# Mathematical scope

Conditional formulas only. No article-specific numerical result or factual claim is certified by this record.

The Lean library checks complementary fractions, the deduction of nonnegative costs, and the conversion of a percentage-point gap to a probability gap. Their assumptions must be established separately.

Source: [ResearchModels.lean](../ResearchModels.lean). Proof log: [verification.json](../verification.json).

Body SHA-256: `489554e56497613c0a949fe39140a2fc4e3014d8e4ad189b2bbbca8f4680d047`. This identifies the scoped publication content; it is not a proof of its truth.

The original article keeps its existing publication date and access rules.

25 Oct 2026: the body hash now leaves out the photograph block (image), as it already left out sources and updatedAt. The scope is unchanged. Previous body SHA-256: 13df060eb22eeae3005cdc7ea243b9abde515c37658fc9053eb995bac35fdef4.