Shell-Level Saturation and the Conditional Fibre-to-Rate Prescription

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 and an additional cross-substrate identification, the O7 relation β^* = 1/(δₚₐᵢᵣ + 1/2) defines a conditional phenomenological prescription. The fibre construction does not supply a native Heisenberg growth equation carrying the pair observable. O22 and O24 discharge the shell-alignment and rank-three conditions on the fibre side of the chain. Those results do not supply the independent Heisenberg growth carrier required by the capacity-to-rate step.