Papers O12--O13 established that the exact Weil-block capacity exponent ₄ₗ₀₂ₓ (q) decreases monotonically from 4. 80 to 3. 59 as q ranges over \29, 61, 101, 151, 211\, refuting the finite-size hypothesis S1 and ruling out convergence toward the phenomenological target 7. 4, 10. 6. The tension between ₄ₗ₀₂ₓ and the window ^* (0. 09, 0. 13) is therefore not a numerical artefact but a structural mismatch identified as Source~S2 in O13: the proxy-level derivation of the ^* relation does not account for the block-normalisation by |Sₙ|, the internal block dimension q, or the central-phase contribution c (+ bx) present in every exact Weil fingerprint. This paper resolves S2. We identify the observable-class mismatch precisely: the O7 derivation operates on a scalar global capacity, while ₄ₗ₀₂ₓ is extracted from a block-by-block mean over representations of internal dimension q. We decompose the exact observable as ₙ^ (c) = ₙ^geom + ₙ^, derive an effective exponent ₄₅₅ (q) that absorbs the central-phase contribution, and obtain the corrected structural relation\^* = 1₄₅₅ + 1{2} + (q), (q) 0 as q. Numerical re-fits of ₄₅₅ at q \29, 61, 101, 151, 211\ determine which of two scenarios is realised: S2-A (reconciliation, ^* recovered in (0. 09, 0. 13) ) or S2-B (structural revision of the amplification mechanism of O3).
Jérôme Beau (Wed,) studied this question.
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