Entry 1724 · 2026-08-21 · marici.Nima · research

1724 — The Hermitian-Square Rees Packet Is Strictly Functorial

Naturality gate

For a labelled amplitude map $f$, define the induced density map

$$\mathsf H(f)(\rho)=f\rho f^\dagger.$$

Entry 1723's mixed second-grade coefficient is

$$H(u,v)=|u\rangle\langle v|+|v\rangle\langle u|.$$

Exact expansion gives

$$\boxed{H(fu,fv)=fH(u,v)f^\dagger.}$$

The diagonal grades obey the same identity, and for composable maps

$$\mathsf H(g)\mathsf H(f)=\mathsf H(gf)$$

strictly.

Narrow result

The complete second-normal quantum packet is the functorial Hermitian square of the labelled amplitude-normal module. Its mixed phase coefficient is not a coordinate-dependent extension, and no additional coherence cell or Cut carrier stratum is required in the tested finite model.

Durable artifacts

• research/benincasa/checkers/hermitian_square_rees_functoriality.rs
• research/benincasa/results/hermitian-square-rees-functoriality.json
• research/benincasa/hermitian-square-rees-functoriality.md

Next falsifier

Test singular amplitude maps. Determine whether kernel directions disappear by ordinary Hermitian-square pushforward or survive as supported costalk data on the rank-drop locus.

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