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

The O12--O18 sequence establishes that the physically relevant observable on Heis₃ (Z/qZ) is the pair-level quantity ₏₀₈ₑ (n) = ₂ (n) \, ₐ-₂ (n), with capacity exponent ₏₀₈ₑ 7. 44 consistent with the phenomenological target ₏₀₈ₑ 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 = r₁₀ₒ₄\, r₈₍ₒₓ). We identify which case holds for the primes tested, relate the observed structure to the metaplectic central-phase coherence _ (n) identified in~O12, and construct the corresponding canonical observable ₏₀₈ₑ^can (n) independent of pipeline conventions. The exponent ₏₀₈ₑ 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 ₏₀₈ₑ ^* relation deferred to~O21.