Abstract

We construct an explicit second charged scalar coefficient from the compact third-order interaction of X-I-ST, without changing its action, the prescribed conical host, or the fixed positive regulator width. Two disjoint third polarizations of the quartic vertex give independently variable compact moments. Their infinitesimal charge matrix has rank two. On a specified local common-flow family their charges agree exactly, whereas a separate compact gauge direction disproves charge matching on the whole relative algebra. The construction therefore supplies a genuine second coefficient for the present selective package, but not the missing universal reference for the earlier convolution observable.

For a supplied value $d$, an explicit destructive amplitude instrument retains a failure outcome of probability $r$ and has the exact separation

It is positive precisely when the signal is nonzero and the nonfailure probability is positive. A finite calibration instance has the exact gap $3/16$, with no numerical quadrature. We prove the corresponding finite-dictionary formula, a complete residual-and-reference instrument identity, an encoding-level higher-order visibility test, and explicit error margins. An additional two-coefficient phase instrument is invariant under the specified common charge direction, including all selective outputs and untouched references, but retains periodic aliases and does not become invariant under independent charge directions.

The principal contribution is the explicit separation between independent classical coefficient construction, restricted charge matching, and complete finite report distinguishability. This provides a controlled calibration target for later interfaces without treating encoded visibility as continuum acquisition or gauge restoration. The measurement identities are finite-dimensional, and the coefficient calculations are classical. The X-I-ST BV structure is unchanged through its retained order; the three-tree plateau is counted once; the reciprocity and convolution obstructions remain separate. No interacting quantum BRST differential, characteristic quantum coefficient, loop-anomaly cancellation, ultraviolet completion, or spacetime emergence is constructed.