Fibre Admissibility Hypotheses and Conditional Pair-Exponent Doubling

The Weil representation of Heis₃(Z/qZ) satisfies the exact conjugation identity ρq-c = ρc̄, valid for every prime q and every c ∈ (Z/qZ)^*, independent of any hypothesis about the non-injective projection Π. We examine whether conjugate blocks ,\,q-c\ constitute the fibres of Π. That identification rests on two independent premises: that Π carries a parity involution Π(x)=Π(-x), and that this involution is realised, in the Weil representation, as the character map c ↦ q-c; neither follows from the conjugation identity alone, and neither is derived from first principles within the Cosmochrony framework. Under a further, separate hypothesis — that a per-block observable σc(n) has a conjugate-pair ratio r(c,q) = σq-c(n)/σc(n) independent of the shell index n — the log-log slope of the pair-level product σc(n)\,σq-c(n) is exactly double that of σc(n), a direct consequence of differentiating a constant-ratio product. On the exact block observable Σₙ(c₁,c₂,c₃) of the O12/O13 pipeline, the proved conjugate-block identity Σₙ(c₁,c₂,c₃) = Σₙ(-c₁,-c₂,-c₃) forces r(c,q) ≡ 1 exactly, so the pair-level product reduces definitionally to the single block squared, with no separate doubling phenomenon to explain. No numerical value of the pair exponent, and no O7 prescription for β^*, is asserted.