Capacity Readouts of Retained Structure Dynamics: Sharp Terminal 4D Carrier, Fisher--Hellinger Presentation, Shannon--Nyquist Packet Normal Form, and Empirical Outputs

The sharp retained-image theorem~\cite{StiegerSharpRetainedImage2026} proves the carrier theorem: a terminal self-rereading universe with exact retention, non-static renewal, connected public viewpoint reconciliation, and terminal closure has a sharp terminal public comparison carrier
\[
E_* = C_{\mathrm{pub}}(M_*)
\]
of real dimension four.  It also supplies the canonical positive comparison form \(g_*\), the exact antisymmetric endpoint renewal line \(\mathbb R U_*=\mathbb R(e_{01}-e_{10})\), the rank-two finite endpoint-reconciliation sector \(I_{\mathrm{rec},*}\), and the local Lorentzian comparison interface.  This paper does not rederive that carrier and does not introduce a replacement carrier.

Starting from the sharp retained carrier constructed in \cite{StiegerSharpRetainedImage2026}, we construct the finite statistical response presentation of the same retained comparison object. The Fisher--Hellinger response cotangent space is proved to be a presentation of \(E_*\), not an independent metric or Hilbert-space postulate.  From that presentation we derive the Shannon--Nyquist cubic normal form, the minimal \(32\)-point polarization stencil \(S_{32}\), the centered \(19\)-point first-shadow quadrature packet \(P_{19}\), the packet comparator and its first unresolved-order certificates, the quartic source and its orthogonal lock, and the finite positive packet-capacity operator \(C_*\).

The spectral functional calculus of \(C_*\) generates a closed logarithmic capacity ledger.  No scalar term enters the ledger unless it is the logarithm of a positive retained capacity ratio generated by the packet-capacity operator and its descendants.  Empirical readouts are admitted only through unique minimum closed paths whose symmetry type, dimensional status, and response role match the reported physical variable.  The fine-structure constant and the electron anomaly are then downstream minimum-path outputs of the closed capacity calculus, not fitted inputs and not ingredients in the carrier theorem.