Dated notes

7 September 2026. Two matters of record. Nothing in the body is altered.

1. The second-order correction written in §5 as a divisor, Δ_bare/(1 + α²/8π), reads as the multiplier, Δ_bare·(1 − α²/8π): the isotropic-leakage lemma has one form everywhere in the corpus, because a returned leak is not an expression and does not itself leak (AP30 dated note 9; AP49 §4). At this paper's precision the two differ by 4.5 × 10⁻¹²; no digit moves.

2. §5's retirement of the identification of the four dimensions with the four conditions applies to this paper's derivation chain, which did not need it; it is not a ruling against AP10, which identifies each of the four axioms with one face of the manifold.