[huashengshao]

A physical transverse-boosted gluon point can acquire a tiny imaginary residual when the identity norm is evaluated as an ordered complex Gram sum. A consumer with no justified error bound correctly rejects that result. This change constructs the real Hermitian quadratic form before numerical evaluation, instead of dropping a computed imaginary part.

Preparation verifies the exact directed Gram matrix is Hermitian, then lowers it to adjacent real/imaginary amplitude components using the existing coefficient evaluator. Full complex amplitudes and their phases remain unchanged. The runtime preserves the original scalar carrier and each Float component's tracked precision, and still accepts legacy norm instructions with one complex input per coefficient. Scalar saved norm programs remain compatible. No positivity clipping, precision padding or error bound is added.

The synthetic regression compares a complex Hermitian Gram matrix and rational complex vector against an independent exact directed double sum, including an imaginary off-diagonal entry. Non-Hermitian matrices fail before lowering. Existing physical quark/gluon tests now demand exactly real norms at original and boosted points. All 83 native unit tests pass on the standalone pinned dependency family (9cdc2949) and the ROULETTE consumer family (e93c3c73), with Python and external compilers absent from PATH. The consumer bridge's 10 checks also pass, including the previously rejected boosted gluon point. Independent source review approved the Hermitian lowering and precision handling.

Stacked on codex/native-tree-parameters at 0025a0d (PR18). This leaves the native amplitude-generation and directed correlation paths unchanged.