Canonical Pair Observables in Weil Blocks: Structure of the Residual Amplitude Factor and Pipeline-Independent Formulation

The O12–O18 sequence identifies the pair-level quantity σₚₐᵢᵣ(n) = σc(n)\,σq-c(n) as the structurally motivated candidate observable on Heis₃(Z/qZ), with capacity exponent δₚₐᵢᵣ ≈ 7.44 consistent with the phenomenological target δₚₐᵢᵣ ∈ [7.4, 10.6]. However, a residual amplitude factor r(c,q) ∈ \1,2,3,4\ persists in the current pipeline, reflecting a dependence on the Gram–Schmidt initialisation parameters (b₁, b₂) identified in O17 but not yet resolved. The present paper begins by making explicit the implicit normalisation factor D(c, b₁, b₂, n) of the O12/O13 implementation, separating its dependence on the initial basis, the block instance, and the normalisation convention. We then determine the dependence structure of r(c,q) by two independent tests: variation under basis change at fixed block instance (Test P2), and variation under block-instance change at rigidly fixed basis (Test P3). Three outcomes are possible: r(c,q) is a pure basis artefact (Case A, eliminable by canonical choice), a discrete instance invariant (Case B, requiring a canonical quotient), or a mixed quantity with both components (Case C, requiring a decomposition r = rbase\,rᵢₙₛₜ). We identify which case holds for the primes tested, relate the observed structure to the metaplectic central-phase coherence γ(n) identified in O12, and construct the corresponding canonical observable σₚₐᵢᵣᶜᵃⁿ(n) independent of pipeline conventions. The exponent δₚₐᵢᵣ is unaffected in all cases; the contribution of this paper concerns the amplitude structure, which is a prerequisite for the fibre-level derivation of the δₚₐᵢᵣ → β* relation deferred to O21.