This paper organizes the mod-6 ±1 composite program into an explicit ladder of claims. At the bottom stands a deterministic structural core: the 6-wheel candidate space, the canonical least-prime-factor partition of its composite subset, the explicit 6p geometry of the raw divisibility layers, and the resulting interval sieve identity. Above this we place a hard-test layer built from 5-adic shell observables, branch-aware transfer statistics, bad-set overlaps, and stress-tested null models. We then formulate a structural carrier/filament model that interprets residual badness as a superposition of a finite least-prime-factor carrier horizon and a localized filament or gate layer, typically concentrated near p4 switch points. Finally, we state a conditional GL1 bridge: if capture, pushforward covariance, guards, and a lift from counting measure to diagonal energy hold, then discrete transport control implies a T5-like remainder bound. The point of the paper is not to add another speculative layer, but to make explicit what is already proved, what is hard-testable, what is only structural modeling, and where the main open knots remain.
Stephen Steiner (Tue,) studied this question.