Resolves the exponent discrepancy in Weil-block capacities, demonstrating that fibres exhibit a power law behavior.
The O-series has established that the Weil-block capacity exponent δ̂exact ≈ 3.72 ± 0.06 falls systematically below the phenomenological target range δ ∈ [7.4, 10.6], and that this discrepancy is structural: no reweighting of block data can raise the exponent (O15, Corollary~4.8). The present paper resolves the discrepancy by identifying a misidentification of the physically relevant observable. The non-injectivity of the projection~Π, established from the Born--Infeld constraint, implies that admissibility is a property of complete fibres of~Π, not of individual preimage configurations. In the Weil realisation of Heis₃(Z/qZ), these fibres are organised as conjugate pairs , q-c\ under the exact identity ρq-c = ρc̄. The pair-level observable σₚₐᵢᵣ(n) = σc(n)\,σq-c(n) follows a clean power law with exponent δₚₐᵢᵣ = 2\,δc ≈ 7.44 ± 0.12, confirmed numerically with R² > 0.9999 and a factor-of-six reduction in slope variance. This result does not modify the underlying model; it identifies the correct unit of observation.
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Jérôme Beau (2026) studied this question.
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