Shell-Level Saturation and the Fibre-Level Transfer δpair →β∗

The spectral admissibility sub-programme of Cosmochrony has identified the canonical fibre-level observable σₚₐᵢᵣᶜᵃⁿ(n) as the relevant quantity for the lepton mass hierarchy. However, existing saturation criteria rely on the power-law fit σ(n) ~ C\,n-δ, whose amplitude C and exponent δ depend on the fitting window and are not intrinsic.We construct a fully observable saturation rank n₃ᵒᵇˢ(n₀, n₁, q) by eliminating both C and δ using two local measurements of σₚₐᵢᵣᶜᵃⁿ. This rank is invariant under global rescaling and all pipeline-dependent normalisations, and depends only on directly measurable quantities.We conjecture that physical admissibility requires n₃ᵒᵇˢ to align with a BFS shell of the Cayley graph Cay(Gq, Sq), providing a geometric interpretation of saturation. Under this shell-alignment hypothesis, the O7 structural relation β^* = 1/(δₚₐᵢᵣ + 1/2) becomes valid at the fibre level. The obstruction identified in O15 is thereby resolved: the transfer fails at the block level because the observable was mis-identified, not mis-measured.Two problems remain open: establishing the shell-alignment conjecture, and deriving the relation Σc(n₃) = 3 from the Born--Infeld admissibility structure rather than assumed as an input to the threshold definition.