GCFT-0423: Lepton Hierarchy Gate — Koide Relation and S3 Closure Audit

An audit of the charged-lepton hierarchy within the GCFT Standard Model program. The paper evaluates whether the Koide relation and an S3/Peter–Weyl construction provide a genuine derivation of electron, muon, and tau masses or merely reproduce an observed numerical compression. The analysis concludes that Koide's remarkable numerical relation is successfully reproduced, but the required BF amplitude and phase remain underived, leaving the hierarchy as an explicit open derivation gate rather than a completed prediction.