent exact-count ranking.

Consequently a positive multiplier common to every score in a tensor does not protect that tensor through a fixed per-tensor pruning allocation.

Proof. Positive multiplication preserves inequalities, ties, and ordering.

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