Minimal Fibre Structure of the Non-Injective Projection from Born-Infeld Indiscernability: Derivation of the Parity Involution

The identification of conjugate Weil blocks \c, \, q-c\ as the fibres of the non-injective projection: was stated as a structurally motivated hypothesis in O16 and used in O17 to derive the pair-level observable and the exponent doubling ₏₀₈ₑ = 2\, ₂ 7. 44. The present paper provides the foundational derivation of the underlying involution. We proceed in two stages. At the abstract level, we show that the Born--Infeld action S is even in, and we define a notion of BI-indiscernability for configurations that produce identical effective responses under all BI-admissible perturbations. Evenness of S immediately implies that and - are BI-indiscernible, so every projective fibre contains the orbit \, -\. We then prove a conditional minimality result: in the absence of any symmetry of S beyond its parity, the minimal fibre is exactly the involution -. At the concrete level, the O17 result ₐ-₂ = ₂ together with the norm-invariance of Gram--Schmidt orthogonalisation identifies the involution c q-c as the Weil-representation instance of the abstract parity. This closes the logical gap in O16--O17 by deriving the fibre structure from first principles rather than postulating it.